/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES 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 0 0 | | 0 1 0 0 0 | | 0 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 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 0 | | 0 0 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 1 | | 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 1 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 | \ / Remains to prove termination of the 43-rule system { 0 2 1 4 -> 0 4 1 2 3 , 0 2 1 4 -> 0 4 1 3 2 , 0 2 1 4 -> 2 0 4 1 4 , 0 2 1 4 -> 5 5 0 4 1 2 , 0 2 1 5 -> 5 0 4 1 2 , 0 2 2 4 -> 0 4 2 2 5 , 0 2 2 4 -> 0 4 2 5 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 2 3 4 -> 2 0 4 1 0 3 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 1 5 1 4 -> 4 5 0 3 1 1 , 0 2 1 4 4 -> 0 4 1 2 4 3 , 0 2 1 4 5 -> 0 4 1 2 5 2 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 4 -> 4 0 4 1 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 0 0 | | 0 0 0 0 0 | | 0 1 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 1 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 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 | \ / 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 1 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 | \ / Remains to prove termination of the 36-rule system { 0 2 1 5 -> 5 0 4 1 2 , 0 2 2 4 -> 0 4 2 2 5 , 0 2 2 4 -> 0 4 2 5 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 2 3 4 -> 2 0 4 1 0 3 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 1 5 1 4 -> 4 5 0 3 1 1 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 1 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 | \ / 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 | \ / 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 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 1 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 35-rule system { 0 2 1 5 -> 5 0 4 1 2 , 0 2 2 4 -> 0 4 2 2 5 , 0 2 2 4 -> 0 4 2 5 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 2 3 4 -> 2 0 4 1 0 3 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 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 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 1 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 | \ / Remains to prove termination of the 33-rule system { 0 2 1 5 -> 5 0 4 1 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 2 3 4 -> 2 0 4 1 0 3 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 | \ / 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 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 | \ / 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 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 1 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 | \ / Remains to prove termination of the 32-rule system { 0 2 1 5 -> 5 0 4 1 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 4 -> 0 4 0 3 1 4 , 0 1 4 3 4 -> 3 0 4 1 5 4 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 | \ / 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 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 | \ / 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 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 1 0 | | 0 0 0 0 0 0 | | 0 1 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 | \ / Remains to prove termination of the 30-rule system { 0 2 1 5 -> 5 0 4 1 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 0 2 5 1 4 -> 0 0 5 4 1 2 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 | \ / 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 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 | \ / 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 | \ / 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 1 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 29-rule system { 0 2 1 5 -> 5 0 4 1 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 1 5 4 -> 5 0 2 0 4 1 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 1 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 1 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 | \ / 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 1 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 0 0 | | 0 0 0 0 0 0 | | 0 1 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 | \ / Remains to prove termination of the 28-rule system { 0 2 1 5 -> 5 0 4 1 2 , 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 0 1 4 5 -> 0 4 1 0 3 5 , 0 1 4 0 2 -> 0 4 1 5 0 2 , 0 1 4 1 5 -> 2 5 0 4 1 1 , 0 1 4 3 5 -> 5 4 5 0 3 1 , 0 1 5 0 2 -> 0 0 4 1 2 5 , 0 2 4 1 5 -> 5 0 4 1 5 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 3 0 1 3 2 -> 0 3 1 0 3 2 , 3 0 2 1 5 -> 5 3 2 0 4 1 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 1 2 -> 0 4 2 0 3 1 , 3 4 0 1 4 -> 0 4 1 5 3 4 , 3 4 0 1 5 -> 0 4 1 5 5 3 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 0 0 | | 0 0 0 0 0 | | 0 0 1 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 1 0 0 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 1 0 | | 0 0 0 0 0 | | 0 0 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 | | 1 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 1 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 | \ / Remains to prove termination of the 16-rule system { 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 0 2 4 3 5 -> 0 4 5 2 5 3 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 0 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 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 | \ / 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 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 1 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 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 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 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 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 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 | \ / Remains to prove termination of the 15-rule system { 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 3 0 4 0 2 -> 0 3 4 0 4 2 , 3 0 4 0 2 -> 0 4 1 2 0 3 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 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 0 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 1 0 0 0 | \ / 3 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 | \ / 4 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 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 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 13-rule system { 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 2 -> 3 1 2 2 5 4 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 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 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 1 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 0 0 0 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 1 | | 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 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 | \ / 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 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 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 | \ / 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 12-rule system { 3 4 0 2 -> 3 0 4 5 2 , 3 4 0 2 -> 3 5 0 4 2 , 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 0 2 4 -> 0 3 4 0 4 2 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 1 | | 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 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 1 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 0 0 0 0 | \ / 4 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 | \ / 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 | \ / Remains to prove termination of the 9-rule system { 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 0 5 1 5 -> 0 4 1 3 5 5 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 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 | \ / 3 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 | \ / 4 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 | \ / 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 1 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / Remains to prove termination of the 8-rule system { 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 1 3 5 -> 4 3 0 3 1 5 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 1 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 | \ / 3 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 1 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 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 | \ / 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 1 0 0 0 0 | \ / Remains to prove termination of the 7-rule system { 3 0 5 1 4 -> 3 0 4 1 1 5 , 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 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 | \ / 3 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 | \ / 4 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 | \ / 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 6-rule system { 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 2 5 , 3 5 2 1 4 -> 3 5 1 0 4 2 } 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 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 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 | \ / 3 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 | \ / 4 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 | \ / 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 | \ / Remains to prove termination of the 5-rule system { 3 2 4 1 5 -> 3 1 4 5 2 5 , 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 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 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 1 | | 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 | \ / 3 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 | \ / 4 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 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 0 | | 0 1 0 0 0 0 | \ / Remains to prove termination of the 4-rule system { 3 4 1 2 4 -> 0 4 1 2 4 3 , 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 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 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 1 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 1 | | 0 0 0 0 0 0 | \ / 3 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 | \ / 4 is interpreted by / \ | 1 0 1 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 | \ / 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 | \ / Remains to prove termination of the 3-rule system { 3 4 3 0 2 -> 3 3 0 4 1 2 , 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 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 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 | \ / 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 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 1 0 0 0 0 | \ / 3 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 1 0 | | 0 0 0 0 0 0 | | 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 1 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 | \ / Remains to prove termination of the 2-rule system { 3 4 5 0 2 -> 0 3 0 4 2 5 , 3 5 0 2 2 -> 0 3 2 5 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 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 | \ / 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 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 1 0 0 0 0 | \ / 3 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 | \ / 4 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 | \ / 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 1-rule system { 3 5 0 2 2 -> 0 3 2 5 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 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 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 1 | | 0 1 0 0 0 0 | \ / 3 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 | \ / 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 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.