From 9d8a9caa56d40c515a76112e2ac4f614bf777285 Mon Sep 17 00:00:00 2001
From: Shoooooon <san7@rice.edu>
Date: Fri, 1 Mar 2024 14:13:55 -0600
Subject: [PATCH] Corrected reversed inputs and outputs in Messy benchmarks.

---
 benchmarks/messy/README.md                    |   3 +
 .../correct_input_outputs/BVtest_ADD_01.sem   |  36 ++++
 .../correct_input_outputs/BVtest_AND_01.sem   |  33 ++++
 .../correct_input_outputs/BVtest_AND_02.sem   |  33 ++++
 .../correct_input_outputs/BVtest_AND_03.sem   |  36 ++++
 .../correct_input_outputs/BVtest_MAX_01.sem   |  43 +++++
 .../correct_input_outputs/BVtest_NAND_01.sem  |  36 ++++
 .../correct_input_outputs/BVtest_PLUS_01.sem  |  33 ++++
 .../BVtest_Swap_XOR_01.sem                    |  44 +++++
 .../BVtest_Swap_XOR_02.sem                    |  46 +++++
 .../BVtest_Swap_XOR_03.sem                    |  40 ++++
 .../BVtest_While_01_XOR_by_AND_OR.sem         |  62 ++++++
 .../BVtest_While_02_XOR_by_AND_OR_ADD.sem     |  62 ++++++
 .../correct_input_outputs/BVtest_XOR_01.sem   |  37 ++++
 .../correct_input_outputs/BVtest_XOR_02.sem   |  40 ++++
 .../correct_input_outputs/BVtest_XOR_03.sem   |  42 ++++
 .../BVtest_ADD_01.sem                         |   0
 .../BVtest_AND_01.sem                         |   0
 .../BVtest_AND_02.sem                         |   0
 .../BVtest_AND_03.sem                         |   0
 .../BVtest_MAX_01.sem                         |   0
 .../BVtest_NAND_01.sem                        |   0
 .../BVtest_PLUS_01.sem                        |   0
 .../BVtest_Swap_XOR_01.sem                    |   0
 .../BVtest_Swap_XOR_02.sem                    |   0
 .../BVtest_Swap_XOR_03.sem                    |   0
 .../BVtest_While_01_XOR_by_AND_OR.sem         |   0
 .../BVtest_While_02_XOR_by_AND_OR_ADD.sem     |   0
 .../BVtest_XOR_01.sem                         |   0
 .../BVtest_XOR_02.sem                         |   0
 .../BVtest_XOR_03.sem                         |   0
 .../basicTest_AddByWhileLoop_01.sem           |  57 ++++++
 .../basicTest_AddByWhileLoop_02.sem           |  58 ++++++
 .../basicTest_AddByWhileLoop_03.sem           |  51 +++++
 .../basicTest_AddByWhileLoop_04.sem           |  65 +++++++
 .../basicTest_AddByWhileLoop_05.sem           |  68 +++++++
 .../basicTest_AddOne_01.sem                   |  34 ++++
 .../basicTest_Fib_01.sem                      |  73 +++++++
 .../basicTest_MAX_01.sem                      |  45 +++++
 .../basicTest_MAX_02.sem                      |  49 +++++
 .../basicTest_MAX_03.sem                      |  59 ++++++
 .../basicTest_MultByWhileLoop_01.sem          | 131 +++++++++++++
 .../basicTest_MultByWhileLoop_02.sem          |  82 ++++++++
 .../basicTest_Sanity01.sem                    |  75 ++++++++
 .../basicTest_SetBothtoLarger_01.sem          |  60 ++++++
 .../basicTest_SumByWhileLoop_01.sem           |  73 +++++++
 .../basicTest_SumWithLimitedOps_01.sem        |  45 +++++
 .../basicTest_SumWithLimitedOps_02.sem        |  53 +++++
 .../correct_input_outputs/minimal_unsat.sem   |  78 ++++++++
 .../basicTest_AddByWhileLoop_01.sem           |   0
 .../basicTest_AddByWhileLoop_02.sem           |   0
 .../basicTest_AddByWhileLoop_03.sem           |   0
 .../basicTest_AddByWhileLoop_04.sem           |   0
 .../basicTest_AddByWhileLoop_05.sem           |   0
 .../basicTest_AddOne_01.sem                   |   0
 .../basicTest_Fib_01.sem                      |   0
 .../basicTest_MAX_01.sem                      |   0
 .../basicTest_MAX_02.sem                      |   0
 .../basicTest_MAX_03.sem                      |   0
 .../basicTest_MultByWhileLoop_01.sem          |   0
 .../basicTest_MultByWhileLoop_02.sem          |   0
 .../basicTest_Sanity01.sem                    |   0
 .../basicTest_SetBothtoLarger_01.sem          |   0
 .../basicTest_SumByWhileLoop_01.sem           |   0
 .../basicTest_SumWithLimitedOps_01.sem        |   0
 .../basicTest_SumWithLimitedOps_02.sem        |   0
 .../minimal_unsat.sem                         |   0
 .../no01_factorialTest_01.sem                 |  75 ++++++++
 .../no01_factorialTest_02.sem                 |  69 +++++++
 .../no01_factorialTest_03.sem                 |  71 +++++++
 .../no01_factorialTest_04.sem                 |  73 +++++++
 .../no01_factorialTest_05.sem                 |  63 ++++++
 .../no01_factorialTest_06.sem                 |  98 ++++++++++
 .../no01_factorialTest_07.sem                 |  88 +++++++++
 .../no01_factorialTest_08.sem                 |  85 ++++++++
 .../no01_factorialTest_09.sem                 |  75 ++++++++
 .../no01_factorialTest_10.sem                 |  85 ++++++++
 .../no01_factorialTest_11.sem                 |  89 +++++++++
 .../no02_doubleFactorialTest_01.sem           |  78 ++++++++
 .../no02_doubleFactorialTest_02.sem           |  69 +++++++
 .../no02_doubleFactorialTest_03.sem           |  74 +++++++
 .../no02_doubleFactorialTest_04.sem           |  76 ++++++++
 .../no02_doubleFactorialTest_05.sem           |  66 +++++++
 .../no02_doubleFactorialTest_06.sem           | 101 ++++++++++
 .../no02_doubleFactorialTest_07.sem           |  88 +++++++++
 .../no02_doubleFactorialTest_08.sem           |  85 ++++++++
 .../no02_doubleFactorialTest_09.sem           |  75 ++++++++
 .../no02_doubleFactorialTest_10.sem           |  88 +++++++++
 .../no02_doubleFactorialTest_11.sem           |  92 +++++++++
 .../no03_sigmaTest_01.sem                     |  71 +++++++
 .../no03_sigmaTest_02.sem                     |  65 +++++++
 .../no03_sigmaTest_03.sem                     |  67 +++++++
 .../no03_sigmaTest_04.sem                     |  69 +++++++
 .../no03_sigmaTest_05.sem                     |  63 ++++++
 .../no03_sigmaTest_06.sem                     | 104 ++++++++++
 .../no03_sigmaTest_07.sem                     |  94 +++++++++
 .../no03_sigmaTest_08.sem                     |  91 +++++++++
 .../no03_sigmaTest_09.sem                     |  85 ++++++++
 .../no03_sigmaTest_10.sem                     |  81 ++++++++
 .../no03_sigmaTest_11.sem                     |  85 ++++++++
 .../no04_sigmaSquare_01.sem                   |  85 ++++++++
 .../no04_sigmaSquare_02.sem                   |  79 ++++++++
 .../no04_sigmaSquare_03.sem                   |  77 ++++++++
 .../no04_sigmaSquare_04.sem                   |  79 ++++++++
 .../no04_sigmaSquare_05.sem                   |  73 +++++++
 .../no04_sigmaSquare_06.sem                   | 118 ++++++++++++
 .../no04_sigmaSquare_07.sem                   | 104 ++++++++++
 .../no04_sigmaSquare_08.sem                   | 106 ++++++++++
 .../no04_sigmaSquare_09.sem                   | 100 ++++++++++
 .../no04_sigmaSquare_10.sem                   |  95 +++++++++
 .../no04_sigmaSquare_11.sem                   | 104 ++++++++++
 .../correct_input_output/no05_piSquare_01.sem |  85 ++++++++
 .../correct_input_output/no05_piSquare_02.sem |  79 ++++++++
 .../correct_input_output/no05_piSquare_03.sem |  81 ++++++++
 .../correct_input_output/no05_piSquare_04.sem |  85 ++++++++
 .../correct_input_output/no05_piSquare_05.sem |  75 ++++++++
 .../correct_input_output/no05_piSquare_06.sem | 115 +++++++++++
 .../correct_input_output/no05_piSquare_07.sem | 101 ++++++++++
 .../correct_input_output/no05_piSquare_08.sem | 106 ++++++++++
 .../correct_input_output/no05_piSquare_09.sem | 100 ++++++++++
 .../correct_input_output/no05_piSquare_10.sem |  95 +++++++++
 .../correct_input_output/no05_piSquare_11.sem | 104 ++++++++++
 .../correct_input_output/no06_power_01.sem    |  86 +++++++++
 .../correct_input_output/no06_power_02.sem    |  80 ++++++++
 .../correct_input_output/no06_power_03.sem    |  82 ++++++++
 .../correct_input_output/no06_power_04.sem    |  84 ++++++++
 .../correct_input_output/no06_power_05.sem    |  74 +++++++
 .../correct_input_output/no06_power_06.sem    | 119 ++++++++++++
 .../correct_input_output/no06_power_07.sem    | 109 +++++++++++
 .../correct_input_output/no06_power_08.sem    | 106 ++++++++++
 .../correct_input_output/no06_power_09.sem    |  96 ++++++++++
 .../correct_input_output/no06_power_10.sem    |  96 ++++++++++
 .../correct_input_output/no06_power_11.sem    | 100 ++++++++++
 .../correct_input_output/no07_suma2n_01.sem   |  81 ++++++++
 .../correct_input_output/no07_suma2n_02.sem   |  75 ++++++++
 .../correct_input_output/no07_suma2n_03.sem   |  77 ++++++++
 .../correct_input_output/no07_suma2n_04.sem   |  79 ++++++++
 .../correct_input_output/no07_suma2n_05.sem   |  73 +++++++
 .../correct_input_output/no07_suma2n_06.sem   | 125 ++++++++++++
 .../correct_input_output/no07_suma2n_07.sem   | 115 +++++++++++
 .../correct_input_output/no07_suma2n_08.sem   | 112 +++++++++++
 .../correct_input_output/no07_suma2n_09.sem   | 106 ++++++++++
 .../correct_input_output/no07_suma2n_10.sem   |  91 +++++++++
 .../correct_input_output/no07_suma2n_11.sem   |  95 +++++++++
 .../correct_input_output/no08_proda2n_01.sem  |  85 ++++++++
 .../correct_input_output/no08_proda2n_02.sem  |  79 ++++++++
 .../correct_input_output/no08_proda2n_03.sem  |  75 ++++++++
 .../correct_input_output/no08_proda2n_04.sem  |  83 ++++++++
 .../correct_input_output/no08_proda2n_05.sem  |  73 +++++++
 .../correct_input_output/no08_proda2n_06.sem  | 118 ++++++++++++
 .../correct_input_output/no08_proda2n_07.sem  | 108 +++++++++++
 .../correct_input_output/no08_proda2n_08.sem  | 105 ++++++++++
 .../correct_input_output/no08_proda2n_09.sem  |  95 +++++++++
 .../correct_input_output/no08_proda2n_10.sem  |  95 +++++++++
 .../correct_input_output/no08_proda2n_11.sem  |  99 ++++++++++
 .../no13_fibonacci_01.sem                     |  85 ++++++++
 .../no13_fibonacci_02.sem                     |  76 ++++++++
 .../no13_fibonacci_03.sem                     |  81 ++++++++
 .../no13_fibonacci_04.sem                     |  94 +++++++++
 .../no13_fibonacci_05.sem                     |  84 ++++++++
 .../no13_fibonacci_06.sem                     | 118 ++++++++++++
 .../no13_fibonacci_07.sem                     | 105 ++++++++++
 .../no13_fibonacci_08.sem                     | 107 +++++++++++
 .../no13_fibonacci_09.sem                     | 101 ++++++++++
 .../no13_fibonacci_10.sem                     |  95 +++++++++
 .../no13_fibonacci_11.sem                     | 104 ++++++++++
 .../no14_nestedsum_01.sem                     |  92 +++++++++
 .../no14_nestedsum_02.sem                     |  86 +++++++++
 .../no14_nestedsum_03.sem                     |  78 ++++++++
 .../no14_nestedsum_04.sem                     |  80 ++++++++
 .../no14_nestedsum_05.sem                     |  74 +++++++
 .../no14_nestedsum_06.sem                     | 177 +++++++++++++++++
 .../no14_nestedsum_07.sem                     | 169 ++++++++++++++++
 .../no14_nestedsum_08.sem                     | 173 +++++++++++++++++
 .../no14_nestedsum_09.sem                     | 167 ++++++++++++++++
 .../no14_nestedsum_10.sem                     | 102 ++++++++++
 .../no14_nestedsum_11.sem                     | 106 ++++++++++
 .../no15_nestedprod_01.sem                    |  96 ++++++++++
 .../no15_nestedprod_02.sem                    |  90 +++++++++
 .../no15_nestedprod_03.sem                    |  78 ++++++++
 .../no15_nestedprod_04.sem                    |  80 ++++++++
 .../no15_nestedprod_05.sem                    |  74 +++++++
 .../no15_nestedprod_06.sem                    | 181 ++++++++++++++++++
 .../no15_nestedprod_07.sem                    | 169 ++++++++++++++++
 .../no15_nestedprod_08.sem                    | 173 +++++++++++++++++
 .../no15_nestedprod_09.sem                    | 167 ++++++++++++++++
 .../no15_nestedprod_10.sem                    | 106 ++++++++++
 .../no15_nestedprod_11.sem                    | 110 +++++++++++
 .../no01_factorialTest_01.sem                 |   0
 .../no01_factorialTest_02.sem                 |   0
 .../no01_factorialTest_03.sem                 |   0
 .../no01_factorialTest_04.sem                 |   0
 .../no01_factorialTest_05.sem                 |   0
 .../no01_factorialTest_06.sem                 |   0
 .../no01_factorialTest_07.sem                 |   0
 .../no01_factorialTest_08.sem                 |   0
 .../no01_factorialTest_09.sem                 |   0
 .../no01_factorialTest_10.sem                 |   0
 .../no01_factorialTest_11.sem                 |   0
 .../no02_doubleFactorialTest_01.sem           |   0
 .../no02_doubleFactorialTest_02.sem           |   0
 .../no02_doubleFactorialTest_03.sem           |   0
 .../no02_doubleFactorialTest_04.sem           |   0
 .../no02_doubleFactorialTest_05.sem           |   0
 .../no02_doubleFactorialTest_06.sem           |   0
 .../no02_doubleFactorialTest_07.sem           |   0
 .../no02_doubleFactorialTest_08.sem           |   0
 .../no02_doubleFactorialTest_09.sem           |   0
 .../no02_doubleFactorialTest_10.sem           |   0
 .../no02_doubleFactorialTest_11.sem           |   0
 .../no03_sigmaTest_01.sem                     |   0
 .../no03_sigmaTest_02.sem                     |   0
 .../no03_sigmaTest_03.sem                     |   0
 .../no03_sigmaTest_04.sem                     |   0
 .../no03_sigmaTest_05.sem                     |   0
 .../no03_sigmaTest_06.sem                     |   0
 .../no03_sigmaTest_07.sem                     |   0
 .../no03_sigmaTest_08.sem                     |   0
 .../no03_sigmaTest_09.sem                     |   0
 .../no03_sigmaTest_10.sem                     |   0
 .../no03_sigmaTest_11.sem                     |   0
 .../no04_sigmaSquare_01.sem                   |   0
 .../no04_sigmaSquare_02.sem                   |   0
 .../no04_sigmaSquare_03.sem                   |   0
 .../no04_sigmaSquare_04.sem                   |   0
 .../no04_sigmaSquare_05.sem                   |   0
 .../no04_sigmaSquare_06.sem                   |   0
 .../no04_sigmaSquare_07.sem                   |   0
 .../no04_sigmaSquare_08.sem                   |   0
 .../no04_sigmaSquare_09.sem                   |   0
 .../no04_sigmaSquare_10.sem                   |   0
 .../no04_sigmaSquare_11.sem                   |   0
 .../no05_piSquare_01.sem                      |   0
 .../no05_piSquare_02.sem                      |   0
 .../no05_piSquare_03.sem                      |   0
 .../no05_piSquare_04.sem                      |   0
 .../no05_piSquare_05.sem                      |   0
 .../no05_piSquare_06.sem                      |   0
 .../no05_piSquare_07.sem                      |   0
 .../no05_piSquare_08.sem                      |   0
 .../no05_piSquare_09.sem                      |   0
 .../no05_piSquare_10.sem                      |   0
 .../no05_piSquare_11.sem                      |   0
 .../no06_power_01.sem                         |   0
 .../no06_power_02.sem                         |   0
 .../no06_power_03.sem                         |   0
 .../no06_power_04.sem                         |   0
 .../no06_power_05.sem                         |   0
 .../no06_power_06.sem                         |   0
 .../no06_power_07.sem                         |   0
 .../no06_power_08.sem                         |   0
 .../no06_power_09.sem                         |   0
 .../no06_power_10.sem                         |   0
 .../no06_power_11.sem                         |   0
 .../no07_suma2n_01.sem                        |   0
 .../no07_suma2n_02.sem                        |   0
 .../no07_suma2n_03.sem                        |   0
 .../no07_suma2n_04.sem                        |   0
 .../no07_suma2n_05.sem                        |   0
 .../no07_suma2n_06.sem                        |   0
 .../no07_suma2n_07.sem                        |   0
 .../no07_suma2n_08.sem                        |   0
 .../no07_suma2n_09.sem                        |   0
 .../no07_suma2n_10.sem                        |   0
 .../no07_suma2n_11.sem                        |   0
 .../no08_proda2n_01.sem                       |   0
 .../no08_proda2n_02.sem                       |   0
 .../no08_proda2n_03.sem                       |   0
 .../no08_proda2n_04.sem                       |   0
 .../no08_proda2n_05.sem                       |   0
 .../no08_proda2n_06.sem                       |   0
 .../no08_proda2n_07.sem                       |   0
 .../no08_proda2n_08.sem                       |   0
 .../no08_proda2n_09.sem                       |   0
 .../no08_proda2n_10.sem                       |   0
 .../no08_proda2n_11.sem                       |   0
 .../no13_fibonacci_01.sem                     |   0
 .../no13_fibonacci_02.sem                     |   0
 .../no13_fibonacci_03.sem                     |   0
 .../no13_fibonacci_04.sem                     |   0
 .../no13_fibonacci_05.sem                     |   0
 .../no13_fibonacci_06.sem                     |   0
 .../no13_fibonacci_07.sem                     |   0
 .../no13_fibonacci_08.sem                     |   0
 .../no13_fibonacci_09.sem                     |   0
 .../no13_fibonacci_10.sem                     |   0
 .../no13_fibonacci_11.sem                     |   0
 .../no14_nestedsum_01.sem                     |   0
 .../no14_nestedsum_02.sem                     |   0
 .../no14_nestedsum_03.sem                     |   0
 .../no14_nestedsum_04.sem                     |   0
 .../no14_nestedsum_05.sem                     |   0
 .../no14_nestedsum_06.sem                     |   0
 .../no14_nestedsum_07.sem                     |   0
 .../no14_nestedsum_08.sem                     |   0
 .../no14_nestedsum_09.sem                     |   0
 .../no14_nestedsum_10.sem                     |   0
 .../no14_nestedsum_11.sem                     |   0
 .../no15_nestedprod_01.sem                    |   0
 .../no15_nestedprod_02.sem                    |   0
 .../no15_nestedprod_03.sem                    |   0
 .../no15_nestedprod_04.sem                    |   0
 .../no15_nestedprod_05.sem                    |   0
 .../no15_nestedprod_06.sem                    |   0
 .../no15_nestedprod_07.sem                    |   0
 .../no15_nestedprod_08.sem                    |   0
 .../no15_nestedprod_09.sem                    |   0
 .../no15_nestedprod_10.sem                    |   0
 .../no15_nestedprod_11.sem                    |   0
 309 files changed, 13220 insertions(+)
 create mode 100644 benchmarks/messy/README.md
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_ADD_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_02.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_03.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_MAX_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_NAND_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_PLUS_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_02.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_03.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_01.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_02.sem
 create mode 100644 benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_03.sem
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_ADD_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_AND_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_AND_02.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_AND_03.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_MAX_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_NAND_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_PLUS_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_Swap_XOR_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_Swap_XOR_02.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_Swap_XOR_03.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_While_01_XOR_by_AND_OR.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_While_02_XOR_by_AND_OR_ADD.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_XOR_01.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_XOR_02.sem (100%)
 rename benchmarks/messy/basic_bv/{ => inverted_input_outputs}/BVtest_XOR_03.sem (100%)
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_02.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_03.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_04.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_05.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddOne_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Fib_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_02.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_03.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_02.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Sanity01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SetBothtoLarger_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumByWhileLoop_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_01.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_02.sem
 create mode 100644 benchmarks/messy/basic_impv/correct_input_outputs/minimal_unsat.sem
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddByWhileLoop_01.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddByWhileLoop_02.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddByWhileLoop_03.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddByWhileLoop_04.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddByWhileLoop_05.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_AddOne_01.sem (100%)
 rename benchmarks/messy/basic_impv/{ => inverted_input_outputs}/basicTest_Fib_01.sem (100%)
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 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no14_nestedsum_11.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_01.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_02.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_03.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_04.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_05.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_06.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_07.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_08.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_09.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_10.sem (100%)
 rename benchmarks/messy/simpl_no_array/{ => inverted_input_output}/no15_nestedprod_11.sem (100%)

diff --git a/benchmarks/messy/README.md b/benchmarks/messy/README.md
new file mode 100644
index 0000000..2d8cfe8
--- /dev/null
+++ b/benchmarks/messy/README.md
@@ -0,0 +1,3 @@
+# Messy Benchmarks
+
+There are 2 sorts of benchmarks in each category. The first, under "correct_input_output", are the synthesis queries one would expect from the filename. The second, under "inverted_input_output", are the same queries with inputs and outputs reversed (i.e., we take inputs as outputs and vice versa.)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_ADD_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_ADD_01.sem
new file mode 100644
index 0000000..eab2169
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_ADD_01.sem
@@ -0,0 +1,36 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVary )
+($bvsub E E)
+($bvadd E E)
+($IBVVarx ))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvsub E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 (bvneg r__2)))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvadd E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_ADD_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_ADD_01 #x00000003 y #x00000004 #x00000004)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_01.sem
new file mode 100644
index 0000000..df95150
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_01.sem
@@ -0,0 +1,33 @@
+(declare-term-types
+((E 0) (Start 0))
+((($bvxor E E)
+($IBVVarx )
+($IBVVary ))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  ((($bvxor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor (bvand r__1 (bvnot r__2)) (bvand (bvnot r__1) r__2)))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_AND_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_01 #x00000000 y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_01 #x00000024 y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_02.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_02.sem
new file mode 100644
index 0000000..815e9a3
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_02.sem
@@ -0,0 +1,33 @@
+(declare-term-types
+((E 0) (Start 0))
+((($bvadd E E)
+($IBVVarx )
+($IBVVary ))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  ((($bvadd E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_AND_02() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_02 #x00000000 y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_02 #x00000024 y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_03.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_03.sem
new file mode 100644
index 0000000..2b5118c
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_AND_03.sem
@@ -0,0 +1,36 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($bvneg E)
+($IBVVary )
+($bvor E E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+(($bvneg E_term_1) (exists ((r__1 (_ BitVec 32))) (and (= r__0 (bvnot r__1))
+  (E.Sem E_term_1 r__1 x y))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_AND_03() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_03 #x00000000 y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_AND_03 #x00000024 y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_MAX_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_MAX_01.sem
new file mode 100644
index 0000000..0a260ff
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_MAX_01.sem
@@ -0,0 +1,43 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($bvadd E E)
+($IBVVary )
+($bvor E E)
+($bvand E E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+(($bvadd E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_MAX_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_MAX_01 #x00000009 y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_MAX_01 #x000000f7 y #x0000002c #x000000f7)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_MAX_01 #x00000020 y #x00000020 #x00000011)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_MAX_01 #x0000008e y #x0000008e #x0000008e)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_NAND_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_NAND_01.sem
new file mode 100644
index 0000000..d107182
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_NAND_01.sem
@@ -0,0 +1,36 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($IBVVary )
+($bvand E E)
+($bvneg E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvneg E_term_1) (exists ((r__1 (_ BitVec 32))) (and (= r__0 (bvnot r__1))
+  (E.Sem E_term_1 r__1 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_NAND_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_NAND_01 #x0000001f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_NAND_01 #x000000d1 y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_PLUS_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_PLUS_01.sem
new file mode 100644
index 0000000..56ac93d
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_PLUS_01.sem
@@ -0,0 +1,33 @@
+(declare-term-types
+((E 0) (Start 0))
+((($bvand E E)
+($IBVVarx )
+($IBVVary ))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  ((($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_PLUS_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_PLUS_01 #x0000000f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_PLUS_01 #x00000123 y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_01.sem
new file mode 100644
index 0000000..a825ce7
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_01.sem
@@ -0,0 +1,44 @@
+(declare-term-types
+((E 0) (Start 0) (Start1 0) (V 0))
+((($bvxor V V))
+(($seq Start1 Start1))
+(($bv=x E)
+($bv=y E))
+(($IBVVary )
+($IBVVarx ))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start1.Sem ((Start1_term_0 Start1) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(V.Sem ((V_term_0 V) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  ((($bvxor V_term_1 V_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor (bvand r__1 (bvnot r__2)) (bvand (bvnot r__1) r__2)))
+  (V.Sem V_term_1 r__1 x y)
+  (V.Sem V_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($seq Start1_term_1 Start1_term_2) (exists ((x_r1 (_ BitVec 32)) (y_r1 (_ BitVec 32))) (and (Start1.Sem Start1_term_1 x_r1 y_r1 x y)
+  (Start1.Sem Start1_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start1_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))
+(($bv=y E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x x_r0)
+  (= y_r0 r__1))
+  (E.Sem E_term_1 r__1 x y))))))
+(match V_term_0
+  (($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))))))
+
+
+(synth-fun BVtest_Swap_XOR_01() Start)
+
+
+(constraint (Start.Sem BVtest_Swap_XOR_01 #x00000006 #x00000009 #x00000009 #x00000006))
+(constraint (Start.Sem BVtest_Swap_XOR_01 #x0000002c #x000000f7 #x000000f7 #x0000002c))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_02.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_02.sem
new file mode 100644
index 0000000..98f24cb
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_02.sem
@@ -0,0 +1,46 @@
+SAME AS XOR_01
+
+(declare-term-types
+((E 0) (Start 0) (Start1 0) (V 0))
+((($bvxor V V))
+(($seq Start1 Start1))
+(($bv=x E)
+($bv=y E))
+(($IBVVary )
+($IBVVarx ))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start1.Sem ((Start1_term_0 Start1) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(V.Sem ((V_term_0 V) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  ((($bvxor V_term_1 V_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor (bvand r__1 (bvnot r__2)) (bvand (bvnot r__1) r__2)))
+  (V.Sem V_term_1 r__1 x y)
+  (V.Sem V_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($seq Start1_term_1 Start1_term_2) (exists ((x_r1 (_ BitVec 32)) (y_r1 (_ BitVec 32))) (and (Start1.Sem Start1_term_1 x_r1 y_r1 x y)
+  (Start1.Sem Start1_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start1_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))
+(($bv=y E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x x_r0)
+  (= y_r0 r__1))
+  (E.Sem E_term_1 r__1 x y))))))
+(match V_term_0
+  (($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))))))
+
+
+(synth-fun BVtest_Swap_XOR_02() Start)
+
+
+(constraint (Start.Sem BVtest_Swap_XOR_02 #x00000006 #x00000009 #x00000009 #x00000006))
+(constraint (Start.Sem BVtest_Swap_XOR_02 #x0000002c #x000000f7 #x000000f7 #x0000002c))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_03.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_03.sem
new file mode 100644
index 0000000..2da84f3
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_Swap_XOR_03.sem
@@ -0,0 +1,40 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVary )
+($IBVVarx )
+($bvxor E E))
+(($seq Start Start)
+($bv=x E)
+($bv=y E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+(($bvxor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor (bvand r__1 (bvnot r__2)) (bvand (bvnot r__1) r__2)))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($seq Start_term_1 Start_term_2) (exists ((x_r1 (_ BitVec 32)) (y_r1 (_ BitVec 32))) (and (Start.Sem Start_term_1 x_r1 y_r1 x y)
+  (Start.Sem Start_term_2 x_r0 y_r0 x_r1 y_r1))))
+(($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))
+(($bv=y E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x x_r0)
+  (= y_r0 r__1))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_Swap_XOR_03() Start)
+
+
+(constraint (Start.Sem BVtest_Swap_XOR_03 #x00000006 #x00000009 #x00000009 #x00000006))
+(constraint (Start.Sem BVtest_Swap_XOR_03 #x0000002c #x000000f7 #x000000f7 #x0000002c))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem
new file mode 100644
index 0000000..8486fb6
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem
@@ -0,0 +1,62 @@
+(declare-term-types
+((B 0) (E1 0) (S 0) (Start 0))
+((($bvult E1 E1))
+(($bvor E1 E1)
+($IBVVary )
+($bvand E1 E1)
+($IBVVarx ))
+(($bv=y E1)
+($bv=x E1)
+($seq S S))
+(($while B S))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(S.Sem ((S_term_0 S) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match B_term_0
+  ((($bvult E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvult r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))))
+(match E1_term_0
+  ((($bvor E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvand E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match S_term_0
+  ((($bv=y E1_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x x_r0)
+  (= y r__1))
+  (E1.Sem E1_term_1 r__1 x y))))
+(($bv=x E1_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E1.Sem E1_term_1 r__1 x y))))
+(($seq S_term_1 S_term_2) (exists ((x_r1 (_ BitVec 32)) (y_r1 (_ BitVec 32))) (and (S.Sem S_term_1 x_r1 y_r1 x y)
+  (S.Sem S_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 (_ BitVec 32)) (y_r2 (_ BitVec 32))) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (S.Sem S_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))))))
+
+
+(synth-fun BVtest_While_01_XOR_by_AND_OR() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_01_XOR_by_AND_OR #x0000000f y #x00000006 #x00000009)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_01_XOR_by_AND_OR #x000000db y #x000000f7 #x0000002c)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_01_XOR_by_AND_OR #x00000001 y #x0000000e #x0000000f)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem
new file mode 100644
index 0000000..2fac017
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem
@@ -0,0 +1,62 @@
+(declare-term-types
+((B 0) (E1 0) (S 0) (Start 0))
+((($bvult E1 E1))
+(($bvor E1 E1)
+($IBVVary )
+($bvadd E1 E1)
+($bvand E1 E1)
+($IBVVarx ))
+(($bv=x E1)
+($seq S S))
+(($while B S))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(S.Sem ((S_term_0 S) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match B_term_0
+  ((($bvult E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvult r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))))
+(match E1_term_0
+  ((($bvor E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvadd E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))
+(($bvand E1_term_1 E1_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E1.Sem E1_term_1 r__1 x y)
+  (E1.Sem E1_term_2 r__2 x y))))
+($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match S_term_0
+  ((($bv=x E1_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E1.Sem E1_term_1 r__1 x y))))
+(($seq S_term_1 S_term_2) (exists ((x_r1 (_ BitVec 32)) (y_r1 (_ BitVec 32))) (and (S.Sem S_term_1 x_r1 y_r1 x y)
+  (S.Sem S_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 (_ BitVec 32)) (y_r2 (_ BitVec 32))) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (S.Sem S_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))))))
+
+
+(synth-fun BVtest_While_02_XOR_by_AND_OR_ADD() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_02_XOR_by_AND_OR_ADD #x0000000f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_02_XOR_by_AND_OR_ADD #x000000db y #x000000f7 #x0000002c)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_While_02_XOR_by_AND_OR_ADD #x00000001 y #x0000000e #x0000000f)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_01.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_01.sem
new file mode 100644
index 0000000..44bf772
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_01.sem
@@ -0,0 +1,37 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($IBVVary )
+($bvand E E)
+($bvor E E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_XOR_01() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_01 #x0000000f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_01 #x000000db y #x000000f7 #x0000002c)))
+
+(check-synth)
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_02.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_02.sem
new file mode 100644
index 0000000..722616b
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_02.sem
@@ -0,0 +1,40 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($bvneg E)
+($IBVVary )
+($bvand E E)
+($bvor E E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+(($bvneg E_term_1) (exists ((r__1 (_ BitVec 32))) (and (= r__0 (bvnot r__1))
+  (E.Sem E_term_1 r__1 x y))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_XOR_02() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_02 #x0000000f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_02 #x000000db y #x000000f7 #x0000002c)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_03.sem b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_03.sem
new file mode 100644
index 0000000..524939c
--- /dev/null
+++ b/benchmarks/messy/basic_bv/correct_input_outputs/BVtest_XOR_03.sem
@@ -0,0 +1,42 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IBVVarx )
+($IBVVary )
+($bvand E E)
+($bvor E E)
+($bvadd E E))
+(($bv=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 (_ BitVec 32)) (y_r0 (_ BitVec 32)) (x (_ BitVec 32)) (y (_ BitVec 32))) Bool))
+
+((match E_term_0
+  (($IBVVarx (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 x))))
+($IBVVary (exists ((r__1 (_ BitVec 32))) (and (= r__0 r__1)
+  (= r__1 y))))
+(($bvand E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvand r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvor E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvor r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+(($bvadd E_term_1 E_term_2) (exists ((r__1 (_ BitVec 32)) (r__2 (_ BitVec 32))) (and (= r__0 (bvadd r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($bv=x E_term_1) (exists ((r__1 (_ BitVec 32))) (and (and (= x_r0 r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun BVtest_XOR_03() Start)
+
+
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_03 #x0000000f y #x00000009 #x00000006)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_03 #x000000db y #x000000f7 #x0000002c)))
+(constraint (exists ((y (_ BitVec 32))) (Start.Sem BVtest_XOR_03 #x00000001 y #x0000000e #x0000000f)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_bv/BVtest_ADD_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_ADD_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_ADD_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_ADD_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_AND_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_AND_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_AND_02.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_02.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_AND_02.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_02.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_AND_03.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_03.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_AND_03.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_AND_03.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_MAX_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_MAX_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_MAX_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_MAX_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_NAND_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_NAND_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_NAND_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_NAND_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_PLUS_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_PLUS_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_PLUS_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_PLUS_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_Swap_XOR_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_Swap_XOR_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_Swap_XOR_02.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_02.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_Swap_XOR_02.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_02.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_Swap_XOR_03.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_03.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_Swap_XOR_03.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_Swap_XOR_03.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_While_01_XOR_by_AND_OR.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_While_01_XOR_by_AND_OR.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_While_01_XOR_by_AND_OR.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_While_02_XOR_by_AND_OR_ADD.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_While_02_XOR_by_AND_OR_ADD.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_While_02_XOR_by_AND_OR_ADD.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_XOR_01.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_01.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_XOR_01.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_01.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_XOR_02.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_02.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_XOR_02.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_02.sem
diff --git a/benchmarks/messy/basic_bv/BVtest_XOR_03.sem b/benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_03.sem
similarity index 100%
rename from benchmarks/messy/basic_bv/BVtest_XOR_03.sem
rename to benchmarks/messy/basic_bv/inverted_input_outputs/BVtest_XOR_03.sem
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_01.sem
new file mode 100644
index 0000000..13ff5d9
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_01.sem
@@ -0,0 +1,57 @@
+(declare-term-types
+((B 0) (E 0) (Start 0) (Y 0))
+((($< E Y))
+(($+ E E)
+($IInt1 )
+($IVarx ))
+(($while B Start)
+($int=y E)
+($int=x E))
+(($IVary ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Y.Sem ((Y_term_0 Y) (r__0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 Y_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (Y.Sem Y_term_2 r__2 x y))))))
+(match E_term_0
+  ((($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match Start_term_0
+  ((($while B_term_1 Start_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (Start.Sem Start_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))
+(($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1))
+  (E.Sem E_term_1 r__1 x y))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))
+(match Y_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))))
+
+
+(synth-fun basicTest_AddByWhileLoop_01() Start)
+
+
+(constraint (Start.Sem basicTest_AddByWhileLoop_01 10 10 4 10))
+(constraint (Start.Sem basicTest_AddByWhileLoop_01 20 20 12 20))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_02.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_02.sem
new file mode 100644
index 0000000..89999e9
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_02.sem
@@ -0,0 +1,58 @@
+(declare-term-types
+((B 0) (E 0) (Start 0) (Y 0))
+((($< E Y))
+(($+ E E)
+($IInt1 )
+($IVarx ))
+(($while B Start)
+($int=y E)
+($int=x E))
+(($IVary ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Y.Sem ((Y_term_0 Y) (r__0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 Y_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (Y.Sem Y_term_2 r__2 x y))))))
+(match E_term_0
+  ((($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match Start_term_0
+  ((($while B_term_1 Start_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (Start.Sem Start_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))
+(($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1))
+  (E.Sem E_term_1 r__1 x y))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))
+(match Y_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))))
+
+
+(synth-fun basicTest_AddByWhileLoop_02() Start)
+
+
+(constraint (Start.Sem basicTest_AddByWhileLoop_02 10 10 4 10))
+(constraint (Start.Sem basicTest_AddByWhileLoop_02 20 20 12 20))
+(constraint (Start.Sem basicTest_AddByWhileLoop_02 12 12 20 12))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_03.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_03.sem
new file mode 100644
index 0000000..b3655a1
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_03.sem
@@ -0,0 +1,51 @@
+(declare-term-types
+((B 0) (E 0) (Start 0) (Y 0))
+((($< E Y))
+(($IVarx ))
+(($while B Start)
+($int=y E)
+($int=x E))
+(($IVary ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Y.Sem ((Y_term_0 Y) (r__0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 Y_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (Y.Sem Y_term_2 r__2 x y))))))
+(match E_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match Start_term_0
+  ((($while B_term_1 Start_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (Start.Sem Start_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))
+(($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1))
+  (E.Sem E_term_1 r__1 x y))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))
+(match Y_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))))
+
+
+(synth-fun basicTest_AddByWhileLoop_03() Start)
+
+
+(constraint (Start.Sem basicTest_AddByWhileLoop_03 10 10 4 10))
+(constraint (Start.Sem basicTest_AddByWhileLoop_03 20 20 12 20))
+(constraint (Start.Sem basicTest_AddByWhileLoop_03 12 12 20 12))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_04.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_04.sem
new file mode 100644
index 0000000..a0eb73c
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_04.sem
@@ -0,0 +1,65 @@
+(declare-term-types
+((B 0) (E 0) (E1 0) (RN1 0) (RN2 0) (S1 0) (Start 0) (Y 0))
+((($< E Y))
+(($IVarx ))
+(($+ RN1 RN2))
+(($IVarx ))
+(($IInt1 ))
+(($int=x E1))
+(($while B S1))
+(($IVary ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 Int) (x Int) (y Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (x Int) (y Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (x Int) (y Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Y.Sem ((Y_term_0 Y) (r__0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 Y_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (Y.Sem Y_term_2 r__2 x y))))))
+(match E_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match E1_term_0
+  ((($+ RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 x y)
+  (RN2.Sem RN2_term_2 r__2 x y))))))
+(match RN1_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S1_term_0
+  ((($int=x E1_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E1.Sem E1_term_1 r__1 x y))))))
+(match Start_term_0
+  ((($while B_term_1 S1_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (S1.Sem S1_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))))
+(match Y_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))))
+
+
+(synth-fun basicTest_AddByWhileLoop_04() Start)
+
+
+(constraint (Start.Sem basicTest_AddByWhileLoop_04 10 10 4 10))
+(constraint (Start.Sem basicTest_AddByWhileLoop_04 20 20 12 20))
+(constraint (Start.Sem basicTest_AddByWhileLoop_04 12 12 20 12))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_05.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_05.sem
new file mode 100644
index 0000000..2b6d16b
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddByWhileLoop_05.sem
@@ -0,0 +1,68 @@
+(declare-term-types
+((B 0) (E 0) (E1 0) (RN1 0) (RN3 0) (RN4 0) (S1 0) (Start 0))
+((($< E RN1))
+(($IVarx ))
+(($+ RN3 RN4))
+(($IVary ))
+(($IVarx ))
+(($IInt1 ))
+(($int=x E1)
+($seq S1 S1))
+(($while B S1))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 Int) (x Int) (y Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (x Int) (y Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (x Int) (y Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (x Int) (y Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 RN1_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (RN1.Sem RN1_term_2 r__2 x y))))))
+(match E_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match E1_term_0
+  ((($+ RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 x y)
+  (RN4.Sem RN4_term_2 r__2 x y))))))
+(match RN1_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))
+(match RN3_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S1_term_0
+  ((($int=x E1_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E1.Sem E1_term_1 r__1 x y))))
+(($seq S1_term_1 S1_term_2) (exists ((x_r1 Int) (y_r1 Int)) (and (S1.Sem S1_term_1 x_r1 y_r1 x y)
+  (S1.Sem S1_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start_term_0
+  ((($while B_term_1 S1_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (S1.Sem S1_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))))))
+
+
+(synth-fun basicTest_AddByWhileLoop_05() Start)
+
+
+(constraint (Start.Sem basicTest_AddByWhileLoop_05 10 10 4 10))
+(constraint (Start.Sem basicTest_AddByWhileLoop_05 20 20 12 20))
+(constraint (Start.Sem basicTest_AddByWhileLoop_05 12 12 20 12))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddOne_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddOne_01.sem
new file mode 100644
index 0000000..5ac2344
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_AddOne_01.sem
@@ -0,0 +1,34 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IVarx )
+($IInt1 )
+($+ E E))
+(($int=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 Int) (x Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (x Int)) Bool))
+
+((match E_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x)
+  (E.Sem E_term_2 r__2 x))))))
+(match Start_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (= x r__1)
+  (E.Sem E_term_1 r__1 x))))))))
+
+
+(synth-fun basicTest_AddOne_01() Start)
+
+
+(constraint (Start.Sem basicTest_AddOne_01 5 4))
+(constraint (Start.Sem basicTest_AddOne_01 3 2))
+(constraint (Start.Sem basicTest_AddOne_01 2 1))
+(constraint (Start.Sem basicTest_AddOne_01 9 8))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Fib_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Fib_01.sem
new file mode 100644
index 0000000..5dfb4a8
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Fib_01.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((B1 0) (E 0) (E1 0) (E2 0) (S 0) (Start 0))
+((($< E2 E2))
+(($IVary )
+($IVarx )
+($IInt1 )
+($+ E E))
+(($IInt1 )
+($IVari ))
+(($IInt2 )
+($IVari ))
+(($int=i E1)
+($int=x E)
+($seq S S))
+(($seq S S))))
+
+
+(define-funs-rec
+((B1.Sem ((B1_term_0 B1) (r__0 Bool) (x Int) (y Int) (i Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int) (i Int)) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 Int) (x Int) (y Int) (i Int)) Bool)
+(E2.Sem ((E2_term_0 E2) (r__0 Int) (x Int) (y Int) (i Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (y_r0 Int) (i_r0 Int) (x Int) (y Int) (i Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (i_r0 Int) (x Int) (y Int) (i Int)) Bool))
+
+((match B1_term_0
+  ((($< E2_term_1 E2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E2.Sem E2_term_1 r__1 x y i)
+  (E2.Sem E2_term_2 r__2 x y i))))))
+(match E_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y i)
+  (E.Sem E_term_2 r__2 x y i))))))
+(match E1_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVari (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 i))))))
+(match E2_term_0
+  (($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVari (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 i))))))
+(match S_term_0
+  ((($int=i E1_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y y_r0)
+  (= i r__1))
+  (E1.Sem E1_term_1 r__1 x y i))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0)
+  (= i i_r0))
+  (E.Sem E_term_1 r__1 x y i))))
+(($seq S_term_1 S_term_2) (exists ((x_r1 Int) (y_r1 Int) (i_r1 Int)) (and (S.Sem S_term_1 x_r1 y_r1 i_r1 x y i)
+  (S.Sem S_term_2 x_r0 y_r0 i_r0 x_r1 y_r1 i_r1))))))
+(match Start_term_0
+  ((($seq S_term_1 S_term_2) (exists ((x_r1 Int) (y_r1 Int) (i_r1 Int)) (and (S.Sem S_term_1 x_r1 y_r1 i_r1 x y i)
+  (S.Sem S_term_2 x_r0 y_r0 i_r0 x_r1 y_r1 i_r1))))))))
+
+
+(synth-fun basicTest_Fib_01() Start)
+
+
+(constraint (exists ((i Int) (y Int)) (Start.Sem basicTest_Fib_01 1 y i 1 1 1)))
+(constraint (exists ((i Int) (y Int)) (Start.Sem basicTest_Fib_01 5 y i 1 1 5)))
+(constraint (exists ((i Int) (y Int)) (Start.Sem basicTest_Fib_01 55 y i 1 1 10)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_01.sem
new file mode 100644
index 0000000..9594336
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_01.sem
@@ -0,0 +1,45 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IVarx )
+($IVary )
+($IInt1 )
+($IInt0 )
+($+ E E))
+(($int=y E)
+($int=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool))
+
+((match E_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match Start_term_0
+  ((($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1))
+  (E.Sem E_term_1 r__1 x y))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))))))
+
+
+(synth-fun basicTest_MAX_01() Start)
+
+
+(constraint (Start.Sem basicTest_MAX_01 4 1 4 1))
+(constraint (Start.Sem basicTest_MAX_01 6 2 2 6))
+(constraint (Start.Sem basicTest_MAX_01 1 1 1 1))
+(constraint (Start.Sem basicTest_MAX_01 8 8 8 8))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_02.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_02.sem
new file mode 100644
index 0000000..f21557d
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_02.sem
@@ -0,0 +1,49 @@
+(declare-term-types
+((B 0) (E 0) (Start 0))
+((($< E E))
+(($IVary )
+($IVarx )
+($eite B E E))
+(($int=y E)
+($int=x E)
+($seq Start Start))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match E_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+(($eite B_term_1 E_term_2 E_term_3) (exists ((r__1 Bool) (r__2 Int) (r__3 Int)) (and (= r__0 (ite r__1 r__2 r__3))
+  (B.Sem B_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y)
+  (E.Sem E_term_3 r__3 x y))))))
+(match Start_term_0
+  ((($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1))
+  (E.Sem E_term_1 r__1 x y))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))
+(($seq Start_term_1 Start_term_2) (exists ((x_r1 Int) (y_r1 Int)) (and (Start.Sem Start_term_1 x_r1 y_r1 x y)
+  (Start.Sem Start_term_2 x_r0 y_r0 x_r1 y_r1))))))))
+
+
+(synth-fun basicTest_MAX_02() Start)
+
+
+(constraint (Start.Sem basicTest_MAX_02 4 1 4 1))
+(constraint (Start.Sem basicTest_MAX_02 6 2 2 6))
+(constraint (Start.Sem basicTest_MAX_02 1 1 1 1))
+(constraint (Start.Sem basicTest_MAX_02 8 8 8 8))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_03.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_03.sem
new file mode 100644
index 0000000..38c116c
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MAX_03.sem
@@ -0,0 +1,59 @@
+(declare-term-types
+((B 0) (E 0) (Start 0))
+((($< E E))
+(($IVarc )
+($IVary )
+($IVarx )
+($eite B E E))
+(($int=y E)
+($int=x E)
+($int=c E)
+($seq Start Start))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int) (c Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int) (c Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (y Int) (c Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y c)
+  (E.Sem E_term_2 r__2 x y c))))))
+(match E_term_0
+  (($IVarc (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 c))))
+($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+(($eite B_term_1 E_term_2 E_term_3) (exists ((r__1 Bool) (r__2 Int) (r__3 Int)) (and (= r__0 (ite r__1 r__2 r__3))
+  (B.Sem B_term_1 r__1 x y c)
+  (E.Sem E_term_2 r__2 x y c)
+  (E.Sem E_term_3 r__3 x y c))))))
+(match Start_term_0
+  ((($int=y E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y r__1)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x y c))))
+(($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x y c))))
+(($int=c E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y y_r0)
+  (= c r__1))
+  (E.Sem E_term_1 r__1 x y c))))
+(($seq Start_term_1 Start_term_2) (exists ((x_r1 Int) (y_r1 Int) (c_r1 Int)) (and (Start.Sem Start_term_1 x_r1 y_r1 c_r1 x y c)
+  (Start.Sem Start_term_2 x_r0 y_r0 c_r0 x_r1 y_r1 c_r1))))))))
+
+
+(synth-fun basicTest_MAX_03() Start)
+
+
+(constraint (exists ((c Int)) (Start.Sem basicTest_MAX_03 4 1 c 4 1 4123)))
+(constraint (exists ((c Int)) (Start.Sem basicTest_MAX_03 6 2 c 2 6 4123)))
+(constraint (exists ((c Int)) (Start.Sem basicTest_MAX_03 1 1 c 1 1 4123)))
+(constraint (exists ((c Int)) (Start.Sem basicTest_MAX_03 8 8 c 8 8 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_01.sem
new file mode 100644
index 0000000..7c34abc
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_01.sem
@@ -0,0 +1,131 @@
+(declare-term-types
+((B 0) (E 0) (NS 0) (S 0) (Start 0) (V 0))
+((($< V V))
+(($IInt0 )
+($IVarj )
+($IInt1 )
+($IVari )
+($+ E E)
+($IVarc ))
+(($int=c E)
+($int=i E)
+($seq NS NS)
+($int=j E))
+(($int=j E)
+($while B NS)
+($seq S S)
+($int=i E))
+(($while B S))
+(($IVary )
+($IVari )
+($IVarc )
+($IVarx )
+($IVarj ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool)
+(NS.Sem ((NS_term_0 NS) (x_r0 Int) (j_r0 Int) (i_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (j_r0 Int) (i_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (j_r0 Int) (i_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool)
+(V.Sem ((V_term_0 V) (r__0 Int) (x Int) (j Int) (i Int) (y Int) (c Int)) Bool))
+
+((match B_term_0
+  ((($< V_term_1 V_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (V.Sem V_term_1 r__1 x j i y c)
+  (V.Sem V_term_2 r__2 x j i y c))))))
+(match E_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarj (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 j))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVari (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 i))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x j i y c)
+  (E.Sem E_term_2 r__2 x j i y c))))
+($IVarc (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 c))))))
+(match NS_term_0
+  ((($int=c E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= j j_r0)
+  (= i i_r0)
+  (= y y_r0)
+  (= c r__1))
+  (E.Sem E_term_1 r__1 x j i y c))))
+(($int=i E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= j j_r0)
+  (= i r__1)
+  (= y y_r0)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x j i y c))))
+(($seq NS_term_1 NS_term_2) (exists ((x_r1 Int) (j_r1 Int) (i_r1 Int) (y_r1 Int) (c_r1 Int)) (and (NS.Sem NS_term_1 x_r1 j_r1 i_r1 y_r1 c_r1 x j i y c)
+  (NS.Sem NS_term_2 x_r0 j_r0 i_r0 y_r0 c_r0 x_r1 j_r1 i_r1 y_r1 c_r1))))
+(($int=j E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= j r__1)
+  (= i i_r0)
+  (= y y_r0)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x j i y c))))))
+(match S_term_0
+  ((($int=j E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= j r__1)
+  (= i i_r0)
+  (= y y_r0)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x j i y c))))
+(($while B_term_1 NS_term_2) (exists ((r__1 Bool) (x_r2 Int) (j_r2 Int) (i_r2 Int) (y_r2 Int) (c_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x j i y c)
+  (NS.Sem NS_term_2 x_r2 j_r2 i_r2 y_r2 c_r2 x j i y c)
+  (S.Sem S_term_0 x_r0 j_r0 i_r0 y_r0 c_r0 x_r2 j_r2 i_r2 y_r2 c_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x j i y c)
+  (and (= x x_r0)
+  (= j j_r0)
+  (= i i_r0)
+  (= y y_r0)
+  (= c c_r0)))))
+(($seq S_term_1 S_term_2) (exists ((x_r1 Int) (j_r1 Int) (i_r1 Int) (y_r1 Int) (c_r1 Int)) (and (S.Sem S_term_1 x_r1 j_r1 i_r1 y_r1 c_r1 x j i y c)
+  (S.Sem S_term_2 x_r0 j_r0 i_r0 y_r0 c_r0 x_r1 j_r1 i_r1 y_r1 c_r1))))
+(($int=i E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= j j_r0)
+  (= i r__1)
+  (= y y_r0)
+  (= c c_r0))
+  (E.Sem E_term_1 r__1 x j i y c))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 Int) (j_r2 Int) (i_r2 Int) (y_r2 Int) (c_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x j i y c)
+  (S.Sem S_term_2 x_r2 j_r2 i_r2 y_r2 c_r2 x j i y c)
+  (Start.Sem Start_term_0 x_r0 j_r0 i_r0 y_r0 c_r0 x_r2 j_r2 i_r2 y_r2 c_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x j i y c)
+  (and (= x x_r0)
+  (= j j_r0)
+  (= i i_r0)
+  (= y y_r0)
+  (= c c_r0)))))))
+(match V_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVari (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 i))))
+($IVarc (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 c))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IVarj (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 j))))))))
+
+
+(synth-fun basicTest_MultByWhileLoop_01() Start)
+
+
+(constraint (exists ((y Int) (i Int) (j Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_01 x j i y 40 4 0 0 10 0)))
+(constraint (exists ((y Int) (i Int) (j Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_01 x j i y 30 5 0 0 6 0)))
+(constraint (exists ((y Int) (i Int) (j Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_01 x j i y 24 8 0 0 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_02.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_02.sem
new file mode 100644
index 0000000..13beb0f
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_MultByWhileLoop_02.sem
@@ -0,0 +1,82 @@
+(declare-term-types
+((B 0) (E 0) (NS 0) (S 0) (Start 0) (V 0))
+((($< V V))
+(($IInt0 )
+($+ E E)
+($IVarc )
+($IInt1 ))
+(($seq NS NS)
+($int=c E))
+(($while B NS))
+(($while B S))
+(($IVary )
+($IVarx )
+($IVarc ))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int) (c Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int) (c Int)) Bool)
+(NS.Sem ((NS_term_0 NS) (x_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (y Int) (c Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (y Int) (c Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (c_r0 Int) (x Int) (y Int) (c Int)) Bool)
+(V.Sem ((V_term_0 V) (r__0 Int) (x Int) (y Int) (c Int)) Bool))
+
+((match B_term_0
+  ((($< V_term_1 V_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (V.Sem V_term_1 r__1 x y c)
+  (V.Sem V_term_2 r__2 x y c))))))
+(match E_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y c)
+  (E.Sem E_term_2 r__2 x y c))))
+($IVarc (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 c))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match NS_term_0
+  ((($seq NS_term_1 NS_term_2) (exists ((x_r1 Int) (y_r1 Int) (c_r1 Int)) (and (NS.Sem NS_term_1 x_r1 y_r1 c_r1 x y c)
+  (NS.Sem NS_term_2 x_r0 y_r0 c_r0 x_r1 y_r1 c_r1))))
+(($int=c E_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= y y_r0)
+  (= c r__1))
+  (E.Sem E_term_1 r__1 x y c))))))
+(match S_term_0
+  ((($while B_term_1 NS_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int) (c_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y c)
+  (NS.Sem NS_term_2 x_r2 y_r2 c_r2 x y c)
+  (S.Sem S_term_0 x_r0 y_r0 c_r0 x_r2 y_r2 c_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y c)
+  (and (= x x_r0)
+  (= y y_r0)
+  (= c c_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int) (c_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y c)
+  (S.Sem S_term_2 x_r2 y_r2 c_r2 x y c)
+  (Start.Sem Start_term_0 x_r0 y_r0 c_r0 x_r2 y_r2 c_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y c)
+  (and (= x x_r0)
+  (= y y_r0)
+  (= c c_r0)))))))
+(match V_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IVarc (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 c))))))))
+
+
+(synth-fun basicTest_MultByWhileLoop_02() Start)
+
+
+(constraint (exists ((y Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_02 x y 40 4 10 0)))
+(constraint (exists ((y Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_02 x y 30 5 6 0)))
+(constraint (exists ((y Int) (x Int)) (Start.Sem basicTest_MultByWhileLoop_02 x y 24 8 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Sanity01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Sanity01.sem
new file mode 100644
index 0000000..525e315
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_Sanity01.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((B 0) (C 0) (E 0) (RN1 0) (RN2 0) (RN3 0) (RN5 0) (RN6 0) (S 0) (Start 0))
+((($< RN3 C))
+(($IInt200 ))
+(($+ RN1 RN2)
+($- RN5 RN6))
+(($IVarx ))
+(($IVarx ))
+(($IVarx ))
+(($IVarx ))
+(($IVarx ))
+(($int=x E))
+(($while B S))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int)) Bool)
+(C.Sem ((C_term_0 C) (r__0 Int) (x Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (x Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (x Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (x Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (x Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (x Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (x Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (x Int)) Bool))
+
+((match B_term_0
+  ((($< RN3_term_1 C_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 x)
+  (C.Sem C_term_2 r__2 x))))))
+(match C_term_0
+  (($IInt200 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 200))))))
+(match E_term_0
+  ((($+ RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 x)
+  (RN2.Sem RN2_term_2 r__2 x))))
+(($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 x)
+  (RN6.Sem RN6_term_2 r__2 x))))))
+(match RN1_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN2_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN3_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN5_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match RN6_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match S_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (= x r__1)
+  (E.Sem E_term_1 r__1 x))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x)
+  (S.Sem S_term_2 x_r2 x)
+  (Start.Sem Start_term_0 x_r0 x_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x)
+  (= x x_r0))))))))
+
+
+(synth-fun basicTest_Sanity01() Start)
+
+
+(constraint (Start.Sem basicTest_Sanity01 10 4))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SetBothtoLarger_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SetBothtoLarger_01.sem
new file mode 100644
index 0000000..296f59b
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SetBothtoLarger_01.sem
@@ -0,0 +1,60 @@
+(declare-term-types
+((B 0) (E 0) (S 0) (Start 0))
+((($< E E))
+(($IVary )
+($IInt1 )
+($+ E E)
+($IInt-1 )
+($IVarx ))
+(($int=x E)
+($seq S S))
+(($while B S))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (y Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (y Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (y_r0 Int) (x Int) (y Int)) Bool))
+
+((match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))))
+(match E_term_0
+  (($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 x y)
+  (E.Sem E_term_2 r__2 x y))))
+($IInt-1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 (- 1)))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match S_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= y y_r0))
+  (E.Sem E_term_1 r__1 x y))))
+(($seq S_term_1 S_term_2) (exists ((x_r1 Int) (y_r1 Int)) (and (S.Sem S_term_1 x_r1 y_r1 x y)
+  (S.Sem S_term_2 x_r0 y_r0 x_r1 y_r1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 Int) (y_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x y)
+  (S.Sem S_term_2 x_r2 y_r2 x y)
+  (Start.Sem Start_term_0 x_r0 y_r0 x_r2 y_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x y)
+  (and (= x x_r0)
+  (= y y_r0)))))))))
+
+
+(synth-fun basicTest_SetBothtoLarger_01() Start)
+
+
+(constraint (Start.Sem basicTest_SetBothtoLarger_01 10 10 4 10))
+(constraint (Start.Sem basicTest_SetBothtoLarger_01 20 20 12 20))
+(constraint (Start.Sem basicTest_SetBothtoLarger_01 20 20 20 12))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumByWhileLoop_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumByWhileLoop_01.sem
new file mode 100644
index 0000000..7f85b42
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumByWhileLoop_01.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((B 0) (E 0) (RN1 0) (S 0) (Start 0))
+((($< RN1 E))
+(($IVarz )
+($IVarx )
+($+ E E)
+($IVarv )
+($IVary )
+($IVarw )
+($IInt1 ))
+(($IVarx ))
+(($int=x E))
+(($while B S))))
+
+
+(define-funs-rec
+((B.Sem ((B_term_0 B) (r__0 Bool) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(S.Sem ((S_term_0 S) (w_r0 Int) (z_r0 Int) (y_r0 Int) (x_r0 Int) (v_r0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (w_r0 Int) (z_r0 Int) (y_r0 Int) (x_r0 Int) (v_r0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool))
+
+((match B_term_0
+  ((($< RN1_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 w z y x v)
+  (E.Sem E_term_2 r__2 w z y x v))))))
+(match E_term_0
+  (($IVarz (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 z))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 w z y x v)
+  (E.Sem E_term_2 r__2 w z y x v))))
+($IVarv (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 v))))
+($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarw (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 w))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN1_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match S_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (and (= w w_r0)
+  (= z z_r0)
+  (= y y_r0)
+  (= x r__1)
+  (= v v_r0))
+  (E.Sem E_term_1 r__1 w z y x v))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (w_r2 Int) (z_r2 Int) (y_r2 Int) (x_r2 Int) (v_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 w z y x v)
+  (S.Sem S_term_2 w_r2 z_r2 y_r2 x_r2 v_r2 w z y x v)
+  (Start.Sem Start_term_0 w_r0 z_r0 y_r0 x_r0 v_r0 w_r2 z_r2 y_r2 x_r2 v_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 w z y x v)
+  (and (= w w_r0)
+  (= z z_r0)
+  (= y y_r0)
+  (= x x_r0)
+  (= v v_r0)))))))))
+
+
+(synth-fun basicTest_SumByWhileLoop_01() Start)
+
+
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumByWhileLoop_01 w z y 15 v 2 5 4 3 1)))
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumByWhileLoop_01 w z y 70 v 21 16 13 11 9)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_01.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_01.sem
new file mode 100644
index 0000000..1eebb99
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_01.sem
@@ -0,0 +1,45 @@
+(declare-term-types
+((E 0) (Start 0))
+((($IVarv )
+($IVary )
+($IVarw )
+($IVarz )
+($+ E E)
+($IVarx ))
+(($int=x E))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (w_r0 Int) (z_r0 Int) (y_r0 Int) (x_r0 Int) (v_r0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool))
+
+((match E_term_0
+  (($IVarv (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 v))))
+($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))
+($IVarw (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 w))))
+($IVarz (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 z))))
+(($+ E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E.Sem E_term_1 r__1 w z y x v)
+  (E.Sem E_term_2 r__2 w z y x v))))
+($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match Start_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (and (= w w_r0)
+  (= z z_r0)
+  (= y y_r0)
+  (= x r__1)
+  (= v v_r0))
+  (E.Sem E_term_1 r__1 w z y x v))))))))
+
+
+(synth-fun basicTest_SumWithLimitedOps_01() Start)
+
+
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumWithLimitedOps_01 w z y 15 v 2 5 4 3 1)))
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumWithLimitedOps_01 w z y 70 v 21 16 13 11 9)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_02.sem b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_02.sem
new file mode 100644
index 0000000..1a7630a
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/basicTest_SumWithLimitedOps_02.sem
@@ -0,0 +1,53 @@
+(declare-term-types
+((E 0) (E1 0) (Start 0) (V 0))
+((($+ E1 E1))
+(($+ V V))
+(($int=x E))
+(($IVarx )
+($IVarz )
+($IVarv )
+($IVarw )
+($IVary ))))
+
+
+(define-funs-rec
+((E.Sem ((E_term_0 E) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(E1.Sem ((E1_term_0 E1) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (w_r0 Int) (z_r0 Int) (y_r0 Int) (x_r0 Int) (v_r0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool)
+(V.Sem ((V_term_0 V) (r__0 Int) (w Int) (z Int) (y Int) (x Int) (v Int)) Bool))
+
+((match E_term_0
+  ((($+ E1_term_1 E1_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (E1.Sem E1_term_1 r__1 w z y x v)
+  (E1.Sem E1_term_2 r__2 w z y x v))))))
+(match E1_term_0
+  ((($+ V_term_1 V_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (V.Sem V_term_1 r__1 w z y x v)
+  (V.Sem V_term_2 r__2 w z y x v))))))
+(match Start_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (and (= w w_r0)
+  (= z z_r0)
+  (= y y_r0)
+  (= x r__1)
+  (= v v_r0))
+  (E.Sem E_term_1 r__1 w z y x v))))))
+(match V_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))
+($IVarz (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 z))))
+($IVarv (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 v))))
+($IVarw (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 w))))
+($IVary (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 y))))))))
+
+
+(synth-fun basicTest_SumWithLimitedOps_02() Start)
+
+
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumWithLimitedOps_02 w z y 15 v 2 5 4 3 1)))
+(constraint (exists ((v Int) (y Int) (z Int) (w Int)) (Start.Sem basicTest_SumWithLimitedOps_02 w z y 70 v 21 16 13 11 9)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/correct_input_outputs/minimal_unsat.sem b/benchmarks/messy/basic_impv/correct_input_outputs/minimal_unsat.sem
new file mode 100644
index 0000000..a44baa2
--- /dev/null
+++ b/benchmarks/messy/basic_impv/correct_input_outputs/minimal_unsat.sem
@@ -0,0 +1,78 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (N 0) (ON 0) (RN1 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarx ))
+(($< RN1 N))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt1 ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=x E))
+(($int=n ON))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (x Int) (n Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (x Int) (n Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (x Int) (n Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (x Int) (n Int)) Bool)
+(ON.Sem ((ON_term_0 ON) (r__0 Int) (x Int) (n Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (x Int) (n Int)) Bool)
+(S.Sem ((S_term_0 S) (x_r0 Int) (n_r0 Int) (x Int) (n Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (x_r0 Int) (n_r0 Int) (x Int) (n Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (x_r0 Int) (n_r0 Int) (x Int) (n Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (x_r0 Int) (n_r0 Int) (x Int) (n Int)) Bool))
+
+((match A_term_0
+  (($IVarx (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 x))))))
+(match B_term_0
+  ((($< RN1_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 x n)
+  (N.Sem N_term_2 r__2 x n))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 x n)
+  (A.Sem A_term_2 r__2 x n))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 x n)
+  (A.Sem A_term_2 r__2 x n))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match ON_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN1_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((x_r1 Int) (n_r1 Int)) (and (S1.Sem S1_term_1 x_r1 n_r1 x n)
+  (S2.Sem S2_term_2 x_r0 n_r0 x_r1 n_r1))))))
+(match S1_term_0
+  ((($int=x E_term_1) (exists ((r__1 Int)) (and (and (= x r__1)
+  (= n n_r0))
+  (E.Sem E_term_1 r__1 x n))))))
+(match S2_term_0
+  ((($int=n ON_term_1) (exists ((r__1 Int)) (and (and (= x x_r0)
+  (= n r__1))
+  (ON.Sem ON_term_1 r__1 x n))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (x_r2 Int) (n_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 x n)
+  (S.Sem S_term_2 x_r2 n_r2 x n)
+  (Start.Sem Start_term_0 x_r0 n_r0 x_r2 n_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 x n)
+  (and (= x x_r0)
+  (= n n_r0)))))))))
+
+
+(synth-fun minimal_unsat() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem minimal_unsat 2 n 5 4)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_02.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_02.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_02.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_02.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_03.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_03.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_03.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_03.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_04.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_04.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_04.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_04.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_05.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_05.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddByWhileLoop_05.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddByWhileLoop_05.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_AddOne_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddOne_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_AddOne_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_AddOne_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_Fib_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_Fib_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_Fib_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_Fib_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_MAX_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_MAX_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_MAX_02.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_02.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_MAX_02.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_02.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_MAX_03.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_03.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_MAX_03.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MAX_03.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_MultByWhileLoop_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MultByWhileLoop_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_MultByWhileLoop_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MultByWhileLoop_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_MultByWhileLoop_02.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MultByWhileLoop_02.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_MultByWhileLoop_02.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_MultByWhileLoop_02.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_Sanity01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_Sanity01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_Sanity01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_Sanity01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_SetBothtoLarger_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SetBothtoLarger_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_SetBothtoLarger_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SetBothtoLarger_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_SumByWhileLoop_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumByWhileLoop_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_SumByWhileLoop_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumByWhileLoop_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_SumWithLimitedOps_01.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumWithLimitedOps_01.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_SumWithLimitedOps_01.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumWithLimitedOps_01.sem
diff --git a/benchmarks/messy/basic_impv/basicTest_SumWithLimitedOps_02.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumWithLimitedOps_02.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/basicTest_SumWithLimitedOps_02.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/basicTest_SumWithLimitedOps_02.sem
diff --git a/benchmarks/messy/basic_impv/minimal_unsat.sem b/benchmarks/messy/basic_impv/inverted_input_outputs/minimal_unsat.sem
similarity index 100%
rename from benchmarks/messy/basic_impv/minimal_unsat.sem
rename to benchmarks/messy/basic_impv/inverted_input_outputs/minimal_unsat.sem
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_01.sem
new file mode 100644
index 0000000..d46b79b
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_01.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_01() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_01 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_01 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_01 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_01 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_02.sem
new file mode 100644
index 0000000..52e5cc3
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_02.sem
@@ -0,0 +1,69 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_02() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_02 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_02 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_02 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_02 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_03.sem
new file mode 100644
index 0000000..c7702b6
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_03.sem
@@ -0,0 +1,71 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_03() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_03 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_03 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_03 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_03 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_04.sem
new file mode 100644
index 0000000..1643847
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_04.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_04() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_04 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_04 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_04 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_04 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_05.sem
new file mode 100644
index 0000000..3088da4
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_05.sem
@@ -0,0 +1,63 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (A.Sem A_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_05() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_05 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_05 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_05 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_05 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_06.sem
new file mode 100644
index 0000000..fb68f71
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_06.sem
@@ -0,0 +1,98 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A)
+($* A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_06() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_06 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_06 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_06 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_06 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_07.sem
new file mode 100644
index 0000000..ddcaa9e
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_07.sem
@@ -0,0 +1,88 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_07() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_07 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_07 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_07 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_07 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_08.sem
new file mode 100644
index 0000000..12608ee
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_08.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_08() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_08 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_08 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_08 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_08 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_09.sem
new file mode 100644
index 0000000..d1c824b
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_09.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_09() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_09 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_09 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_09 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_09 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_10.sem
new file mode 100644
index 0000000..51b20a7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_10.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (N 0) (O 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< N O))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_10() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_10 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_10 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_10 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_10 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_11.sem
new file mode 100644
index 0000000..ed71d99
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no01_factorialTest_11.sem
@@ -0,0 +1,89 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< N O))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no01_factorialTest_11() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_11 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_11 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_11 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no01_factorialTest_11 n 6 3 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_01.sem
new file mode 100644
index 0000000..46fdf45
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_01.sem
@@ -0,0 +1,78 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< E E))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 n r)
+  (E.Sem E_term_2 r__2 n r))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_01() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_01 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_01 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_01 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_01 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_02.sem
new file mode 100644
index 0000000..04794a5
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_02.sem
@@ -0,0 +1,69 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< E E))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 n r)
+  (E.Sem E_term_2 r__2 n r))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_02() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_02 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_02 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_02 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_02 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_03.sem
new file mode 100644
index 0000000..33abd65
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_03.sem
@@ -0,0 +1,74 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< E E))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 n r)
+  (E.Sem E_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_03() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_03 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_03 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_03 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_03 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_04.sem
new file mode 100644
index 0000000..3cabd17
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_04.sem
@@ -0,0 +1,76 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< E E))
+(($+ A A)
+($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< E_term_1 E_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (E.Sem E_term_1 r__1 n r)
+  (E.Sem E_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_04() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_04 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_04 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_04 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_04 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_05.sem
new file mode 100644
index 0000000..26894d3
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_05.sem
@@ -0,0 +1,66 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (A.Sem A_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_05() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_05 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_05 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_05 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_05 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_06.sem
new file mode 100644
index 0000000..6f285fc
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_06.sem
@@ -0,0 +1,101 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A)
+($* A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_06() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_06 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_06 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_06 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_06 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_07.sem
new file mode 100644
index 0000000..89ea08f
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_07.sem
@@ -0,0 +1,88 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_07() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_07 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_07 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_07 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_07 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_08.sem
new file mode 100644
index 0000000..82e5bdc
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_08.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- A A)
+($+ A A))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_08() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_08 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_08 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_08 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_08 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_09.sem
new file mode 100644
index 0000000..143a94a
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_09.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< O N))
+(($- N O))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< O_term_1 N_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (O.Sem O_term_1 r__1 n r)
+  (N.Sem N_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_09() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_09 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_09 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_09 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_09 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_10.sem
new file mode 100644
index 0000000..25df5c1
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_10.sem
@@ -0,0 +1,88 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (N 0) (O 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< N O))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_10() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_10 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_10 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_10 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_10 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_11.sem
new file mode 100644
index 0000000..16f8157
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no02_doubleFactorialTest_11.sem
@@ -0,0 +1,92 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (N 0) (O 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IInt2 )
+($IVarn ))
+(($< N O))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(N.Sem ((N_term_0 N) (r__0 Int) (n Int) (r Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< N_term_1 O_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (N.Sem N_term_1 r__1 n r)
+  (O.Sem O_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match N_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match O_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no02_doubleFactorialTest_11() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_11 n 1 0 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_11 n 1 1 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_11 n 2 2 1)))
+(constraint (exists ((n Int)) (Start.Sem no02_doubleFactorialTest_11 n 15 5 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_01.sem
new file mode 100644
index 0000000..1fc69fe
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_01.sem
@@ -0,0 +1,71 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_01() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_01 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_01 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_01 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_01 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_02.sem
new file mode 100644
index 0000000..6638b3d
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_02.sem
@@ -0,0 +1,65 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_02() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_02 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_02 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_02 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_02 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_03.sem
new file mode 100644
index 0000000..556fd13
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_03.sem
@@ -0,0 +1,67 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_03() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_03 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_03 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_03 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_03 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_04.sem
new file mode 100644
index 0000000..963ddad
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_04.sem
@@ -0,0 +1,69 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_04() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_04 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_04 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_04 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_04 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_05.sem
new file mode 100644
index 0000000..f6b9efb
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_05.sem
@@ -0,0 +1,63 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (A.Sem A_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_05() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_05 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_05 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_05 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_05 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_06.sem
new file mode 100644
index 0000000..fb6a06d
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_06.sem
@@ -0,0 +1,104 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($- RN5 RN6))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r)
+  (RN2.Sem RN2_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r)
+  (RN6.Sem RN6_term_2 r__2 n r))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_06() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_06 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_06 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_06 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_06 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_07.sem
new file mode 100644
index 0000000..79c4408
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_07.sem
@@ -0,0 +1,94 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN5 RN6))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r)
+  (RN2.Sem RN2_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r)
+  (RN6.Sem RN6_term_2 r__2 n r))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S1.Sem S1_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_07() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_07 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_07 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_07 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_07 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_08.sem
new file mode 100644
index 0000000..b7a9ee2
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_08.sem
@@ -0,0 +1,91 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN5 RN6))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r)
+  (RN2.Sem RN2_term_2 r__2 n r))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r)
+  (RN6.Sem RN6_term_2 r__2 n r))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_08() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_08 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_08 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_08 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_08 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_09.sem
new file mode 100644
index 0000000..dad6c30
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_09.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (RN2 0) (RN3 0) (RN4 0) (RN5 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($- RN4 RN5))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r)
+  (RN3.Sem RN3_term_2 r__2 n r))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r)
+  (RN5.Sem RN5_term_2 r__2 n r))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (A.Sem A_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (M.Sem M_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_09() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_09 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_09 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_09 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_09 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_10.sem
new file mode 100644
index 0000000..cea0d9f
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_10.sem
@@ -0,0 +1,81 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r)
+  (RN2.Sem RN2_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 n r)
+  (S.Sem S_term_2 n_r0 r_r0 n_r1 r_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_10() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_10 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_10 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_10 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_10 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_11.sem
new file mode 100644
index 0000000..7c391b9
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no03_sigmaTest_11.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S1 S2))
+(($int=r E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (n Int) (r Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r)
+  (RN2.Sem RN2_term_2 r__2 n r))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r)
+  (A.Sem A_term_2 r__2 n r))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 n r)
+  (S2.Sem S2_term_2 n_r0 r_r0 n_r1 r_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1))
+  (E.Sem E_term_1 r__1 n r))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0))
+  (E.Sem E_term_1 r__1 n r))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r)
+  (S.Sem S_term_2 n_r2 r_r2 n r)
+  (Start.Sem Start_term_0 n_r0 r_r0 n_r2 r_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r)
+  (and (= n n_r0)
+  (= r r_r0)))))))))
+
+
+(synth-fun no03_sigmaTest_11() Start)
+
+
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_11 n 0 0 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_11 n 1 1 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_11 n 3 2 0)))
+(constraint (exists ((n Int)) (Start.Sem no03_sigmaTest_11 n 6 3 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_01.sem
new file mode 100644
index 0000000..1bfaa21
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_01.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A)
+($* A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_01() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_01 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_01 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_01 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_02.sem
new file mode 100644
index 0000000..cacd174
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_02.sem
@@ -0,0 +1,79 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A)
+($* A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_02() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_02 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_02 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_02 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_03.sem
new file mode 100644
index 0000000..660e832
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_03.sem
@@ -0,0 +1,77 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($int=t1 E)
+($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_03() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_03 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_03 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_03 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_04.sem
new file mode 100644
index 0000000..666d772
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_04.sem
@@ -0,0 +1,79 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S1.Sem S1_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_04() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_04 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_04 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_04 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_05.sem
new file mode 100644
index 0000000..355fa56
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_05.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=t1 A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S1.Sem S1_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))
+(($int=t1 A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (A.Sem A_term_1 r__1 n r t1))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_05() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_05 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_05 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_05 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_06.sem
new file mode 100644
index 0000000..2cfcc98
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_06.sem
@@ -0,0 +1,118 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($- RN6 RN7))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=t1 E)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r t1)
+  (RN7.Sem RN7_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S1.Sem S1_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_06() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_06 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_06 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_06 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_07.sem
new file mode 100644
index 0000000..8f6ae93
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_07.sem
@@ -0,0 +1,104 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN6 RN7))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=t1 E)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r t1)
+  (RN7.Sem RN7_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S1.Sem S1_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_07() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_07 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_07 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_07 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_08.sem
new file mode 100644
index 0000000..23c632f
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_08.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN5 RN6))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r E)
+($int=t1 E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r t1)
+  (RN6.Sem RN6_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_08() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_08 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_08 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_08 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_09.sem
new file mode 100644
index 0000000..1044e95
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_09.sem
@@ -0,0 +1,100 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (RN2 0) (RN3 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($- RN5 RN6))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r A)
+($int=t1 A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r t1)
+  (RN3.Sem RN3_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r t1)
+  (RN6.Sem RN6_term_2 r__2 n r t1))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))
+(($int=t1 A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (A.Sem A_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_09() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_09 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_09 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_09 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_10.sem
new file mode 100644
index 0000000..91bacb5
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_10.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_10() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_10 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_10 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_10 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_11.sem
new file mode 100644
index 0000000..285a242
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no04_sigmaSquare_11.sem
@@ -0,0 +1,104 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN2 0) (RN3 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=t1 E)
+($int=r E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r t1)
+  (RN3.Sem RN3_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no04_sigmaSquare_11() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_11 n 1 t1 1 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_11 n 5 t1 2 0 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no04_sigmaSquare_11 n 14 t1 3 0 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_01.sem
new file mode 100644
index 0000000..a37c035
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_01.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A)
+($* A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_01() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_01 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_01 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_01 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_02.sem
new file mode 100644
index 0000000..7837d02
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_02.sem
@@ -0,0 +1,79 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A)
+($* A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_02() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_02 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_02 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_02 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_03.sem
new file mode 100644
index 0000000..661308a
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_03.sem
@@ -0,0 +1,81 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($int=t1 E)
+($seq S S)
+($int=r E)
+($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_03() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_03 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_03 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_03 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_04.sem
new file mode 100644
index 0000000..052cf84
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_04.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S1 S2))
+(($int=r E)
+($int=t1 E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_04() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_04 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_04 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_04 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_05.sem
new file mode 100644
index 0000000..87c61cb
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_05.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S2))
+(($int=r A)
+($int=t1 A))
+(($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))
+(($int=t1 A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (A.Sem A_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_05() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_05 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_05 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_05 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_06.sem
new file mode 100644
index 0000000..5a075c4
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_06.sem
@@ -0,0 +1,115 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E)
+($int=t1 E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r t1)
+  (RN4.Sem RN4_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_06() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_06 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_06 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_06 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_07.sem
new file mode 100644
index 0000000..f539528
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_07.sem
@@ -0,0 +1,101 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E)
+($int=t1 E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r t1)
+  (RN4.Sem RN4_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_07() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_07 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_07 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_07 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_08.sem
new file mode 100644
index 0000000..01ba263
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_08.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r E)
+($int=t1 E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r t1)
+  (RN4.Sem RN4_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_08() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_08 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_08 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_08 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_09.sem
new file mode 100644
index 0000000..3df7d5f
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_09.sem
@@ -0,0 +1,100 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (RN2 0) (RN3 0) (RN4 0) (RN5 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($- RN4 RN5))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r A)
+($int=t1 A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r t1)
+  (RN3.Sem RN3_term_2 r__2 n r t1))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r t1)
+  (RN5.Sem RN5_term_2 r__2 n r t1))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (A.Sem A_term_1 r__1 n r t1))))
+(($int=t1 A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (A.Sem A_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (M.Sem M_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_09() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_09 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_09 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_09 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_10.sem
new file mode 100644
index 0000000..7cea0a7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_10.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A)
+($* A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=t1 E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S.Sem S_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_10() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_10 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_10 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_10 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_11.sem
new file mode 100644
index 0000000..866b873
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no05_piSquare_11.sem
@@ -0,0 +1,104 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVart1 )
+($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=t1 E)
+($int=r E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (t1 Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (t1_r0 Int) (n Int) (r Int) (t1 Int)) Bool))
+
+((match A_term_0
+  (($IVart1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 t1))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r t1)
+  (RN2.Sem RN2_term_2 r__2 n r t1))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r t1)
+  (A.Sem A_term_2 r__2 n r t1))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S2.Sem S2_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (t1_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 t1_r1 n r t1)
+  (S11.Sem S11_term_2 n_r0 r_r0 t1_r0 n_r1 r_r1 t1_r1))))))
+(match S11_term_0
+  ((($int=t1 E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= t1 r__1))
+  (E.Sem E_term_1 r__1 n r t1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= t1 t1_r0))
+  (E.Sem E_term_1 r__1 n r t1))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (t1_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r t1)
+  (S.Sem S_term_2 n_r2 r_r2 t1_r2 n r t1)
+  (Start.Sem Start_term_0 n_r0 r_r0 t1_r0 n_r2 r_r2 t1_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r t1)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= t1 t1_r0)))))))))
+
+
+(synth-fun no05_piSquare_11() Start)
+
+
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_11 n 1 t1 1 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_11 n 4 t1 2 1 4123)))
+(constraint (exists ((t1 Int) (n Int)) (Start.Sem no05_piSquare_11 n 36 t1 3 1 4123)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_01.sem
new file mode 100644
index 0000000..809d22e
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_01.sem
@@ -0,0 +1,86 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_01 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_01 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_01 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_01 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_02.sem
new file mode 100644
index 0000000..e187fc0
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_02.sem
@@ -0,0 +1,80 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_02 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_02 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_02 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_02 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_03.sem
new file mode 100644
index 0000000..905c9f0
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_03.sem
@@ -0,0 +1,82 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_03 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_03 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_03 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_03 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_04.sem
new file mode 100644
index 0000000..d220f74
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_04.sem
@@ -0,0 +1,84 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_04 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_04 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_04 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_04 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_05.sem
new file mode 100644
index 0000000..e06051b
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_05.sem
@@ -0,0 +1,74 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=a A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_05 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_05 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_05 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_05 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_06.sem
new file mode 100644
index 0000000..1807b26
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_06.sem
@@ -0,0 +1,119 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_06 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_06 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_06 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_06 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_07.sem
new file mode 100644
index 0000000..6e75dea
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_07.sem
@@ -0,0 +1,109 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_07 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_07 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_07 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_07 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_08.sem
new file mode 100644
index 0000000..c2e673e
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_08.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_08 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_08 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_08 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_08 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_09.sem
new file mode 100644
index 0000000..b9987ed
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_09.sem
@@ -0,0 +1,96 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (RN2 0) (RN3 0) (RN4 0) (RN5 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($- RN4 RN5))
+(($IInt0 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A)
+($int=a A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_09 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_09 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_09 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_09 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_10.sem
new file mode 100644
index 0000000..5791828
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_10.sem
@@ -0,0 +1,96 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_10 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_10 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_10 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_10 n 25 a 2 1 5)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_11.sem
new file mode 100644
index 0000000..39b2d41
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no06_power_11.sem
@@ -0,0 +1,100 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN2 0) (RN3 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r E)
+($int=a E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no06_power_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_11 n 1 a 0 1 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_11 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_11 n 27 a 3 1 3)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no06_power_115 n 25 a 2 1 )))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_01.sem
new file mode 100644
index 0000000..2bcf469
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_01.sem
@@ -0,0 +1,81 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_01 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_01 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_01 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_02.sem
new file mode 100644
index 0000000..16747f0
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_02.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_02 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_02 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_02 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_03.sem
new file mode 100644
index 0000000..bfd757c
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_03.sem
@@ -0,0 +1,77 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_03 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_03 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_03 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_04.sem
new file mode 100644
index 0000000..01e4a85
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_04.sem
@@ -0,0 +1,79 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_04 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_04 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_04 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_05.sem
new file mode 100644
index 0000000..ca03fc2
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_05.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=a A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_05 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_05 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_05 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_06.sem
new file mode 100644
index 0000000..33a082a
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_06.sem
@@ -0,0 +1,125 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (M1 0) (RN1 0) (RN2 0) (RN5 0) (RN7 0) (RN8 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt0 ))
+(($< M1 RN5))
+(($+ A A)
+($- A A))
+(($- RN7 RN8))
+(($- RN1 RN2))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=a E)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M1.Sem ((M1_term_0 M1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN8.Sem ((RN8_term_0 RN8) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match B_term_0
+  ((($< M1_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (M1.Sem M1_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN7_term_1 RN8_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN7.Sem RN7_term_1 r__1 n r a)
+  (RN8.Sem RN8_term_2 r__2 n r a))))))
+(match M1_term_0
+  ((($- RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN5_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN8_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_06 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_06 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_06 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_07.sem
new file mode 100644
index 0000000..0827399
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_07.sem
@@ -0,0 +1,115 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (M1 0) (RN1 0) (RN2 0) (RN3 0) (RN7 0) (RN8 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< M1 RN1))
+(($- A A))
+(($- RN7 RN8))
+(($- RN2 RN3))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=a E)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M1.Sem ((M1_term_0 M1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN8.Sem ((RN8_term_0 RN8) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< M1_term_1 RN1_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (M1.Sem M1_term_1 r__1 n r a)
+  (RN1.Sem RN1_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN7_term_1 RN8_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN7.Sem RN7_term_1 r__1 n r a)
+  (RN8.Sem RN8_term_2 r__2 n r a))))))
+(match M1_term_0
+  ((($- RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN3_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN7_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN8_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_07 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_07 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_07 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_08.sem
new file mode 100644
index 0000000..e816097
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_08.sem
@@ -0,0 +1,112 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (M1 0) (RN1 0) (RN2 0) (RN3 0) (RN7 0) (RN8 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< M1 RN1))
+(($- A A))
+(($- RN7 RN8))
+(($- RN2 RN3))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=a E)
+($int=r E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M1.Sem ((M1_term_0 M1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN8.Sem ((RN8_term_0 RN8) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< M1_term_1 RN1_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (M1.Sem M1_term_1 r__1 n r a)
+  (RN1.Sem RN1_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN7_term_1 RN8_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN7.Sem RN7_term_1 r__1 n r a)
+  (RN8.Sem RN8_term_2 r__2 n r a))))))
+(match M1_term_0
+  ((($- RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN3_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN7_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN8_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_08 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_08 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_08 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_09.sem
new file mode 100644
index 0000000..65915e6
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_09.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (M1 0) (RN2 0) (RN3 0) (RN4 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< M1 RN2))
+(($- RN3 RN4))
+(($- RN6 RN7))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A)
+($int=a A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M1.Sem ((M1_term_0 M1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< M1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (M1.Sem M1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match M1_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN6_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_09 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_09 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_09 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_10.sem
new file mode 100644
index 0000000..de24834
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_10.sem
@@ -0,0 +1,91 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN4 0) (RN5 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN4 RN5))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IVara ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_10 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_10 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_10 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_11.sem
new file mode 100644
index 0000000..6be4afb
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no07_suma2n_11.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN3 0) (RN4 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN3 RN4))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IVara ))
+(($seq S1 S2))
+(($int=r E)
+($int=a E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no07_suma2n_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_11 n 6 a 3 0 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_11 n 5 a 3 0 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no07_suma2n_11 n 12 a 5 0 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_01.sem
new file mode 100644
index 0000000..a41a7b4
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_01.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_01 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_01 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_01 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_02.sem
new file mode 100644
index 0000000..5391265
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_02.sem
@@ -0,0 +1,79 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_02 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_02 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_02 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_03.sem
new file mode 100644
index 0000000..c5debc3
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_03.sem
@@ -0,0 +1,75 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_03 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_03 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_03 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_04.sem
new file mode 100644
index 0000000..bb56048
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_04.sem
@@ -0,0 +1,83 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_04 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_04 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_04 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_05.sem
new file mode 100644
index 0000000..43891cc
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_05.sem
@@ -0,0 +1,73 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=a A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_05 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_05 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_05 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_06.sem
new file mode 100644
index 0000000..03c8c05
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_06.sem
@@ -0,0 +1,118 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (P 0) (RN3 0) (RN4 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN3 RN4))
+(($* A A)
+($+ A A)
+($- A A))
+(($+ RN6 RN7))
+(($IVara ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=n E)
+($seq S1 S1)
+($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match P_term_0
+  ((($+ RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN3_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_06 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_06 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_06 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_07.sem
new file mode 100644
index 0000000..bba117c
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_07.sem
@@ -0,0 +1,108 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (P 0) (RN3 0) (RN4 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN3 RN4))
+(($+ A A)
+($- A A))
+(($+ RN6 RN7))
+(($IVara ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=n E)
+($seq S1 S1)
+($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match P_term_0
+  ((($+ RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN3_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_07 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_07 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_07 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_08.sem
new file mode 100644
index 0000000..929b7fa
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_08.sem
@@ -0,0 +1,105 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (P 0) (RN3 0) (RN4 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN3 RN4))
+(($+ A A)
+($- A A))
+(($+ RN6 RN7))
+(($IVara ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=n E)
+($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match P_term_0
+  ((($+ RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN3_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_08 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_08 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_08 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_09.sem
new file mode 100644
index 0000000..4ad1036
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_09.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (P 0) (RN3 0) (RN4 0) (RN5 0) (RN6 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN3 RN4))
+(($+ RN5 RN6))
+(($IVara ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($seq S1 S2))
+(($int=r A)
+($int=n A))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match P_term_0
+  ((($+ RN5_term_1 RN6_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN5.Sem RN5_term_1 r__1 n r a)
+  (RN6.Sem RN6_term_2 r__2 n r a))))))
+(match RN3_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN6_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_09 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_09 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_09 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_10.sem
new file mode 100644
index 0000000..22b0dc3
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_10.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN4 0) (RN5 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN4 RN5))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IVara ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_10 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_10 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_10 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_11.sem
new file mode 100644
index 0000000..d774806
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no08_proda2n_11.sem
@@ -0,0 +1,99 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN4 0) (RN5 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN4 RN5))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IVara ))
+(($seq S1 S2))
+(($int=n E)
+($int=r E))
+(($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no08_proda2n_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_11 n 2 a 2 2 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_11 n 24 a 4 4 2)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no08_proda2n_11 n 60 a 5 5 3)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_01.sem
new file mode 100644
index 0000000..679c115
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_01.sem
@@ -0,0 +1,85 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 )
+($IInt3 ))
+(($< A A))
+(($- A A)
+($+ A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_01 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_01 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_01 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_01 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_02.sem
new file mode 100644
index 0000000..70396d7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_02.sem
@@ -0,0 +1,76 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_02 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_02 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_02 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_02 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_03.sem
new file mode 100644
index 0000000..83e849e
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_03.sem
@@ -0,0 +1,81 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IInt3 )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_03 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_03 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_03 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_03 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_04.sem
new file mode 100644
index 0000000..53de77f
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_04.sem
@@ -0,0 +1,94 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (S11 0) (S12 0) (Start 0))
+((($IInt0 )
+($IVarr )
+($IVarn )
+($IInt1 )
+($IVara )
+($IInt3 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S1 S12))
+(($seq S11 S11))
+(($int=r E)
+($int=a E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S12.Sem ((S12_term_0 S12) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S12_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S12.Sem S12_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 a_r1 n r a)
+  (S11.Sem S11_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S11_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S12_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_04 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_04 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_04 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_04 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_05.sem
new file mode 100644
index 0000000..0912b7c
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_05.sem
@@ -0,0 +1,84 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (S11 0) (S12 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IInt3 )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S12))
+(($seq S11 S11))
+(($int=r A)
+($int=a A))
+(($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S12.Sem ((S12_term_0 S12) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S12_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S12.Sem S12_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 a_r1 n r a)
+  (S11.Sem S11_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S11_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S12_term_0
+  ((($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_05 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_05 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_05 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_05 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_06.sem
new file mode 100644
index 0000000..1bc9c50
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_06.sem
@@ -0,0 +1,118 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IInt3 )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A)
+($+ A A))
+(($- RN6 RN7))
+(($IInt2 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_06 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_06 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_06 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_06 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_07.sem
new file mode 100644
index 0000000..2037fc7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_07.sem
@@ -0,0 +1,105 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN1 0) (RN2 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($- A A))
+(($- RN6 RN7))
+(($IInt2 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S1 S1)
+($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_07 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_07 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_07 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_07 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_08.sem
new file mode 100644
index 0000000..9d63def
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_08.sem
@@ -0,0 +1,107 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (M 0) (RN2 0) (RN3 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVarr )
+($IVara )
+($IVarn ))
+(($< RN2 RN3))
+(($- A A))
+(($- RN6 RN7))
+(($IInt2 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r E)
+($int=a E))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN2_term_0
+  (($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 a_r1 n r a)
+  (S11.Sem S11_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S11_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_08 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_08 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_08 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_08 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_09.sem
new file mode 100644
index 0000000..7fce3ca
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_09.sem
@@ -0,0 +1,101 @@
+(declare-term-types
+((A 0) (B 0) (M 0) (RN2 0) (RN3 0) (RN6 0) (RN7 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< RN2 RN3))
+(($- RN6 RN7))
+(($IInt2 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r A)
+($int=a A))
+(($int=n M))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN6.Sem ((RN6_term_0 RN6) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN7.Sem ((RN7_term_0 RN7) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN2_term_1 RN3_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN2.Sem RN2_term_1 r__1 n r a)
+  (RN3.Sem RN3_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN6_term_1 RN7_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN6.Sem RN6_term_1 r__1 n r a)
+  (RN7.Sem RN7_term_2 r__2 n r a))))))
+(match RN2_term_0
+  (($IInt2 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 2))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN6_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN7_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 a_r1 n r a)
+  (S11.Sem S11_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S11_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_09 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_09 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_09 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_09 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_10.sem
new file mode 100644
index 0000000..2dd154e
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_10.sem
@@ -0,0 +1,95 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt3 ))
+(($< RN1 RN2))
+(($- A A)
+($+ A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_10 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_10 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_10 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_10 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_11.sem
new file mode 100644
index 0000000..c99c832
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no13_fibonacci_11.sem
@@ -0,0 +1,104 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (S1 0) (S11 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVarr )
+($IVarn )
+($IVara )
+($IInt3 ))
+(($< RN1 RN2))
+(($- A A)
+($+ A A))
+(($IVarn ))
+(($IInt1 ))
+(($seq S1 S2))
+(($seq S11 S11))
+(($int=r E)
+($int=a E))
+(($int=n E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S11.Sem ((S11_term_0 S11) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IInt3 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 3))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($seq S11_term_1 S11_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S11.Sem S11_term_1 n_r1 r_r1 a_r1 n r a)
+  (S11.Sem S11_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S11_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no13_fibonacci_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_11 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_11 n 1 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_11 n 2 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no13_fibonacci_11 n 21 a 8 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_01.sem
new file mode 100644
index 0000000..156dedc
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_01.sem
@@ -0,0 +1,92 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_01 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_01 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_01 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_01 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_02.sem
new file mode 100644
index 0000000..a3121f7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_02.sem
@@ -0,0 +1,86 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_02 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_02 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_02 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_02 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_03.sem
new file mode 100644
index 0000000..5da5745
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_03.sem
@@ -0,0 +1,78 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_03 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_03 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_03 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_03 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_04.sem
new file mode 100644
index 0000000..cd4aa53
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_04.sem
@@ -0,0 +1,80 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_04 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_04 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_04 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_04 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_05.sem
new file mode 100644
index 0000000..3f4b3c1
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_05.sem
@@ -0,0 +1,74 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=a A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_05 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_05 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_05 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_05 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_06.sem
new file mode 100644
index 0000000..603a984
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_06.sem
@@ -0,0 +1,177 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN4 0) (RN5 0) (RN9 0) (S 0) (S1 0) (S2 0) (S3 0) (S31 0) (Start 0))
+((($IInt1 )
+($IVarr )
+($IVarn )
+($IInt0 )
+($IVara ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($+ A A)
+($- A A))
+(($- RN4 RN5))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($while B2 S3)
+($int=n M)
+($seq S2 S2))
+(($seq S31 S31))
+(($seq S31 S31)
+($int=r E)
+($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))
+(($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))
+(($seq S2_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S2.Sem S2_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S3_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_06 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_06 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_06 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_06 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_07.sem
new file mode 100644
index 0000000..8333c15
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_07.sem
@@ -0,0 +1,169 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN3 0) (RN4 0) (RN9 0) (S 0) (S1 0) (S2 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVarr )
+($IVarn )
+($IVara ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($while B2 S3)
+($seq S2 S2)
+($int=n M))
+(($seq S31 S32))
+(($seq S31 S31)
+($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))
+(($seq S2_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S2.Sem S2_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_07 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_07 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_07 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_07 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_08.sem
new file mode 100644
index 0000000..9c69c47
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_08.sem
@@ -0,0 +1,173 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN3 0) (RN4 0) (RN9 0) (S 0) (S1 0) (S2 0) (S21 0) (S22 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVarn )
+($IVara )
+($IVarr ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($seq S21 S22))
+(($while B2 S3))
+(($int=n M))
+(($seq S31 S32)
+($seq S31 S32))
+(($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S21.Sem ((S21_term_0 S21) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S22.Sem ((S22_term_0 S22) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($seq S21_term_1 S22_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S21.Sem S21_term_1 n_r1 r_r1 a_r1 n r a)
+  (S22.Sem S22_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S21_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S21.Sem S21_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match S22_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_08 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_08 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_08 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_08 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_09.sem
new file mode 100644
index 0000000..cd7c3b4
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_09.sem
@@ -0,0 +1,167 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN4 0) (RN5 0) (RN9 0) (S 0) (S1 0) (S2 0) (S21 0) (S22 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVara )
+($IVarn )
+($IVarr ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- RN4 RN5))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($seq S21 S22))
+(($while B2 S3))
+(($int=n M))
+(($seq S31 S32)
+($seq S31 S32))
+(($int=r A))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S21.Sem ((S21_term_0 S21) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S22.Sem ((S22_term_0 S22) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($seq S21_term_1 S22_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S21.Sem S21_term_1 n_r1 r_r1 a_r1 n r a)
+  (S22.Sem S22_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S21_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S21.Sem S21_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match S22_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_09 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_09 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_09 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_09 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_10.sem
new file mode 100644
index 0000000..ed15d89
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_10.sem
@@ -0,0 +1,102 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_10 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_10 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_10 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_10 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_11.sem
new file mode 100644
index 0000000..6776a87
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no14_nestedsum_11.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S1 S2))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S1))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B_term_1 S1_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S1.Sem S1_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no14_nestedsum_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_11 n 1 a 1 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_11 n 4 a 2 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_11 n 10 a 3 0 0)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no14_nestedsum_11 n 20 a 4 0 0)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_01.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_01.sem
new file mode 100644
index 0000000..ea68f71
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_01.sem
@@ -0,0 +1,96 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_01() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_01 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_01 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_01 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_01 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_02.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_02.sem
new file mode 100644
index 0000000..86094c0
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_02.sem
@@ -0,0 +1,90 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IVara )
+($IVarr )
+($IVarn ))
+(($< A A))
+(($* A A)
+($+ A A)
+($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_02() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_02 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_02 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_02 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_02 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_03.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_03.sem
new file mode 100644
index 0000000..a9bcca7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_03.sem
@@ -0,0 +1,78 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_03() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_03 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_03 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_03 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_03 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_04.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_04.sem
new file mode 100644
index 0000000..17d3a57
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_04.sem
@@ -0,0 +1,80 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($- A A))
+(($seq S1 S1))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_04() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_04 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_04 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_04 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_04 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_05.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_05.sem
new file mode 100644
index 0000000..21d1dfe
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_05.sem
@@ -0,0 +1,74 @@
+(declare-term-types
+((A 0) (B 0) (S 0) (S1 0) (Start 0))
+((($IInt0 )
+($IVara )
+($IVarr )
+($IVarn )
+($IInt1 ))
+(($< A A))
+(($seq S1 S1))
+(($int=r A)
+($int=a A)
+($int=n A))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match B_term_0
+  ((($< A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match S_term_0
+  ((($seq S1_term_1 S1_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S1.Sem S1_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=a A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (A.Sem A_term_1 r__1 n r a))))
+(($int=n A_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_05() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_05 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_05 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_05 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_05 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_06.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_06.sem
new file mode 100644
index 0000000..566c927
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_06.sem
@@ -0,0 +1,181 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN4 0) (RN5 0) (RN9 0) (S 0) (S1 0) (S2 0) (S3 0) (S31 0) (Start 0))
+((($IInt1 )
+($IVarr )
+($IVarn )
+($IInt0 )
+($IVara ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($* A A)
+($+ A A)
+($- A A))
+(($- RN4 RN5))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($while B2 S3)
+($int=n M)
+($seq S2 S2))
+(($seq S31 S31))
+(($seq S31 S31)
+($int=r E)
+($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))
+(($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))
+(($seq S2_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S2.Sem S2_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S3_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_06() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_06 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_06 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_06 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_06 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_07.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_07.sem
new file mode 100644
index 0000000..877f831
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_07.sem
@@ -0,0 +1,169 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN3 0) (RN4 0) (RN9 0) (S 0) (S1 0) (S2 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVarr )
+($IVarn )
+($IVara ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($while B2 S3)
+($seq S2 S2)
+($int=n M))
+(($seq S31 S32))
+(($seq S31 S31)
+($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))
+(($seq S2_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S2.Sem S2_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($seq S31_term_1 S31_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S31.Sem S31_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_07() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_07 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_07 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_07 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_07 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_08.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_08.sem
new file mode 100644
index 0000000..d880ca7
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_08.sem
@@ -0,0 +1,173 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (E 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN3 0) (RN4 0) (RN9 0) (S 0) (S1 0) (S2 0) (S21 0) (S22 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVarn )
+($IVara )
+($IVarr ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- A A))
+(($- RN3 RN4))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($seq S21 S22))
+(($while B2 S3))
+(($int=n M))
+(($seq S31 S32)
+($seq S31 S32))
+(($int=r E))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN3.Sem ((RN3_term_0 RN3) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S21.Sem ((S21_term_0 S21) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S22.Sem ((S22_term_0 S22) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN3_term_1 RN4_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN3.Sem RN3_term_1 r__1 n r a)
+  (RN4.Sem RN4_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN3_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($seq S21_term_1 S22_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S21.Sem S21_term_1 n_r1 r_r1 a_r1 n r a)
+  (S22.Sem S22_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S21_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S21.Sem S21_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match S22_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_08() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_08 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_08 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_08 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_08 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_09.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_09.sem
new file mode 100644
index 0000000..c783c3a
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_09.sem
@@ -0,0 +1,167 @@
+(declare-term-types
+((A 0) (B 0) (B2 0) (M 0) (O 0) (P 0) (RN1 0) (RN10 0) (RN11 0) (RN12 0) (RN2 0) (RN4 0) (RN5 0) (RN9 0) (S 0) (S1 0) (S2 0) (S21 0) (S22 0) (S3 0) (S31 0) (S32 0) (Start 0))
+((($IVara )
+($IVarn )
+($IVarr ))
+(($< RN1 RN2))
+(($< RN9 RN10))
+(($- RN4 RN5))
+(($IInt0 ))
+(($+ RN11 RN12))
+(($IInt0 ))
+(($IVarn ))
+(($IVara ))
+(($IInt1 ))
+(($IVarn ))
+(($IVarn ))
+(($IInt1 ))
+(($IVara ))
+(($seq S1 S2))
+(($int=a O))
+(($seq S21 S22))
+(($while B2 S3))
+(($int=n M))
+(($seq S31 S32)
+($seq S31 S32))
+(($int=r A))
+(($int=a P))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(B2.Sem ((B2_term_0 B2) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(M.Sem ((M_term_0 M) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(O.Sem ((O_term_0 O) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(P.Sem ((P_term_0 P) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN10.Sem ((RN10_term_0 RN10) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN11.Sem ((RN11_term_0 RN11) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN12.Sem ((RN12_term_0 RN12) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN4.Sem ((RN4_term_0 RN4) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN5.Sem ((RN5_term_0 RN5) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN9.Sem ((RN9_term_0 RN9) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S21.Sem ((S21_term_0 S21) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S22.Sem ((S22_term_0 S22) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S3.Sem ((S3_term_0 S3) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S31.Sem ((S31_term_0 S31) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S32.Sem ((S32_term_0 S32) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match B2_term_0
+  ((($< RN9_term_1 RN10_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN9.Sem RN9_term_1 r__1 n r a)
+  (RN10.Sem RN10_term_2 r__2 n r a))))))
+(match M_term_0
+  ((($- RN4_term_1 RN5_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (RN4.Sem RN4_term_1 r__1 n r a)
+  (RN5.Sem RN5_term_2 r__2 n r a))))))
+(match O_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match P_term_0
+  ((($+ RN11_term_1 RN12_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (RN11.Sem RN11_term_1 r__1 n r a)
+  (RN12.Sem RN12_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match RN10_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN11_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match RN12_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN2_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN4_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN5_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))))
+(match RN9_term_0
+  (($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=a O_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (O.Sem O_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($seq S21_term_1 S22_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S21.Sem S21_term_1 n_r1 r_r1 a_r1 n r a)
+  (S22.Sem S22_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S21_term_0
+  ((($while B2_term_1 S3_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B2.Sem B2_term_1 r__1 n r a)
+  (S3.Sem S3_term_2 n_r2 r_r2 a_r2 n r a)
+  (S21.Sem S21_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B2.Sem B2_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match S22_term_0
+  ((($int=n M_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (M.Sem M_term_1 r__1 n r a))))))
+(match S3_term_0
+  ((($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($seq S31_term_1 S32_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S31.Sem S31_term_1 n_r1 r_r1 a_r1 n r a)
+  (S32.Sem S32_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S31_term_0
+  ((($int=r A_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (A.Sem A_term_1 r__1 n r a))))))
+(match S32_term_0
+  ((($int=a P_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (P.Sem P_term_1 r__1 n r a))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_09() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_09 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_09 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_09 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_09 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_10.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_10.sem
new file mode 100644
index 0000000..555cf71
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_10.sem
@@ -0,0 +1,106 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S S)
+($int=r E)
+($int=n E)
+($int=a E)
+($while B S))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S_term_1 S_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S.Sem S_term_1 n_r1 r_r1 a_r1 n r a)
+  (S.Sem S_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))
+(($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (S.Sem S_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_10() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_10 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_10 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_10 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_10 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_11.sem b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_11.sem
new file mode 100644
index 0000000..cf80709
--- /dev/null
+++ b/benchmarks/messy/simpl_no_array/correct_input_output/no15_nestedprod_11.sem
@@ -0,0 +1,110 @@
+(declare-term-types
+((A 0) (B 0) (E 0) (RN1 0) (RN2 0) (S 0) (S1 0) (S2 0) (Start 0))
+((($IInt1 )
+($IInt0 )
+($IVara )
+($IVarr )
+($IVarn ))
+(($< RN1 RN2))
+(($* A A)
+($+ A A)
+($- A A))
+(($IVarn ))
+(($IInt0 ))
+(($seq S1 S2))
+(($int=n E)
+($int=r E)
+($int=a E))
+(($while B S1))
+(($while B S))))
+
+
+(define-funs-rec
+((A.Sem ((A_term_0 A) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(B.Sem ((B_term_0 B) (r__0 Bool) (n Int) (r Int) (a Int)) Bool)
+(E.Sem ((E_term_0 E) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN1.Sem ((RN1_term_0 RN1) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(RN2.Sem ((RN2_term_0 RN2) (r__0 Int) (n Int) (r Int) (a Int)) Bool)
+(S.Sem ((S_term_0 S) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S1.Sem ((S1_term_0 S1) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(S2.Sem ((S2_term_0 S2) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool)
+(Start.Sem ((Start_term_0 Start) (n_r0 Int) (r_r0 Int) (a_r0 Int) (n Int) (r Int) (a Int)) Bool))
+
+((match A_term_0
+  (($IInt1 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 1))))
+($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))
+($IVara (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 a))))
+($IVarr (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 r))))
+($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match B_term_0
+  ((($< RN1_term_1 RN2_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (< r__1 r__2))
+  (RN1.Sem RN1_term_1 r__1 n r a)
+  (RN2.Sem RN2_term_2 r__2 n r a))))))
+(match E_term_0
+  ((($* A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (* r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($+ A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (+ r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))
+(($- A_term_1 A_term_2) (exists ((r__1 Int) (r__2 Int)) (and (= r__0 (- r__1 r__2))
+  (A.Sem A_term_1 r__1 n r a)
+  (A.Sem A_term_2 r__2 n r a))))))
+(match RN1_term_0
+  (($IVarn (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 n))))))
+(match RN2_term_0
+  (($IInt0 (exists ((r__1 Int)) (and (= r__0 r__1)
+  (= r__1 0))))))
+(match S_term_0
+  ((($seq S1_term_1 S2_term_2) (exists ((n_r1 Int) (r_r1 Int) (a_r1 Int)) (and (S1.Sem S1_term_1 n_r1 r_r1 a_r1 n r a)
+  (S2.Sem S2_term_2 n_r0 r_r0 a_r0 n_r1 r_r1 a_r1))))))
+(match S1_term_0
+  ((($int=n E_term_1) (exists ((r__1 Int)) (and (and (= n r__1)
+  (= r r_r0)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=r E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r__1)
+  (= a a_r0))
+  (E.Sem E_term_1 r__1 n r a))))
+(($int=a E_term_1) (exists ((r__1 Int)) (and (and (= n n_r0)
+  (= r r_r0)
+  (= a r__1))
+  (E.Sem E_term_1 r__1 n r a))))))
+(match S2_term_0
+  ((($while B_term_1 S1_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S1.Sem S1_term_2 n_r2 r_r2 a_r2 n r a)
+  (S2.Sem S2_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))
+(match Start_term_0
+  ((($while B_term_1 S_term_2) (exists ((r__1 Bool) (n_r2 Int) (r_r2 Int) (a_r2 Int)) (and r__1
+  (B.Sem B_term_1 r__1 n r a)
+  (S.Sem S_term_2 n_r2 r_r2 a_r2 n r a)
+  (Start.Sem Start_term_0 n_r0 r_r0 a_r0 n_r2 r_r2 a_r2)))
+(exists ((r__1 Bool)) (and (not r__1)
+  (B.Sem B_term_1 r__1 n r a)
+  (and (= n n_r0)
+  (= r r_r0)
+  (= a a_r0)))))))))
+
+
+(synth-fun no15_nestedprod_11() Start)
+
+
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_11 n 1 a 1 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_11 n 2 a 2 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_11 n 12 a 3 1 1)))
+(constraint (exists ((a Int) (n Int)) (Start.Sem no15_nestedprod_11 n 288 a 4 1 1)))
+
+(check-synth)
\ No newline at end of file
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_01.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_01.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_01.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_01.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_02.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_02.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_02.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_02.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_03.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_03.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_03.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_03.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_04.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_04.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_04.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_04.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_05.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_05.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_05.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_05.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_06.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_06.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_06.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_06.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_07.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_07.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_07.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_07.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_08.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_08.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_08.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_08.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_09.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_09.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_09.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_09.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_10.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_10.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_10.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_10.sem
diff --git a/benchmarks/messy/simpl_no_array/no01_factorialTest_11.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_11.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no01_factorialTest_11.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no01_factorialTest_11.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_01.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_01.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_01.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_01.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_02.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_02.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_02.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_02.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_03.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_03.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_03.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_03.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_04.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_04.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_04.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_04.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_05.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_05.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_05.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_05.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_06.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_06.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_06.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_06.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_07.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_07.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_07.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_07.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_08.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_08.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_08.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_08.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_09.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_09.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_09.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_09.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_10.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_10.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_10.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_10.sem
diff --git a/benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_11.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_11.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no02_doubleFactorialTest_11.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no02_doubleFactorialTest_11.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_01.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_01.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_01.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_01.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_02.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_02.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_02.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_02.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_03.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_03.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_03.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_03.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_04.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_04.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_04.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_04.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_05.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_05.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_05.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_05.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_06.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_06.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_06.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_06.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_07.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_07.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_07.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_07.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_08.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_08.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_08.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_08.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_09.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_09.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_09.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_09.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_10.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_10.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_10.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_10.sem
diff --git a/benchmarks/messy/simpl_no_array/no03_sigmaTest_11.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_11.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no03_sigmaTest_11.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no03_sigmaTest_11.sem
diff --git a/benchmarks/messy/simpl_no_array/no04_sigmaSquare_01.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_01.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no04_sigmaSquare_01.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_01.sem
diff --git a/benchmarks/messy/simpl_no_array/no04_sigmaSquare_02.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_02.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no04_sigmaSquare_02.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_02.sem
diff --git a/benchmarks/messy/simpl_no_array/no04_sigmaSquare_03.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_03.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no04_sigmaSquare_03.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_03.sem
diff --git a/benchmarks/messy/simpl_no_array/no04_sigmaSquare_04.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_04.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no04_sigmaSquare_04.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_04.sem
diff --git a/benchmarks/messy/simpl_no_array/no04_sigmaSquare_05.sem b/benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_05.sem
similarity index 100%
rename from benchmarks/messy/simpl_no_array/no04_sigmaSquare_05.sem
rename to benchmarks/messy/simpl_no_array/inverted_input_output/no04_sigmaSquare_05.sem
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