/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 9: 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 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 | \ / 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 1 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 1 | | 0 0 0 1 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 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 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 | \ / 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 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 | \ / 4 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 1 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 25-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 2 -> 5 3 0 1 3 4 3 2 0 5 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 2 2 -> 4 1 2 0 4 4 4 3 5 5 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 2 4 2 2 2 -> 0 4 2 1 1 0 1 1 5 5 , 4 2 2 5 3 -> 3 3 4 0 5 5 5 0 0 1 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 5 5 4 4 2 -> 5 5 0 3 2 0 1 4 1 2 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 2 2 2 3 4 1 -> 0 3 1 3 5 0 4 2 0 3 , 2 2 2 5 0 0 -> 5 5 1 2 3 3 5 0 4 3 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 1 0 3 2 2 -> 4 1 0 5 4 3 1 2 0 5 , 5 2 4 1 2 2 -> 3 5 4 0 5 3 3 3 1 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 2 4 2 2 2 1 4 -> 3 4 4 1 3 1 5 3 2 2 , 5 1 0 2 2 2 0 -> 1 5 4 5 4 4 3 2 1 3 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 2 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 1 | | 0 1 0 0 0 | \ / 5 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 | \ / 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 | \ / 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 | \ / 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 1 1 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 21-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 2 -> 5 3 0 1 3 4 3 2 0 5 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 5 5 4 4 2 -> 5 5 0 3 2 0 1 4 1 2 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 2 2 2 3 4 1 -> 0 3 1 3 5 0 4 2 0 3 , 2 2 2 5 0 0 -> 5 5 1 2 3 3 5 0 4 3 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 1 0 3 2 2 -> 4 1 0 5 4 3 1 2 0 5 , 5 2 4 1 2 2 -> 3 5 4 0 5 3 3 3 1 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 5 1 0 2 2 2 0 -> 1 5 4 5 4 4 3 2 1 3 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 | \ / 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 1 | \ / 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 | \ / 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 | \ / 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 1 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 20-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 2 -> 5 3 0 1 3 4 3 2 0 5 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 2 2 2 3 4 1 -> 0 3 1 3 5 0 4 2 0 3 , 2 2 2 5 0 0 -> 5 5 1 2 3 3 5 0 4 3 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 1 0 3 2 2 -> 4 1 0 5 4 3 1 2 0 5 , 5 2 4 1 2 2 -> 3 5 4 0 5 3 3 3 1 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 5 1 0 2 2 2 0 -> 1 5 4 5 4 4 3 2 1 3 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 2 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 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 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 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 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 0 | | 0 0 0 0 0 0 0 0 | \ / 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 | \ / 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 1 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 1 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 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 { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 1 0 3 2 2 -> 4 1 0 5 4 3 1 2 0 5 , 5 2 4 1 2 2 -> 3 5 4 0 5 3 3 3 1 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 1 1 0 0 0 0 | \ / 5 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 0 0 0 0 0 1 | \ / 1 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 | \ / 0 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 | \ / 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 | \ / Remains to prove termination of the 15-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 2 4 1 2 2 -> 3 5 4 0 5 3 3 3 1 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 2 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 1 0 0 0 0 0 | \ / 5 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 0 0 0 0 0 1 | \ / 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 0 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 | \ / 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 | \ / 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 1 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 14-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 , 5 4 0 0 2 2 3 -> 4 3 3 0 3 4 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 5 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 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 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 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 13-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 0 2 2 3 -> 4 0 1 5 5 0 2 1 2 1 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 1 0 | | 0 0 0 0 0 1 | | 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 | \ / 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 | \ / 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 | \ / 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 0 0 0 0 0 | \ / Remains to prove termination of the 12-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 5 2 5 2 4 -> 2 5 5 1 1 3 5 0 3 1 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 1 | | 0 0 0 0 1 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 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 1 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 11-rule system { 2 2 -> 5 1 1 0 1 3 2 1 1 2 , 2 2 4 -> 5 1 0 1 3 5 5 0 4 1 , 2 2 4 4 -> 2 0 0 1 3 2 1 4 2 4 , 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 3 2 2 4 5 4 -> 3 3 2 0 5 5 3 5 4 1 , 5 3 2 2 4 1 -> 1 2 1 1 5 5 3 3 4 1 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 , 2 2 5 4 5 4 4 -> 5 5 4 0 1 4 5 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 2 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 1 0 | \ / 5 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 0 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 4 is interpreted by / \ | 1 1 0 | | 0 1 0 | | 0 0 0 | \ / Remains to prove termination of the 5-rule system { 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 4 2 3 2 5 -> 1 4 3 0 4 0 3 5 1 2 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 1 | | 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 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 | \ / 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 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 4-rule system { 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 , 0 0 5 4 5 3 4 -> 5 5 1 5 5 2 2 0 0 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 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 1 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 0 | | 0 1 0 0 0 0 0 0 | \ / 0 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 0 0 0 | | 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 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 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 | \ / Remains to prove termination of the 3-rule system { 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 , 2 2 4 5 4 -> 5 0 2 4 0 1 3 5 3 4 , 1 4 4 2 4 4 -> 4 1 0 1 5 4 3 4 1 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 1-rule system { 2 2 4 5 -> 4 3 3 0 4 0 2 5 1 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 2 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 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 0 | | 0 0 0 0 0 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.