/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 }, it remains to prove termination of the 1-rule system { 0 0 1 0 0 0 0 ⟶ 0 0 0 0 0 0 1 0 0 1 } The system was reversed. After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1 }, it remains to prove termination of the 1-rule system { 0 0 0 0 1 0 0 ⟶ 1 0 0 1 0 0 0 0 0 0 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,0) ↦ 2, (0,3) ↦ 3, (1,1) ↦ 4 }, it remains to prove termination of the 6-rule system { 0 0 0 0 1 2 0 0 ⟶ 1 2 0 1 2 0 0 0 0 0 0 , 0 0 0 0 1 2 0 1 ⟶ 1 2 0 1 2 0 0 0 0 0 1 , 0 0 0 0 1 2 0 3 ⟶ 1 2 0 1 2 0 0 0 0 0 3 , 2 0 0 0 1 2 0 0 ⟶ 4 2 0 1 2 0 0 0 0 0 0 , 2 0 0 0 1 2 0 1 ⟶ 4 2 0 1 2 0 0 0 0 0 1 , 2 0 0 0 1 2 0 3 ⟶ 4 2 0 1 2 0 0 0 0 0 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4 }, it remains to prove termination of the 5-rule system { 0 0 0 0 1 2 0 0 ⟶ 1 2 0 1 2 0 0 0 0 0 0 , 0 0 0 0 1 2 0 1 ⟶ 1 2 0 1 2 0 0 0 0 0 1 , 0 0 0 0 1 2 0 3 ⟶ 1 2 0 1 2 0 0 0 0 0 3 , 2 0 0 0 1 2 0 1 ⟶ 4 2 0 1 2 0 0 0 0 0 1 , 2 0 0 0 1 2 0 3 ⟶ 4 2 0 1 2 0 0 0 0 0 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4 }, it remains to prove termination of the 4-rule system { 0 0 0 0 1 2 0 0 ⟶ 1 2 0 1 2 0 0 0 0 0 0 , 0 0 0 0 1 2 0 1 ⟶ 1 2 0 1 2 0 0 0 0 0 1 , 0 0 0 0 1 2 0 3 ⟶ 1 2 0 1 2 0 0 0 0 0 3 , 2 0 0 0 1 2 0 1 ⟶ 4 2 0 1 2 0 0 0 0 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 1 1 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 4 ↦ 3 }, it remains to prove termination of the 3-rule system { 0 0 0 0 1 2 0 0 ⟶ 1 2 0 1 2 0 0 0 0 0 0 , 0 0 0 0 1 2 0 1 ⟶ 1 2 0 1 2 0 0 0 0 0 1 , 2 0 0 0 1 2 0 1 ⟶ 3 2 0 1 2 0 0 0 0 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 }, it remains to prove termination of the 2-rule system { 0 0 0 0 1 2 0 0 ⟶ 1 2 0 1 2 0 0 0 0 0 0 , 0 0 0 0 1 2 0 1 ⟶ 1 2 0 1 2 0 0 0 0 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 3 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 1 0 1 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.