/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 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 | \ / 1 is interpreted by / \ | 1 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 1 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / Remains to prove termination of the 22-rule system { 0 2 1 -> 0 4 0 1 4 5 1 5 0 1 , 1 1 3 -> 1 2 1 2 2 2 5 1 4 2 , 0 0 0 3 -> 4 2 4 0 2 5 3 3 4 5 , 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 0 5 2 1 3 -> 2 4 2 5 2 4 3 0 2 4 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 2 1 0 2 1 5 -> 2 5 4 1 3 2 2 5 4 5 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 0 5 3 5 3 1 5 -> 0 1 3 4 0 1 4 5 1 5 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 0 2 0 2 1 0 -> 2 0 2 3 4 2 4 4 4 0 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 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 | \ / 1 is interpreted by / \ | 1 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 1 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 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 | \ / 3 is interpreted by / \ | 1 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 1 0 0 0 0 | \ / Remains to prove termination of the 21-rule system { 0 2 1 -> 0 4 0 1 4 5 1 5 0 1 , 1 1 3 -> 1 2 1 2 2 2 5 1 4 2 , 0 0 0 3 -> 4 2 4 0 2 5 3 3 4 5 , 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 2 1 0 2 1 5 -> 2 5 4 1 3 2 2 5 4 5 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 0 5 3 5 3 1 5 -> 0 1 3 4 0 1 4 5 1 5 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 0 2 0 2 1 0 -> 2 0 2 3 4 2 4 4 4 0 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 1 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 | \ / 2 is interpreted by / \ | 1 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 | \ / 1 is interpreted by / \ | 1 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 1 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 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 1 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 | \ / 3 is interpreted by / \ | 1 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 1 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 1 0 | \ / Remains to prove termination of the 20-rule system { 0 2 1 -> 0 4 0 1 4 5 1 5 0 1 , 1 1 3 -> 1 2 1 2 2 2 5 1 4 2 , 0 0 0 3 -> 4 2 4 0 2 5 3 3 4 5 , 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 2 1 0 2 1 5 -> 2 5 4 1 3 2 2 5 4 5 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 0 2 0 2 1 0 -> 2 0 2 3 4 2 4 4 4 0 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 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 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / Remains to prove termination of the 19-rule system { 0 2 1 -> 0 4 0 1 4 5 1 5 0 1 , 1 1 3 -> 1 2 1 2 2 2 5 1 4 2 , 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 2 1 0 2 1 5 -> 2 5 4 1 3 2 2 5 4 5 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 0 2 0 2 1 0 -> 2 0 2 3 4 2 4 4 4 0 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 is interpreted by / \ | 1 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 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 1 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 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 | \ / 5 is interpreted by / \ | 1 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 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 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 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 16-rule system { 1 1 3 -> 1 2 1 2 2 2 5 1 4 2 , 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 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 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 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 1 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 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 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 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 1 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 | \ / 3 is interpreted by / \ | 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 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 | \ / Remains to prove termination of the 15-rule system { 1 0 2 3 -> 1 1 2 5 4 1 2 4 3 2 , 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 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 | \ / 3 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / Remains to prove termination of the 14-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 1 5 2 4 2 1 1 -> 4 4 1 4 1 4 3 1 0 3 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 1 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 | \ / 2 is interpreted by / \ | 1 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 1 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 | \ / 1 is interpreted by / \ | 1 0 1 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 1 | | 0 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 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 | \ / 5 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 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 | \ / Remains to prove termination of the 13-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 2 4 5 5 1 3 5 -> 2 1 2 1 4 4 4 3 4 4 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 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 | \ / 2 is interpreted by / \ | 1 0 1 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 | \ / 1 is interpreted by / \ | 1 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 1 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 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 1 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 1 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 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 1 | | 0 0 0 0 0 0 1 0 | \ / Remains to prove termination of the 12-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 3 0 0 5 5 2 1 -> 0 2 4 3 2 3 2 1 0 3 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 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 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 | \ / 2 is interpreted by / \ | 1 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 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 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 1 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 | \ / 3 is interpreted by / \ | 1 0 1 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 | \ / Remains to prove termination of the 11-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 , 3 1 5 2 3 0 5 -> 5 3 4 0 4 5 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 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 1 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 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 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 | \ / 1 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 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 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 1 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 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 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / Remains to prove termination of the 10-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 0 3 4 5 3 -> 2 0 2 5 1 2 4 4 5 5 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 1 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 | \ / 2 is interpreted by / \ | 1 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 | \ / 1 is interpreted by / \ | 1 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 1 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 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 | \ / 5 is interpreted by / \ | 1 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 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 1 0 0 0 0 | \ / Remains to prove termination of the 9-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 0 5 2 2 2 0 -> 2 5 4 3 0 2 5 1 2 1 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 2 is interpreted by / \ | 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 1 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | \ / 1 is interpreted by / \ | 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 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 | \ / 3 is interpreted by / \ | 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 | \ / Remains to prove termination of the 8-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 2 0 5 3 0 2 -> 2 5 3 5 1 4 5 0 0 2 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 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 1 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 1 is interpreted by / \ | 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 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 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 7-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 2 0 0 5 2 0 -> 4 0 4 2 1 4 4 4 0 1 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 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 1 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | \ / 1 is interpreted by / \ | 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 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 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 | \ / Remains to prove termination of the 6-rule system { 1 3 5 3 -> 3 5 4 5 2 4 3 2 5 4 , 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 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 | \ / 2 is interpreted by / \ | 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 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / Remains to prove termination of the 5-rule system { 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 1 5 1 4 4 3 -> 1 0 3 4 4 1 0 2 5 5 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 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 | \ / 2 is interpreted by / \ | 1 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 | \ / 1 is interpreted by / \ | 1 0 1 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 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 | \ / 4 is interpreted by / \ | 1 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 1 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 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 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 | \ / 3 is interpreted by / \ | 1 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 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 4-rule system { 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 5 1 5 1 0 2 -> 4 5 0 0 4 3 1 1 0 4 , 0 5 2 2 2 1 0 -> 0 3 2 3 1 4 1 0 1 0 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 2-rule system { 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 , 1 3 2 3 0 5 3 -> 1 4 0 1 5 4 0 3 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / Remains to prove termination of the 1-rule system { 2 1 3 1 0 -> 0 1 4 5 1 5 5 2 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 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 1 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 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 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 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 | \ / 5 is interpreted by / \ | 1 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 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 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.