/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 8: 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 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 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 0 0 0 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 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 | \ / Remains to prove termination of the 59-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 1 0 4 0 5 -> 3 5 1 4 4 5 4 5 5 5 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 3 0 5 1 5 -> 2 3 5 2 5 1 2 3 3 5 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 0 5 4 3 1 5 -> 3 4 0 3 2 5 4 3 5 5 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 5 3 4 3 0 3 1 -> 5 5 2 3 5 4 4 1 3 4 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 0 0 5 3 1 5 ->= 2 3 2 5 5 1 1 2 3 5 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 | \ / 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 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 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 58-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 1 0 4 0 5 -> 3 5 1 4 4 5 4 5 5 5 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 3 0 5 1 5 -> 2 3 5 2 5 1 2 3 3 5 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 0 5 4 3 1 5 -> 3 4 0 3 2 5 4 3 5 5 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 0 0 5 3 1 5 ->= 2 3 2 5 5 1 1 2 3 5 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 57-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 1 0 4 0 5 -> 3 5 1 4 4 5 4 5 5 5 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 0 5 4 3 1 5 -> 3 4 0 3 2 5 4 3 5 5 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 0 0 5 3 1 5 ->= 2 3 2 5 5 1 1 2 3 5 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 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 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 1 | \ / 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 56-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 1 0 4 0 5 -> 3 5 1 4 4 5 4 5 5 5 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 0 0 5 3 1 5 ->= 2 3 2 5 5 1 1 2 3 5 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 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 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 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 1 | \ / 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 | \ / 3 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 55-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 0 0 5 3 1 5 ->= 2 3 2 5 5 1 1 2 3 5 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 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 1 0 0 0 0 | | 0 0 0 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 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 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 | \ / 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 0 | | 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 54-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 2 0 1 0 5 1 5 ->= 0 4 1 0 4 3 5 4 3 5 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 | | 0 0 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 | \ / 5 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 | | 0 0 0 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 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 53-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 3 4 1 5 1 5 -> 3 4 3 5 4 5 4 1 2 5 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 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 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 | \ / 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 | \ / 3 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 52-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 4 5 5 0 4 -> 5 5 0 3 2 0 3 2 0 4 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 | \ / 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 1 0 0 0 | | 0 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 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 1 | | 0 1 0 0 0 0 1 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 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 51-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 0 5 0 1 0 4 -> 5 1 3 2 3 0 0 0 3 0 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 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 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 1 0 0 0 0 1 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 50-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 0 1 0 1 5 1 -> 2 3 5 1 0 1 4 4 1 1 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 | \ / 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 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 49-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 2 5 3 2 5 1 -> 2 5 0 3 3 5 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 | \ / 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 | \ / 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 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 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 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 | \ / Remains to prove termination of the 48-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 2 0 1 5 1 -> 2 4 4 1 2 3 5 4 1 1 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 13: 1 is interpreted by / \ | 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 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 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 0 0 0 | \ / 3 is interpreted by / \ | 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 0 0 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 | | 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 47-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 1 2 1 2 4 -> 0 3 0 2 3 2 3 3 2 4 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 1 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 | \ / 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 46-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 0 1 0 3 1 2 -> 3 3 4 3 5 4 3 5 4 2 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 1 | | 0 1 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 1 0 0 0 0 0 | \ / 0 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 | \ / 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 0 | | 0 1 0 0 0 0 0 | \ / Remains to prove termination of the 45-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 0 1 0 1 2 ->= 0 1 1 1 1 3 2 2 3 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 1 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 | \ / 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 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 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 | \ / 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 | \ / Remains to prove termination of the 44-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 0 4 0 3 1 4 0 ->= 3 3 3 2 1 3 0 2 3 0 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 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 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 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 | \ / 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 | \ / 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 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 43-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 0 0 1 4 3 0 -> 0 4 3 2 3 2 0 2 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 2 4 0 4 -> 0 4 3 3 1 3 3 5 1 1 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 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 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 1 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 41-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 1 3 3 4 -> 0 2 0 0 4 1 1 3 3 4 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 | | 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 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 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 40-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 3 3 0 3 1 0 -> 3 2 4 1 1 3 3 5 4 0 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 1 0 | | 0 0 0 0 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 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 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 1 0 0 0 0 | | 0 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 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 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 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 39-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 1 5 3 0 1 2 -> 2 3 5 5 5 3 5 4 5 2 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 | | 0 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 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 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 38-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 1 5 1 4 0 2 -> 3 0 4 3 5 0 2 0 0 2 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 0 0 0 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 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 37-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 3 2 4 3 1 2 -> 0 2 2 2 2 3 5 1 3 4 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 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 | \ / 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 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 1 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 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 36-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 0 5 5 1 5 0 -> 4 2 0 0 2 0 3 0 3 0 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 0 0 0 0 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 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 | \ / 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 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 1 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 35-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 3 0 5 4 3 1 0 ->= 3 2 2 3 4 4 3 2 1 0 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 0 0 0 0 0 1 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 34-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 2 1 0 3 1 2 -> 3 3 5 3 2 4 1 1 1 1 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 1 | | 0 1 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 1 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 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 1 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 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 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 | \ / Remains to prove termination of the 33-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 1 5 1 4 2 -> 3 3 2 3 5 1 4 4 1 3 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 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 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 | | 0 0 0 0 0 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 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 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 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 | \ / 3 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 32-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 0 5 4 2 4 5 2 -> 0 3 3 3 5 3 5 5 1 1 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 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 0 | | 0 1 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 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 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 | \ / 5 is interpreted by / \ | 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 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 1 | | 0 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 | \ / 3 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 3 1 5 4 0 1 -> 2 5 3 0 3 0 0 3 0 1 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 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 | \ / 5 is interpreted by / \ | 1 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 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 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 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 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 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 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 30-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 4 1 0 1 2 -> 3 4 4 3 5 4 2 3 2 4 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 1 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 1 0 0 0 | \ / Remains to prove termination of the 29-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 0 2 5 3 0 2 -> 3 5 4 1 1 4 1 0 0 2 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 0 0 0 0 | | 0 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 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 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 1 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 | \ / 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 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 28-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 1 4 0 1 -> 5 4 1 2 3 3 5 4 1 4 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 1 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 1 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 1 0 0 0 0 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 | \ / 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 1 5 3 4 1 -> 4 4 5 4 3 4 3 5 5 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 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 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 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 26-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 5 1 0 3 1 ->= 5 4 4 1 1 1 5 4 1 1 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 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 1 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 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 | \ / 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 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 | \ / 3 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 1 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / Remains to prove termination of the 25-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 1 5 1 2 0 4 -> 3 5 2 3 2 0 2 0 5 1 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 1 0 0 0 0 | \ / 0 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 | \ / 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 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 1 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 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 0 3 4 0 2 -> 0 3 0 4 3 5 0 2 2 3 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 1 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 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 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 23-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 0 5 5 1 5 -> 3 2 3 2 1 1 1 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 14: 1 is interpreted by / \ | 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 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 is interpreted by / \ | 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 | \ / 5 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 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 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 1 0 0 0 | | 0 0 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 | \ / 3 is interpreted by / \ | 1 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 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 22-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 4 5 2 2 4 4 2 -> 4 5 4 2 1 4 1 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 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 | \ / 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / Remains to prove termination of the 21-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 4 5 0 5 0 1 2 -> 5 4 5 2 1 4 1 0 4 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 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 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 20-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 0 0 1 5 0 1 -> 3 4 0 0 2 3 0 3 0 1 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 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 1 0 0 0 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 19-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 0 2 3 1 1 -> 1 3 0 2 2 2 2 5 1 1 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 1 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | \ / 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 | \ / 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 1 0 0 0 0 | | 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 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 18-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 4 0 1 1 5 2 5 -> 2 0 3 2 4 1 4 1 1 5 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 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 | \ / 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 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 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 | \ / 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 | \ / 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 | \ / 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 1 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 17-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 1 5 0 2 1 5 0 -> 3 2 5 3 0 2 3 0 2 0 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 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 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 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 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 | | 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 { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 2 0 1 3 0 1 3 -> 2 2 3 4 1 4 1 4 1 3 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 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 | \ / 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 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 0 | | 0 1 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 15-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 5 5 0 1 2 2 -> 5 4 4 3 3 2 4 4 1 3 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 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 1 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 1 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 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 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 | \ / 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 0 0 0 0 0 | \ / Remains to prove termination of the 14-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 2 4 5 0 5 4 2 -> 2 3 5 5 5 1 1 3 2 1 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 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 1 | | 0 1 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 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 13-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 1 5 5 1 2 0 ->= 1 5 5 0 2 2 3 0 2 0 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 1 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 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 | \ / 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 1 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 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 | \ / Remains to prove termination of the 12-rule system { 1 4 0 5 3 -> 1 4 1 1 1 1 1 4 2 3 , 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 0 1 0 2 1 5 2 -> 3 2 4 5 5 4 1 4 1 1 , 0 4 5 1 5 5 3 -> 5 3 4 5 4 5 4 5 4 3 , 0 5 0 5 0 5 3 -> 3 5 4 3 1 2 3 5 5 5 , 1 1 4 0 5 2 5 -> 4 1 3 4 4 5 5 4 4 5 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 , 5 1 2 2 0 5 3 -> 5 1 1 4 2 2 3 5 4 3 , 5 3 0 3 1 5 2 -> 5 2 2 3 2 2 3 5 5 2 , 0 2 4 5 2 5 3 ->= 3 2 3 3 5 5 1 2 3 3 , 4 0 2 4 2 1 3 ->= 2 5 2 2 3 5 5 2 1 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 3-rule system { 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 1 2 1 0 5 3 -> 3 0 3 5 3 4 2 3 5 3 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 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 1 0 0 | | 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 | \ / 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 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 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 | \ / 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 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / Remains to prove termination of the 2-rule system { 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 , 3 1 3 0 4 5 2 -> 3 5 5 2 1 2 0 1 1 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 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 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 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 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / Remains to prove termination of the 1-rule system { 1 3 4 5 3 0 -> 1 3 3 2 4 4 1 1 3 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / Remains to prove termination of the 0-rule system { } The system is trivially terminating.