/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo the bijection { a ↦ 0, b ↦ 1, c ↦ 2, C ↦ 3, B ↦ 4, A ↦ 5 }, it remains to prove termination of the 12-rule system { 0 1 2 ⟶ 2 1 0 , 3 4 5 ⟶ 5 4 3 , 1 0 3 ⟶ 3 0 1 , 2 5 4 ⟶ 4 5 2 , 5 2 1 ⟶ 1 2 5 , 4 3 0 ⟶ 0 3 4 , 0 5 ⟶ , 5 0 ⟶ , 1 4 ⟶ , 4 1 ⟶ , 2 3 ⟶ , 3 2 ⟶ } The system was reversed. After renaming modulo the bijection { 2 ↦ 0, 1 ↦ 1, 0 ↦ 2, 5 ↦ 3, 4 ↦ 4, 3 ↦ 5 }, it remains to prove termination of the 12-rule system { 0 1 2 ⟶ 2 1 0 , 3 4 5 ⟶ 5 4 3 , 5 2 1 ⟶ 1 2 5 , 4 3 0 ⟶ 0 3 4 , 1 0 3 ⟶ 3 0 1 , 2 5 4 ⟶ 4 5 2 , 3 2 ⟶ , 2 3 ⟶ , 4 1 ⟶ , 1 4 ⟶ , 5 0 ⟶ , 0 5 ⟶ } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 }, it remains to prove termination of the 6-rule system { 0 1 2 ⟶ 2 1 0 , 3 4 5 ⟶ 5 4 3 , 5 2 1 ⟶ 1 2 5 , 4 3 0 ⟶ 0 3 4 , 1 0 3 ⟶ 3 0 1 , 2 5 4 ⟶ 4 5 2 } Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols. After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (2,↓) ↦ 2, (2,↑) ↦ 3, (0,↓) ↦ 4, (1,↑) ↦ 5, (3,↑) ↦ 6, (4,↓) ↦ 7, (5,↓) ↦ 8, (5,↑) ↦ 9, (3,↓) ↦ 10, (4,↑) ↦ 11 }, it remains to prove termination of the 24-rule system { 0 1 2 ⟶ 3 1 4 , 0 1 2 ⟶ 5 4 , 0 1 2 ⟶ 0 , 6 7 8 ⟶ 9 7 10 , 6 7 8 ⟶ 11 10 , 6 7 8 ⟶ 6 , 9 2 1 ⟶ 5 2 8 , 9 2 1 ⟶ 3 8 , 9 2 1 ⟶ 9 , 11 10 4 ⟶ 0 10 7 , 11 10 4 ⟶ 6 7 , 11 10 4 ⟶ 11 , 5 4 10 ⟶ 6 4 1 , 5 4 10 ⟶ 0 1 , 5 4 10 ⟶ 5 , 3 8 7 ⟶ 11 8 2 , 3 8 7 ⟶ 9 2 , 3 8 7 ⟶ 3 , 4 1 2 →= 2 1 4 , 10 7 8 →= 8 7 10 , 8 2 1 →= 1 2 8 , 7 10 4 →= 4 10 7 , 1 4 10 →= 10 4 1 , 2 8 7 →= 7 8 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 6 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 5 ↦ 10, 11 ↦ 11 }, it remains to prove termination of the 12-rule system { 0 1 2 ⟶ 3 1 4 , 5 6 7 ⟶ 8 6 9 , 8 2 1 ⟶ 10 2 7 , 11 9 4 ⟶ 0 9 6 , 10 4 9 ⟶ 5 4 1 , 3 7 6 ⟶ 11 7 2 , 4 1 2 →= 2 1 4 , 9 6 7 →= 7 6 9 , 7 2 1 →= 1 2 7 , 6 9 4 →= 4 9 6 , 1 4 9 →= 9 4 1 , 2 7 6 →= 6 7 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 1 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 1 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 1 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 5 ↦ 0, 6 ↦ 1, 7 ↦ 2, 8 ↦ 3, 9 ↦ 4, 2 ↦ 5, 1 ↦ 6, 10 ↦ 7, 11 ↦ 8, 4 ↦ 9, 0 ↦ 10, 3 ↦ 11 }, it remains to prove termination of the 11-rule system { 0 1 2 ⟶ 3 1 4 , 3 5 6 ⟶ 7 5 2 , 8 4 9 ⟶ 10 4 1 , 7 9 4 ⟶ 0 9 6 , 11 2 1 ⟶ 8 2 5 , 9 6 5 →= 5 6 9 , 4 1 2 →= 2 1 4 , 2 5 6 →= 6 5 2 , 1 4 9 →= 9 4 1 , 6 9 4 →= 4 9 6 , 5 2 1 →= 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 9 ↦ 8 }, it remains to prove termination of the 9-rule system { 0 1 2 ⟶ 3 1 4 , 3 5 6 ⟶ 7 5 2 , 7 8 4 ⟶ 0 8 6 , 8 6 5 →= 5 6 8 , 4 1 2 →= 2 1 4 , 2 5 6 →= 6 5 2 , 1 4 8 →= 8 4 1 , 6 8 4 →= 4 8 6 , 5 2 1 →= 1 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 1 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 1 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 1 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 ⎟ ⎜ 0 1 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎜ 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 3 ↦ 0, 5 ↦ 1, 6 ↦ 2, 7 ↦ 3, 2 ↦ 4, 8 ↦ 5, 4 ↦ 6, 0 ↦ 7, 1 ↦ 8 }, it remains to prove termination of the 8-rule system { 0 1 2 ⟶ 3 1 4 , 3 5 6 ⟶ 7 5 2 , 5 2 1 →= 1 2 5 , 6 8 4 →= 4 8 6 , 4 1 2 →= 2 1 4 , 8 6 5 →= 5 6 8 , 2 5 6 →= 6 5 2 , 1 4 8 →= 8 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 5 ↦ 0, 2 ↦ 1, 1 ↦ 2, 6 ↦ 3, 8 ↦ 4, 4 ↦ 5 }, it remains to prove termination of the 6-rule system { 0 1 2 →= 2 1 0 , 3 4 5 →= 5 4 3 , 5 2 1 →= 1 2 5 , 4 3 0 →= 0 3 4 , 1 0 3 →= 3 0 1 , 2 5 4 →= 4 5 2 } The system is trivially terminating.