/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 10: 5 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 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 1 0 0 | | 0 0 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 | \ / 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 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 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 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 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 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 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 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 1 0 0 0 0 0 1 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / Remains to prove termination of the 53-rule system { 5 4 2 -> 5 5 4 4 3 4 0 1 0 1 , 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 2 5 4 2 4 -> 2 3 2 0 5 0 4 2 0 4 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 0 1 3 5 4 0 -> 5 0 3 4 0 3 2 5 0 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 2 5 4 1 2 -> 3 3 0 0 5 2 4 5 1 2 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 2 4 5 5 4 0 -> 0 2 3 1 3 4 4 4 0 5 , 3 0 4 5 4 2 -> 1 2 3 3 2 0 3 3 4 0 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 0 5 4 0 5 -> 0 0 4 0 4 0 3 1 3 2 , 5 2 5 2 2 4 -> 5 5 0 2 5 1 0 5 2 4 , 5 2 5 4 1 0 -> 5 1 1 5 2 1 0 1 3 2 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 5 4 2 0 4 0 -> 0 1 1 1 1 4 0 2 5 1 , 5 4 2 2 3 0 -> 0 1 1 4 2 1 1 5 1 0 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 2 4 2 4 2 -> 1 4 5 1 2 3 1 2 0 1 , 0 4 2 5 2 2 5 -> 1 4 2 5 3 0 3 1 2 5 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 0 4 5 2 5 4 2 -> 1 4 3 1 1 1 4 2 0 1 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 2 2 5 4 1 4 0 -> 3 1 5 2 3 2 3 2 1 4 , 2 5 4 0 5 5 4 -> 2 0 1 2 0 5 0 4 0 3 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 5 5 4 2 4 0 5 -> 3 4 5 5 2 4 3 0 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 5 4 0 ->= 4 4 5 4 4 0 1 3 2 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 5 4 0 2 2 1 ->= 4 4 2 3 3 4 5 5 0 2 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 2 2 5 4 2 4 ->= 2 4 5 0 3 3 3 2 4 4 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 , 3 0 0 5 4 1 0 ->= 2 1 5 4 3 2 3 3 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 | \ / 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 1 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 1 | | 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 0 | | 0 0 0 0 0 0 0 1 | \ / 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 1 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 | \ / Remains to prove termination of the 52-rule system { 5 4 2 -> 5 5 4 4 3 4 0 1 0 1 , 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 2 5 4 2 4 -> 2 3 2 0 5 0 4 2 0 4 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 0 1 3 5 4 0 -> 5 0 3 4 0 3 2 5 0 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 2 5 4 1 2 -> 3 3 0 0 5 2 4 5 1 2 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 2 4 5 5 4 0 -> 0 2 3 1 3 4 4 4 0 5 , 3 0 4 5 4 2 -> 1 2 3 3 2 0 3 3 4 0 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 0 5 4 0 5 -> 0 0 4 0 4 0 3 1 3 2 , 5 2 5 2 2 4 -> 5 5 0 2 5 1 0 5 2 4 , 5 2 5 4 1 0 -> 5 1 1 5 2 1 0 1 3 2 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 5 4 2 0 4 0 -> 0 1 1 1 1 4 0 2 5 1 , 5 4 2 2 3 0 -> 0 1 1 4 2 1 1 5 1 0 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 2 4 2 4 2 -> 1 4 5 1 2 3 1 2 0 1 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 0 4 5 2 5 4 2 -> 1 4 3 1 1 1 4 2 0 1 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 2 2 5 4 1 4 0 -> 3 1 5 2 3 2 3 2 1 4 , 2 5 4 0 5 5 4 -> 2 0 1 2 0 5 0 4 0 3 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 5 5 4 2 4 0 5 -> 3 4 5 5 2 4 3 0 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 5 4 0 ->= 4 4 5 4 4 0 1 3 2 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 5 4 0 2 2 1 ->= 4 4 2 3 3 4 5 5 0 2 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 2 2 5 4 2 4 ->= 2 4 5 0 3 3 3 2 4 4 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 , 3 0 0 5 4 1 0 ->= 2 1 5 4 3 2 3 3 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 | \ / 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 | \ / 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 1 | | 0 0 0 0 0 1 | \ / 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 | \ / 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 1 0 0 | | 0 0 0 0 0 0 | \ / 1 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 49-rule system { 5 4 2 -> 5 5 4 4 3 4 0 1 0 1 , 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 0 1 3 5 4 0 -> 5 0 3 4 0 3 2 5 0 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 2 5 4 1 2 -> 3 3 0 0 5 2 4 5 1 2 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 2 4 5 5 4 0 -> 0 2 3 1 3 4 4 4 0 5 , 3 0 4 5 4 2 -> 1 2 3 3 2 0 3 3 4 0 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 0 5 4 0 5 -> 0 0 4 0 4 0 3 1 3 2 , 5 2 5 2 2 4 -> 5 5 0 2 5 1 0 5 2 4 , 5 2 5 4 1 0 -> 5 1 1 5 2 1 0 1 3 2 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 5 4 2 0 4 0 -> 0 1 1 1 1 4 0 2 5 1 , 5 4 2 2 3 0 -> 0 1 1 4 2 1 1 5 1 0 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 2 4 2 4 2 -> 1 4 5 1 2 3 1 2 0 1 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 0 4 5 2 5 4 2 -> 1 4 3 1 1 1 4 2 0 1 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 2 2 5 4 1 4 0 -> 3 1 5 2 3 2 3 2 1 4 , 2 5 4 0 5 5 4 -> 2 0 1 2 0 5 0 4 0 3 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 5 4 0 ->= 4 4 5 4 4 0 1 3 2 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 5 4 0 2 2 1 ->= 4 4 2 3 3 4 5 5 0 2 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 , 3 0 0 5 4 1 0 ->= 2 1 5 4 3 2 3 3 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 11: 5 is interpreted by / \ | 1 0 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 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 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 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 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 0 0 0 0 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 | \ / 2 is interpreted by / \ | 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 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 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 | \ / 3 is interpreted by / \ | 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 | | 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 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 0 0 0 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 | | 0 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 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 48-rule system { 5 4 2 -> 5 5 4 4 3 4 0 1 0 1 , 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 0 1 3 5 4 0 -> 5 0 3 4 0 3 2 5 0 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 2 5 4 1 2 -> 3 3 0 0 5 2 4 5 1 2 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 2 4 5 5 4 0 -> 0 2 3 1 3 4 4 4 0 5 , 3 0 4 5 4 2 -> 1 2 3 3 2 0 3 3 4 0 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 0 5 4 0 5 -> 0 0 4 0 4 0 3 1 3 2 , 5 2 5 4 1 0 -> 5 1 1 5 2 1 0 1 3 2 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 5 4 2 0 4 0 -> 0 1 1 1 1 4 0 2 5 1 , 5 4 2 2 3 0 -> 0 1 1 4 2 1 1 5 1 0 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 2 4 2 4 2 -> 1 4 5 1 2 3 1 2 0 1 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 0 4 5 2 5 4 2 -> 1 4 3 1 1 1 4 2 0 1 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 2 2 5 4 1 4 0 -> 3 1 5 2 3 2 3 2 1 4 , 2 5 4 0 5 5 4 -> 2 0 1 2 0 5 0 4 0 3 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 5 4 0 ->= 4 4 5 4 4 0 1 3 2 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 5 4 0 2 2 1 ->= 4 4 2 3 3 4 5 5 0 2 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 , 3 0 0 5 4 1 0 ->= 2 1 5 4 3 2 3 3 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 5 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 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 | \ / 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 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 1 0 0 0 0 1 | | 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 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 | \ / 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 | \ / 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 1 1 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 0 | | 0 0 1 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 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 | \ / Remains to prove termination of the 33-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 2 4 2 4 2 -> 1 4 5 1 2 3 1 2 0 1 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 | \ / 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 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 | \ / 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 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 0 | | 0 0 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 | \ / Remains to prove termination of the 32-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 2 4 0 5 5 4 -> 0 3 1 1 2 0 1 3 4 3 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 1 0 | | 0 0 0 0 0 0 1 | | 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 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 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 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 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 31-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 2 0 4 5 2 1 -> 3 0 3 3 2 5 0 4 3 4 , 4 2 4 1 2 5 -> 3 4 0 5 0 5 1 4 1 5 , 5 3 0 4 2 1 -> 5 2 1 0 2 5 4 4 1 1 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 1 0 4 5 4 3 5 -> 1 2 4 4 3 0 5 3 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 5 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 | | 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 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 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 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 | \ / 2 is interpreted by / \ | 1 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 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 0 0 | | 0 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 | | 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 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 | \ / 1 is interpreted by / \ | 1 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 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 | \ / Remains to prove termination of the 27-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 0 5 4 -> 4 0 4 4 1 3 3 3 5 4 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 0 4 0 5 4 ->= 1 2 4 4 2 1 5 1 0 3 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 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 | \ / 4 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 | \ / 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 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 1 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 | \ / Remains to prove termination of the 25-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 2 2 ->= 0 0 4 5 3 4 4 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 5 is interpreted by / \ | 1 0 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 0 0 | | 0 0 0 0 0 0 1 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 0 | | 0 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 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 | \ / 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 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 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 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 24-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 4 1 2 4 2 2 5 -> 4 2 2 2 0 4 1 0 2 5 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 0 | | 0 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 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 | \ / 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 1 | | 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 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 1 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 | \ / Remains to prove termination of the 23-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 0 5 4 ->= 0 2 3 3 3 5 3 4 3 3 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 2 2 0 5 4 3 ->= 0 5 2 3 2 3 1 1 4 3 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 5 is interpreted by / \ | 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 | \ / 4 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 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 0 | | 0 1 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 1 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 | | 0 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 0 0 0 | | 0 0 0 0 0 0 0 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 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 0 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 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 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 21-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 4 5 3 5 -> 3 4 1 4 4 0 2 1 3 2 , 1 0 4 5 2 -> 1 4 1 0 3 3 1 4 0 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 , 2 4 5 5 5 3 5 ->= 5 4 3 0 0 2 0 0 2 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 1 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 1 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 1 | | 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 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 | \ / Remains to prove termination of the 18-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 5 3 5 3 5 -> 0 5 5 2 4 1 3 2 5 2 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 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 | \ / 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 1 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 1 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 0 0 0 0 | | 0 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 | \ / Remains to prove termination of the 17-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 5 5 3 0 4 3 0 -> 0 1 0 4 0 2 1 1 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 2 3 0 5 ->= 1 0 1 1 3 2 1 5 1 5 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 5 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 | \ / 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 | \ / 2 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 | \ / 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 | \ / 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 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 | \ / Remains to prove termination of the 15-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 5 2 1 5 ->= 0 0 3 3 4 4 2 5 3 2 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 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 | \ / 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 | \ / 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 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 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 | \ / Remains to prove termination of the 14-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 4 0 ->= 4 3 2 5 1 0 2 2 0 1 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 5 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 4 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 0 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 1 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / Remains to prove termination of the 13-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 4 3 0 2 1 5 -> 0 2 0 3 1 5 4 4 2 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 1 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 1 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 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 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 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 | \ / 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 | \ / Remains to prove termination of the 12-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 5 2 3 1 0 4 0 -> 0 2 5 3 4 0 3 5 1 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 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 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 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 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 1 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 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 | \ / Remains to prove termination of the 11-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 , 4 3 0 2 5 ->= 4 3 3 0 3 2 5 5 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 | \ / 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 | \ / 2 is interpreted by / \ | 1 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 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 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 1 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 | \ / Remains to prove termination of the 10-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 4 0 3 5 3 0 -> 5 1 2 4 5 3 4 2 5 0 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 | \ / 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 1 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 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 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 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 | \ / 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 | \ / Remains to prove termination of the 9-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 , 5 3 0 ->= 0 4 4 1 3 0 5 1 5 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 5 is interpreted by / \ | 1 0 1 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 | \ / 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 | \ / 2 is interpreted by / \ | 1 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 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 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 1 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 | \ / Remains to prove termination of the 8-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 1 0 4 3 5 2 -> 1 1 5 3 3 4 4 2 2 2 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 0 4 ->= 0 3 4 1 4 1 5 5 1 4 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 5 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 2 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 0 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 | \ / Remains to prove termination of the 6-rule system { 1 4 2 1 -> 1 0 1 3 2 0 1 4 1 1 , 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 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 | \ / 4 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 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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 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 5-rule system { 0 ->= 0 1 0 0 1 2 2 2 0 1 , 0 0 ->= 0 3 2 4 4 1 0 1 2 1 , 2 4 ->= 3 2 0 1 2 0 1 3 4 4 , 5 0 ->= 5 3 2 5 5 0 2 2 1 0 , 2 2 0 ->= 3 0 2 5 2 5 5 1 0 1 } The system is trivially terminating.