/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 0 0 0 | | 0 1 0 0 0 | | 0 0 1 1 1 | | 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 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 | \ / 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 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 1 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | \ / 5 is interpreted by / \ | 1 0 1 1 1 | | 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 43-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 0 -> 2 1 0 3 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 2 1 2 0 -> 2 2 1 0 3 , 2 3 5 5 -> 5 1 0 3 2 5 , 2 5 3 2 -> 5 1 3 2 2 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 2 3 5 -> 0 1 3 4 5 2 , 0 1 2 3 5 -> 0 2 5 1 0 3 , 0 1 2 3 5 -> 1 0 3 0 2 5 , 0 1 2 3 5 -> 5 1 3 0 2 0 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 0 4 5 3 5 -> 5 1 0 3 4 5 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 2 4 3 5 -> 5 1 3 4 2 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 2 3 1 1 2 -> 4 1 2 2 1 3 , 2 3 2 0 5 -> 2 2 1 0 3 5 , 2 3 3 1 5 -> 1 3 5 1 3 2 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 0 1 2 2 -> 4 1 5 2 0 2 , 5 1 4 2 2 -> 5 1 3 2 4 2 , 5 1 4 3 2 -> 4 5 1 3 4 2 , 5 5 4 3 2 -> 5 1 3 4 5 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 1 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 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 | \ / 5 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 | \ / Remains to prove termination of the 42-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 0 -> 2 1 0 3 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 2 1 2 0 -> 2 2 1 0 3 , 2 3 5 5 -> 5 1 0 3 2 5 , 2 5 3 2 -> 5 1 3 2 2 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 2 3 5 -> 0 1 3 4 5 2 , 0 1 2 3 5 -> 0 2 5 1 0 3 , 0 1 2 3 5 -> 1 0 3 0 2 5 , 0 1 2 3 5 -> 5 1 3 0 2 0 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 0 4 5 3 5 -> 5 1 0 3 4 5 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 2 4 3 5 -> 5 1 3 4 2 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 2 3 1 1 2 -> 4 1 2 2 1 3 , 2 3 2 0 5 -> 2 2 1 0 3 5 , 2 3 3 1 5 -> 1 3 5 1 3 2 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 0 1 2 2 -> 4 1 5 2 0 2 , 5 1 4 2 2 -> 5 1 3 2 4 2 , 5 1 4 3 2 -> 4 5 1 3 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 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 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 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 1 1 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 1 1 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 41-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 0 -> 2 1 0 3 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 2 1 2 0 -> 2 2 1 0 3 , 2 3 5 5 -> 5 1 0 3 2 5 , 2 5 3 2 -> 5 1 3 2 2 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 2 3 5 -> 0 1 3 4 5 2 , 0 1 2 3 5 -> 0 2 5 1 0 3 , 0 1 2 3 5 -> 1 0 3 0 2 5 , 0 1 2 3 5 -> 5 1 3 0 2 0 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 0 4 5 3 5 -> 5 1 0 3 4 5 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 2 4 3 5 -> 5 1 3 4 2 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 2 3 1 1 2 -> 4 1 2 2 1 3 , 2 3 2 0 5 -> 2 2 1 0 3 5 , 2 3 3 1 5 -> 1 3 5 1 3 2 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 0 1 2 2 -> 4 1 5 2 0 2 , 5 1 4 2 2 -> 5 1 3 2 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 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 1 1 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 1 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 0 0 0 1 0 | | 0 0 0 0 1 | \ / 5 is interpreted by / \ | 1 0 1 1 1 | | 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 29-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 0 -> 2 1 0 3 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 0 1 2 2 -> 4 1 5 2 0 2 , 5 1 4 2 2 -> 5 1 3 2 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 1 0 | | 0 1 0 0 0 | \ / 1 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 1 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 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / Remains to prove termination of the 28-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 0 1 2 2 -> 4 1 5 2 0 2 , 5 1 4 2 2 -> 5 1 3 2 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 1 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 1 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 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 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 | \ / 5 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 | \ / Remains to prove termination of the 27-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 2 5 -> 5 1 0 3 2 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 2 1 1 5 -> 5 1 3 2 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 2 5 -> 0 1 3 5 1 2 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 1 4 3 5 -> 5 4 4 1 3 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 , 5 1 4 2 2 -> 5 1 3 2 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 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 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 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 1 | | 0 1 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 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 1 1 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | \ / 5 is interpreted by / \ | 1 0 1 1 0 1 | | 0 2 0 0 0 0 | | 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 22-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 1 4 3 5 -> 1 3 5 4 4 2 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 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 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 1 1 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 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 0 | | 0 1 1 1 0 0 | \ / Remains to prove termination of the 21-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 1 0 1 5 -> 1 0 3 2 5 1 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 } 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 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 | \ / 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 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 0 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 | \ / 2 is interpreted by / \ | 1 0 1 1 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 1 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 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 | \ / 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / Remains to prove termination of the 20-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 2 5 -> 2 1 0 3 5 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 } 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 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 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 | \ / 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 | \ / 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 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 | \ / Remains to prove termination of the 19-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 2 3 1 1 2 -> 1 3 2 1 2 0 , 4 2 0 1 2 -> 4 2 2 1 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 1 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 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 1 | | 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 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 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 | \ / Remains to prove termination of the 18-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 1 5 4 -> 1 4 1 0 3 5 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 4 2 0 1 2 -> 4 2 2 1 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 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 1 1 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 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 17-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 2 1 1 5 -> 2 5 1 4 1 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 4 2 0 1 2 -> 4 2 2 1 3 0 } 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 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 | \ / 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 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 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 | \ / 2 is interpreted by / \ | 1 0 1 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 1 0 0 1 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 | | 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 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 | \ / Remains to prove termination of the 16-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 , 4 2 0 1 2 -> 4 2 2 1 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 1 0 | | 0 1 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 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 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 | \ / 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 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 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 15-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 4 2 -> 2 1 3 4 0 , 0 1 4 2 -> 2 4 1 0 3 , 0 1 4 2 -> 0 2 1 0 3 4 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 , 0 1 4 0 2 -> 4 0 1 3 0 2 , 0 1 4 0 2 -> 4 0 2 1 3 0 } 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 1 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 1 1 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 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 0 0 1 | | 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 10-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 0 1 2 -> 0 2 1 1 3 0 , 0 1 1 4 2 -> 4 1 0 3 2 1 } 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 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 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 1 0 0 0 | | 0 0 0 0 0 0 | | 0 1 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 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 1 | | 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 9-rule system { 0 1 2 -> 2 1 0 3 , 0 1 2 -> 2 1 3 0 , 0 1 2 -> 2 1 3 0 4 , 0 1 2 -> 2 1 3 4 0 , 0 1 2 -> 2 1 3 4 0 4 , 0 0 1 2 -> 0 2 1 0 3 , 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 , 0 1 0 1 2 -> 0 2 1 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 1 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / Remains to prove termination of the 2-rule system { 0 1 1 2 -> 1 0 4 1 2 , 0 1 1 2 -> 1 2 1 0 3 } 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 1 0 0 | | 0 0 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 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 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 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 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 0-rule system { } The system is trivially terminating.