/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 73-rule system { 0 0 0 0 1 2 1 2 2 1 1 2 0 -> 0 0 0 0 1 2 2 2 2 2 2 2 2 2 1 2 0 , 0 0 0 2 1 0 2 1 1 2 0 2 1 -> 0 0 0 1 0 1 2 2 2 2 2 2 2 2 1 2 2 , 0 0 0 2 2 1 0 2 2 0 1 1 0 -> 0 1 2 0 0 0 0 0 0 0 0 0 0 0 2 1 1 , 0 0 1 0 1 0 0 2 0 2 1 0 1 -> 0 0 0 0 0 1 2 1 0 0 0 0 1 2 2 2 0 , 0 0 1 1 1 0 2 1 2 0 2 1 2 -> 0 0 0 1 0 0 0 0 0 1 2 2 0 2 1 2 1 , 0 0 2 0 1 1 0 2 1 1 0 2 2 -> 0 0 0 2 0 2 2 2 2 2 2 1 0 2 2 0 2 , 0 0 2 1 1 2 1 0 2 2 1 0 0 -> 1 0 0 0 0 0 1 2 2 2 0 2 2 2 2 2 0 , 0 0 2 2 0 0 2 2 1 0 2 0 0 -> 2 0 1 0 0 0 0 0 0 0 0 0 1 2 2 0 0 , 0 1 0 0 1 1 1 1 2 1 0 1 1 -> 0 1 0 1 1 0 0 0 2 2 0 2 2 2 2 0 0 , 0 1 0 1 0 1 1 1 1 0 0 1 2 -> 0 0 2 2 2 2 2 0 2 1 0 0 0 1 2 2 2 , 0 1 0 1 1 0 2 0 2 2 1 0 2 -> 0 2 2 0 2 2 2 2 0 2 2 2 2 0 2 2 2 , 0 1 0 1 1 1 2 2 2 1 1 0 2 -> 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 1 0 , 0 1 1 0 1 2 2 0 1 1 0 1 0 -> 0 0 0 0 0 0 1 2 2 1 0 0 0 1 2 0 0 , 0 1 1 0 2 1 0 0 1 2 1 1 2 -> 1 0 0 1 0 1 2 0 2 2 2 2 2 2 2 2 2 , 0 1 1 2 2 2 1 1 2 2 2 2 1 -> 1 2 2 2 2 0 2 2 2 0 2 2 2 2 2 0 2 , 0 1 2 0 0 1 0 0 1 2 1 2 1 -> 0 0 1 2 0 2 2 2 2 2 2 2 0 1 0 0 2 , 0 1 2 0 1 2 2 2 1 1 2 0 2 -> 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 2 2 , 0 1 2 2 0 2 0 2 1 0 1 1 1 -> 0 0 1 2 2 0 2 0 0 0 0 0 0 0 0 0 1 , 0 2 0 1 0 2 2 1 0 0 2 2 0 -> 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 2 0 , 0 2 0 1 1 0 2 2 1 0 2 2 0 -> 2 0 0 0 2 2 2 2 2 2 2 2 1 0 0 0 1 , 0 2 0 1 1 1 2 1 0 2 0 1 1 -> 0 2 0 2 2 2 0 1 0 0 1 0 0 0 0 1 0 , 0 2 1 0 1 2 0 1 0 0 0 1 1 -> 2 1 2 2 2 2 2 2 2 2 0 2 2 0 2 1 0 , 0 2 1 0 2 1 2 2 2 1 0 0 2 -> 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 1 2 , 0 2 1 2 1 2 2 0 2 0 1 1 0 -> 2 0 1 0 0 0 1 2 0 0 0 0 0 0 0 2 0 , 1 0 0 0 1 1 1 1 0 1 0 0 1 -> 2 2 0 1 0 0 0 0 0 0 0 0 0 0 1 2 0 , 1 0 0 1 0 2 1 2 1 0 1 2 0 -> 0 0 2 0 0 0 0 0 1 0 0 0 0 0 2 2 0 , 1 0 0 2 0 0 2 2 1 2 1 1 1 -> 0 1 0 2 1 0 0 0 0 0 0 1 2 0 2 0 0 , 1 0 0 2 0 1 2 2 1 0 0 1 2 -> 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 , 1 0 0 2 1 1 0 1 2 0 0 2 1 -> 1 0 0 2 0 0 0 1 2 2 2 0 2 2 2 0 1 , 1 0 0 2 2 0 0 1 1 0 2 1 1 -> 1 2 0 2 2 2 2 2 2 0 2 2 0 2 0 0 1 , 1 0 1 2 1 2 0 2 0 1 2 1 0 -> 2 0 0 1 0 0 0 0 0 1 2 2 2 2 1 2 0 , 1 0 2 0 1 1 1 0 0 0 1 0 1 -> 1 0 0 0 0 1 0 0 0 0 0 1 2 2 1 2 0 , 1 0 2 0 2 0 1 0 1 1 1 1 1 -> 1 1 0 2 2 2 2 2 2 0 2 0 2 1 0 0 1 , 1 0 2 1 1 0 0 2 1 0 2 0 1 -> 0 1 0 0 0 0 0 0 0 0 1 1 2 2 1 1 1 , 1 0 2 1 2 1 0 1 0 0 2 1 0 -> 2 1 0 0 0 0 0 1 2 2 2 1 0 0 2 0 0 , 1 0 2 1 2 1 1 1 0 2 0 1 2 -> 1 1 0 0 0 0 1 0 0 0 0 2 0 0 2 0 2 , 1 0 2 1 2 2 0 0 0 1 2 2 0 -> 0 0 2 2 2 2 2 2 2 2 2 2 2 0 1 0 2 , 1 1 0 0 1 0 1 1 2 1 0 1 2 -> 1 0 0 0 0 0 0 1 2 2 0 0 1 0 2 0 2 , 1 1 0 1 1 0 2 2 1 0 2 0 0 -> 0 1 0 0 0 0 1 2 2 2 2 1 2 0 0 0 1 , 1 1 0 2 0 1 0 2 1 0 2 1 2 -> 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 , 1 1 0 2 0 1 1 0 0 2 2 1 2 -> 0 2 1 0 0 0 0 0 1 2 2 0 0 0 0 0 2 , 1 1 1 0 0 0 1 1 0 1 1 0 2 -> 0 0 0 2 2 2 2 2 0 2 2 0 2 2 2 1 2 , 1 1 1 0 0 2 0 2 1 0 2 0 2 -> 1 0 2 0 1 2 2 2 2 0 2 2 0 2 2 2 2 , 1 1 1 2 2 2 2 1 0 0 2 1 2 -> 0 0 0 0 0 0 1 0 0 0 0 1 2 2 1 1 2 , 1 1 2 0 2 0 2 0 1 0 0 2 0 -> 2 0 1 0 0 0 0 1 2 2 2 0 2 2 2 2 1 , 1 1 2 1 0 0 0 1 0 2 0 2 2 -> 1 0 2 1 0 0 0 0 0 0 0 1 2 2 2 2 2 , 1 1 2 2 0 0 2 0 1 1 1 1 0 -> 2 0 0 0 0 1 2 1 0 1 2 2 2 2 1 0 0 , 1 2 0 0 1 1 2 2 1 2 2 0 0 -> 1 0 2 0 2 0 0 0 0 0 0 0 0 0 1 2 2 , 1 2 0 0 2 1 0 2 2 2 0 0 1 -> 0 0 0 0 0 1 2 2 2 0 2 0 2 2 1 0 1 , 1 2 0 1 0 0 1 1 1 1 0 1 1 -> 0 0 0 0 2 0 1 0 0 0 0 0 1 2 1 1 0 , 1 2 0 1 2 1 2 2 1 0 1 0 0 -> 1 0 0 0 1 2 0 2 2 2 2 2 1 0 1 0 0 , 1 2 1 1 2 0 0 2 2 1 0 0 1 -> 1 1 0 0 0 0 0 0 1 0 0 1 2 2 2 2 0 , 1 2 2 0 0 1 2 0 2 1 0 0 1 -> 0 1 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 , 1 2 2 0 1 2 2 2 0 1 2 1 1 -> 0 0 0 2 2 2 2 2 0 2 2 1 2 0 0 0 1 , 2 0 0 0 0 1 1 2 0 0 1 0 2 -> 0 1 0 0 0 1 2 2 2 2 0 2 0 2 2 2 2 , 2 0 0 2 1 2 1 0 1 0 1 1 1 -> 1 0 0 0 0 0 0 0 1 1 2 2 2 0 2 0 0 , 2 0 1 0 1 0 0 0 2 0 1 2 1 -> 2 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 , 2 0 2 0 1 1 0 0 2 1 1 0 2 -> 2 2 0 0 0 1 0 0 0 0 1 0 0 0 1 0 2 , 2 0 2 2 0 2 2 0 2 1 2 0 1 -> 2 2 2 2 0 0 0 0 0 0 0 0 0 1 2 2 0 , 2 1 0 2 1 2 1 2 1 2 2 2 1 -> 2 1 0 0 0 1 2 0 2 0 0 0 0 0 1 2 1 , 2 1 1 2 1 1 2 0 1 0 1 0 2 -> 2 2 0 2 0 0 1 2 0 2 2 2 2 2 2 1 2 , 2 1 1 2 2 0 2 0 0 2 0 1 0 -> 2 0 1 0 1 2 2 2 2 2 2 2 0 2 2 0 0 , 2 1 2 0 0 2 2 0 2 0 1 2 2 -> 2 0 0 0 0 2 0 0 1 2 2 2 2 2 2 0 2 , 2 1 2 0 2 2 2 1 1 0 0 1 2 -> 1 2 2 0 0 2 2 2 2 2 0 2 2 2 2 2 2 , 2 1 2 1 0 1 0 0 2 1 2 2 0 -> 2 2 1 1 0 0 0 0 0 0 1 2 1 0 0 0 1 , 2 1 2 2 1 2 2 2 2 1 2 1 0 -> 2 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 , 2 2 0 0 1 2 1 0 2 2 1 0 0 -> 2 2 2 2 2 2 2 0 2 2 0 2 2 0 2 2 0 , 2 2 0 0 2 1 2 1 2 0 1 2 0 -> 2 2 2 2 2 2 0 1 0 0 0 0 1 0 0 2 1 , 2 2 0 2 2 0 1 1 2 1 0 1 0 -> 2 2 2 2 2 2 2 2 2 2 1 0 0 2 0 0 1 , 2 2 0 2 2 1 2 1 2 2 0 2 0 -> 2 2 2 2 0 2 2 2 0 2 2 0 1 0 0 0 1 , 2 2 1 0 2 1 1 2 2 0 1 0 1 -> 2 2 2 2 0 1 0 0 0 1 0 0 0 0 0 1 2 , 2 2 1 1 2 1 0 1 1 2 0 0 2 -> 2 2 2 0 0 0 0 1 2 0 0 0 2 2 2 2 2 , 2 1 2 2 1 2 0 2 0 0 2 1 0 ->= 1 1 2 0 2 2 2 0 2 2 2 2 2 2 1 2 0 } The system was reversed. After renaming modulo { 0->0, 2->1, 1->2 }, it remains to prove termination of the 73-rule system { 0 1 2 2 1 1 2 1 2 0 0 0 0 -> 0 1 2 1 1 1 1 1 1 1 1 1 2 0 0 0 0 , 2 1 0 1 2 2 1 0 2 1 0 0 0 -> 1 1 2 1 1 1 1 1 1 1 1 2 0 2 0 0 0 , 0 2 2 0 1 1 0 2 1 1 0 0 0 -> 2 2 1 0 0 0 0 0 0 0 0 0 0 0 1 2 0 , 2 0 2 1 0 1 0 0 2 0 2 0 0 -> 0 1 1 1 2 0 0 0 0 2 1 2 0 0 0 0 0 , 1 2 1 0 1 2 1 0 2 2 2 0 0 -> 2 1 2 1 0 1 1 2 0 0 0 0 0 2 0 0 0 , 1 1 0 2 2 1 0 2 2 0 1 0 0 -> 1 0 1 1 0 2 1 1 1 1 1 1 0 1 0 0 0 , 0 0 2 1 1 0 2 1 2 2 1 0 0 -> 0 1 1 1 1 1 0 1 1 1 2 0 0 0 0 0 2 , 0 0 1 0 2 1 1 0 0 1 1 0 0 -> 0 0 1 1 2 0 0 0 0 0 0 0 0 0 2 0 1 , 2 2 0 2 1 2 2 2 2 0 0 2 0 -> 0 0 1 1 1 1 0 1 1 0 0 0 2 2 0 2 0 , 1 2 0 0 2 2 2 2 0 2 0 2 0 -> 1 1 1 2 0 0 0 2 1 0 1 1 1 1 1 0 0 , 1 0 2 1 1 0 1 0 2 2 0 2 0 -> 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 , 1 0 2 2 1 1 1 2 2 2 0 2 0 -> 0 2 0 0 0 0 0 0 2 1 0 0 0 0 2 0 0 , 0 2 0 2 2 0 1 1 2 0 2 2 0 -> 0 0 1 2 0 0 0 2 1 1 2 0 0 0 0 0 0 , 1 2 2 1 2 0 0 2 1 0 2 2 0 -> 1 1 1 1 1 1 1 1 1 0 1 2 0 2 0 0 2 , 2 1 1 1 1 2 2 1 1 1 2 2 0 -> 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 2 , 2 1 2 1 2 0 0 2 0 0 1 2 0 -> 1 0 0 2 0 1 1 1 1 1 1 1 0 1 2 0 0 , 1 0 1 2 2 1 1 1 2 0 1 2 0 -> 1 1 0 0 1 0 1 2 0 0 0 0 0 0 0 0 0 , 2 2 2 0 2 1 0 1 0 1 1 2 0 -> 2 0 0 0 0 0 0 0 0 0 1 0 1 1 2 0 0 , 0 1 1 0 0 2 1 1 0 2 0 1 0 -> 0 1 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 , 0 1 1 0 2 1 1 0 2 2 0 1 0 -> 2 0 0 0 2 1 1 1 1 1 1 1 1 0 0 0 1 , 2 2 0 1 0 2 1 2 2 2 0 1 0 -> 0 2 0 0 0 0 2 0 0 2 0 1 1 1 0 1 0 , 2 2 0 0 0 2 0 1 2 0 2 1 0 -> 0 2 1 0 1 1 0 1 1 1 1 1 1 1 1 2 1 , 1 0 0 2 1 1 1 2 1 0 2 1 0 -> 1 2 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 , 0 2 2 0 1 0 1 1 2 1 2 1 0 -> 0 1 0 0 0 0 0 0 0 1 2 0 0 0 2 0 1 , 2 0 0 2 0 2 2 2 2 0 0 0 2 -> 0 1 2 0 0 0 0 0 0 0 0 0 0 2 0 1 1 , 0 1 2 0 2 1 2 1 0 2 0 0 2 -> 0 1 1 0 0 0 0 0 2 0 0 0 0 0 1 0 0 , 2 2 2 1 2 1 1 0 0 1 0 0 2 -> 0 0 1 0 1 2 0 0 0 0 0 0 2 1 0 2 0 , 1 2 0 0 2 1 1 2 0 1 0 0 2 -> 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 , 2 1 0 0 1 2 0 2 2 1 0 0 2 -> 2 0 1 1 1 0 1 1 1 2 0 0 0 1 0 0 2 , 2 2 1 0 2 2 0 0 1 1 0 0 2 -> 2 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 2 , 0 2 1 2 0 1 0 1 2 1 2 0 2 -> 0 1 2 1 1 1 1 2 0 0 0 0 0 2 0 0 1 , 2 0 2 0 0 0 2 2 2 0 1 0 2 -> 0 1 2 1 1 2 0 0 0 0 0 2 0 0 0 0 2 , 2 2 2 2 2 0 2 0 1 0 1 0 2 -> 2 0 0 2 1 0 1 0 1 1 1 1 1 1 0 2 2 , 2 0 1 0 2 1 0 0 2 2 1 0 2 -> 2 2 2 1 1 2 2 0 0 0 0 0 0 0 0 2 0 , 0 2 1 0 0 2 0 2 1 2 1 0 2 -> 0 0 1 0 0 2 1 1 1 2 0 0 0 0 0 2 1 , 1 2 0 1 0 2 2 2 1 2 1 0 2 -> 1 0 1 0 0 1 0 0 0 0 2 0 0 0 0 2 2 , 0 1 1 2 0 0 0 1 1 2 1 0 2 -> 1 0 2 0 1 1 1 1 1 1 1 1 1 1 1 0 0 , 1 2 0 2 1 2 2 0 2 0 0 2 2 -> 1 0 1 0 2 0 0 1 1 2 0 0 0 0 0 0 2 , 0 0 1 0 2 1 1 0 2 2 0 2 2 -> 2 0 0 0 1 2 1 1 1 1 2 0 0 0 0 2 0 , 1 2 1 0 2 1 0 2 0 1 0 2 2 -> 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 , 1 2 1 1 0 0 2 2 0 1 0 2 2 -> 1 0 0 0 0 0 1 1 2 0 0 0 0 0 2 1 0 , 1 0 2 2 0 2 2 0 0 0 2 2 2 -> 1 2 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 , 1 0 1 0 2 1 0 1 0 0 2 2 2 -> 1 1 1 1 0 1 1 0 1 1 1 1 2 0 1 0 2 , 1 2 1 0 0 2 1 1 1 1 2 2 2 -> 1 2 2 1 1 2 0 0 0 0 2 0 0 0 0 0 0 , 0 1 0 0 2 0 1 0 1 0 1 2 2 -> 2 1 1 1 1 0 1 1 1 2 0 0 0 0 2 0 1 , 1 1 0 1 0 2 0 0 0 2 1 2 2 -> 1 1 1 1 1 2 0 0 0 0 0 0 0 2 1 0 2 , 0 2 2 2 2 0 1 0 0 1 1 2 2 -> 0 0 2 1 1 1 1 2 0 2 1 2 0 0 0 0 1 , 0 0 1 1 2 1 1 2 2 0 0 1 2 -> 1 1 2 0 0 0 0 0 0 0 0 0 1 0 1 0 2 , 2 0 0 1 1 1 0 2 1 0 0 1 2 -> 2 0 2 1 1 0 1 0 1 1 1 2 0 0 0 0 0 , 2 2 0 2 2 2 2 0 0 2 0 1 2 -> 0 2 2 1 2 0 0 0 0 0 2 0 1 0 0 0 0 , 0 0 2 0 2 1 1 2 1 2 0 1 2 -> 0 0 2 0 2 1 1 1 1 1 0 1 2 0 0 0 2 , 2 0 0 2 1 1 0 0 1 2 2 1 2 -> 0 1 1 1 1 2 0 0 2 0 0 0 0 0 0 2 2 , 2 0 0 2 1 0 1 2 0 0 1 1 2 -> 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 2 0 , 2 2 1 2 0 1 1 1 2 0 1 1 2 -> 2 0 0 0 1 2 1 1 0 1 1 1 1 1 0 0 0 , 1 0 2 0 0 1 2 2 0 0 0 0 1 -> 1 1 1 1 0 1 0 1 1 1 1 2 0 0 0 2 0 , 2 2 2 0 2 0 2 1 2 1 0 0 1 -> 0 0 1 0 1 1 1 2 2 0 0 0 0 0 0 0 2 , 2 1 2 0 1 0 0 0 2 0 2 0 1 -> 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 1 , 1 0 2 2 1 0 0 2 2 0 1 0 1 -> 1 0 2 0 0 0 2 0 0 0 0 2 0 0 0 1 1 , 2 0 1 2 1 0 1 1 0 1 1 0 1 -> 0 1 1 2 0 0 0 0 0 0 0 0 0 1 1 1 1 , 2 1 1 1 2 1 2 1 2 1 0 2 1 -> 2 1 2 0 0 0 0 0 1 0 1 2 0 0 0 2 1 , 1 0 2 0 2 0 1 2 2 1 2 2 1 -> 1 2 1 1 1 1 1 1 0 1 2 0 0 1 0 1 1 , 0 2 0 1 0 0 1 0 1 1 2 2 1 -> 0 0 1 1 0 1 1 1 1 1 1 1 2 0 2 0 1 , 1 1 2 0 1 0 1 1 0 0 1 2 1 -> 1 0 1 1 1 1 1 1 2 0 0 1 0 0 0 0 1 , 1 2 0 0 2 2 1 1 1 0 1 2 1 -> 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 2 , 0 1 1 2 1 0 0 2 0 2 1 2 1 -> 2 0 0 0 2 1 2 0 0 0 0 0 0 2 2 1 1 , 0 2 1 2 1 1 1 1 2 1 1 2 1 -> 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 1 , 0 0 2 1 1 0 2 1 2 0 0 1 1 -> 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 , 0 1 2 0 1 2 1 2 1 0 0 1 1 -> 2 1 0 0 2 0 0 0 0 2 0 1 1 1 1 1 1 , 0 2 0 2 1 2 2 0 1 1 0 1 1 -> 2 0 0 1 0 0 2 1 1 1 1 1 1 1 1 1 1 , 0 1 0 1 1 2 1 2 1 1 0 1 1 -> 2 0 0 0 2 0 1 1 0 1 1 1 0 1 1 1 1 , 2 0 2 0 1 1 2 2 1 0 2 1 1 -> 1 2 0 0 0 0 0 2 0 0 0 2 0 1 1 1 1 , 1 0 0 1 2 2 0 2 1 2 2 1 1 -> 1 1 1 1 1 0 0 0 1 2 0 0 0 0 1 1 1 , 0 2 1 0 0 1 0 1 2 1 1 2 1 ->= 0 1 2 1 1 1 1 1 1 0 1 1 1 0 1 2 2 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 2]->2, [2, 2]->3, [2, 1]->4, [1, 1]->5, [2, 0]->6, [0, 2]->7, [1, 0]->8 }, it remains to prove termination of the 657-rule system { 0 1 2 3 4 5 2 4 2 6 0 0 0 0 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 0 , 7 4 8 1 2 3 4 8 7 4 8 0 0 0 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 0 , 0 7 3 6 1 5 8 7 4 5 8 0 0 0 -> 7 3 4 8 0 0 0 0 0 0 0 0 0 0 1 2 6 0 , 7 6 7 4 8 1 8 0 7 6 7 6 0 0 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 0 , 1 2 4 8 1 2 4 8 7 3 3 6 0 0 -> 7 4 2 4 8 1 5 2 6 0 0 0 0 7 6 0 0 0 , 1 5 8 7 3 4 8 7 3 6 1 8 0 0 -> 1 8 1 5 8 7 4 5 5 5 5 5 8 1 8 0 0 0 , 0 0 7 4 5 8 7 4 2 3 4 8 0 0 -> 0 1 5 5 5 5 8 1 5 5 2 6 0 0 0 0 7 6 , 0 0 1 8 7 4 5 8 0 1 5 8 0 0 -> 0 0 1 5 2 6 0 0 0 0 0 0 0 0 7 6 1 8 , 7 3 6 7 4 2 3 3 3 6 0 7 6 0 -> 0 0 1 5 5 5 8 1 5 8 0 0 7 3 6 7 6 0 , 1 2 6 0 7 3 3 3 6 7 6 7 6 0 -> 1 5 5 2 6 0 0 7 4 8 1 5 5 5 5 8 0 0 , 1 8 7 4 5 8 1 8 7 3 6 7 6 0 -> 1 5 5 8 1 5 5 5 8 1 5 5 5 8 1 5 8 0 , 1 8 7 3 4 5 5 2 3 3 6 7 6 0 -> 0 7 6 0 0 0 0 0 7 4 8 0 0 0 7 6 0 0 , 0 7 6 7 3 6 1 5 2 6 7 3 6 0 -> 0 0 1 2 6 0 0 7 4 5 2 6 0 0 0 0 0 0 , 1 2 3 4 2 6 0 7 4 8 7 3 6 0 -> 1 5 5 5 5 5 5 5 5 8 1 2 6 7 6 0 7 6 , 7 4 5 5 5 2 3 4 5 5 2 3 6 0 -> 1 8 1 5 5 5 5 8 1 5 5 8 1 5 5 5 2 6 , 7 4 2 4 2 6 0 7 6 0 1 2 6 0 -> 1 8 0 7 6 1 5 5 5 5 5 5 8 1 2 6 0 0 , 1 8 1 2 3 4 5 5 2 6 1 2 6 0 -> 1 5 8 0 1 8 1 2 6 0 0 0 0 0 0 0 0 0 , 7 3 3 6 7 4 8 1 8 1 5 2 6 0 -> 7 6 0 0 0 0 0 0 0 0 1 8 1 5 2 6 0 0 , 0 1 5 8 0 7 4 5 8 7 6 1 8 0 -> 0 1 2 6 0 0 0 0 0 0 0 1 2 6 0 0 0 0 , 0 1 5 8 7 4 5 8 7 3 6 1 8 0 -> 7 6 0 0 7 4 5 5 5 5 5 5 5 8 0 0 1 8 , 7 3 6 1 8 7 4 2 3 3 6 1 8 0 -> 0 7 6 0 0 0 7 6 0 7 6 1 5 5 8 1 8 0 , 7 3 6 0 0 7 6 1 2 6 7 4 8 0 -> 0 7 4 8 1 5 8 1 5 5 5 5 5 5 5 2 4 8 , 1 8 0 7 4 5 5 2 4 8 7 4 8 0 -> 1 2 6 1 8 7 6 0 0 0 0 0 0 0 0 0 0 0 , 0 7 3 6 1 8 1 5 2 4 2 4 8 0 -> 0 1 8 0 0 0 0 0 0 1 2 6 0 0 7 6 1 8 , 7 6 0 7 6 7 3 3 3 6 0 0 7 6 -> 0 1 2 6 0 0 0 0 0 0 0 0 0 7 6 1 5 8 , 0 1 2 6 7 4 2 4 8 7 6 0 7 6 -> 0 1 5 8 0 0 0 0 7 6 0 0 0 0 1 8 0 0 , 7 3 3 4 2 4 5 8 0 1 8 0 7 6 -> 0 0 1 8 1 2 6 0 0 0 0 0 7 4 8 7 6 0 , 1 2 6 0 7 4 5 2 6 1 8 0 7 6 -> 1 8 0 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 , 7 4 8 0 1 2 6 7 3 4 8 0 7 6 -> 7 6 1 5 5 8 1 5 5 2 6 0 0 1 8 0 7 6 , 7 3 4 8 7 3 6 0 1 5 8 0 7 6 -> 7 6 0 1 8 1 5 8 1 5 5 5 5 5 8 1 2 6 , 0 7 4 2 6 1 8 1 2 4 2 6 7 6 -> 0 1 2 4 5 5 5 2 6 0 0 0 0 7 6 0 1 8 , 7 6 7 6 0 0 7 3 3 6 1 8 7 6 -> 0 1 2 4 5 2 6 0 0 0 0 7 6 0 0 0 7 6 , 7 3 3 3 3 6 7 6 1 8 1 8 7 6 -> 7 6 0 7 4 8 1 8 1 5 5 5 5 5 8 7 3 6 , 7 6 1 8 7 4 8 0 7 3 4 8 7 6 -> 7 3 3 4 5 2 3 6 0 0 0 0 0 0 0 7 6 0 , 0 7 4 8 0 7 6 7 4 2 4 8 7 6 -> 0 0 1 8 0 7 4 5 5 2 6 0 0 0 0 7 4 8 , 1 2 6 1 8 7 3 3 4 2 4 8 7 6 -> 1 8 1 8 0 1 8 0 0 0 7 6 0 0 0 7 3 6 , 0 1 5 2 6 0 0 1 5 2 4 8 7 6 -> 1 8 7 6 1 5 5 5 5 5 5 5 5 5 5 8 0 0 , 1 2 6 7 4 2 3 6 7 6 0 7 3 6 -> 1 8 1 8 7 6 0 1 5 2 6 0 0 0 0 0 7 6 , 0 0 1 8 7 4 5 8 7 3 6 7 3 6 -> 7 6 0 0 1 2 4 5 5 5 2 6 0 0 0 7 6 0 , 1 2 4 8 7 4 8 7 6 1 8 7 3 6 -> 1 2 4 5 5 5 5 5 2 3 4 5 5 5 5 5 2 6 , 1 2 4 5 8 0 7 3 6 1 8 7 3 6 -> 1 8 0 0 0 0 1 5 2 6 0 0 0 0 7 4 8 0 , 1 8 7 3 6 7 3 6 0 0 7 3 3 6 -> 1 2 4 5 5 8 1 5 8 1 5 5 5 5 8 0 0 0 , 1 8 1 8 7 4 8 1 8 0 7 3 3 6 -> 1 5 5 5 8 1 5 8 1 5 5 5 2 6 1 8 7 6 , 1 2 4 8 0 7 4 5 5 5 2 3 3 6 -> 1 2 3 4 5 2 6 0 0 0 7 6 0 0 0 0 0 0 , 0 1 8 0 7 6 1 8 1 8 1 2 3 6 -> 7 4 5 5 5 8 1 5 5 2 6 0 0 0 7 6 1 8 , 1 5 8 1 8 7 6 0 0 7 4 2 3 6 -> 1 5 5 5 5 2 6 0 0 0 0 0 0 7 4 8 7 6 , 0 7 3 3 3 6 1 8 0 1 5 2 3 6 -> 0 0 7 4 5 5 5 2 6 7 4 2 6 0 0 0 1 8 , 0 0 1 5 2 4 5 2 3 6 0 1 2 6 -> 1 5 2 6 0 0 0 0 0 0 0 0 1 8 1 8 7 6 , 7 6 0 1 5 5 8 7 4 8 0 1 2 6 -> 7 6 7 4 5 8 1 8 1 5 5 2 6 0 0 0 0 0 , 7 3 6 7 3 3 3 6 0 7 6 1 2 6 -> 0 7 3 4 2 6 0 0 0 0 7 6 1 8 0 0 0 0 , 0 0 7 6 7 4 5 2 4 2 6 1 2 6 -> 0 0 7 6 7 4 5 5 5 5 8 1 2 6 0 0 7 6 , 7 6 0 7 4 5 8 0 1 2 3 4 2 6 -> 0 1 5 5 5 2 6 0 7 6 0 0 0 0 0 7 3 6 , 7 6 0 7 4 8 1 2 6 0 1 5 2 6 -> 1 5 5 5 5 5 5 5 8 1 5 5 5 5 8 7 6 0 , 7 3 4 2 6 1 5 5 2 6 1 5 2 6 -> 7 6 0 0 1 2 4 5 8 1 5 5 5 5 8 0 0 0 , 1 8 7 6 0 1 2 3 6 0 0 0 1 8 -> 1 5 5 5 8 1 8 1 5 5 5 2 6 0 0 7 6 0 , 7 3 3 6 7 6 7 4 2 4 8 0 1 8 -> 0 0 1 8 1 5 5 2 3 6 0 0 0 0 0 0 7 6 , 7 4 2 6 1 8 0 0 7 6 7 6 1 8 -> 0 0 0 0 0 0 0 0 7 6 0 7 6 0 7 6 1 8 , 1 8 7 3 4 8 0 7 3 6 1 8 1 8 -> 1 8 7 6 0 0 7 6 0 0 0 7 6 0 0 1 5 8 , 7 6 1 2 4 8 1 5 8 1 5 8 1 8 -> 0 1 5 2 6 0 0 0 0 0 0 0 0 1 5 5 5 8 , 7 4 5 5 2 4 2 4 2 4 8 7 4 8 -> 7 4 2 6 0 0 0 0 1 8 1 2 6 0 0 7 4 8 , 1 8 7 6 7 6 1 2 3 4 2 3 4 8 -> 1 2 4 5 5 5 5 5 8 1 2 6 0 1 8 1 5 8 , 0 7 6 1 8 0 1 8 1 5 2 3 4 8 -> 0 0 1 5 8 1 5 5 5 5 5 5 2 6 7 6 1 8 , 1 5 2 6 1 8 1 5 8 0 1 2 4 8 -> 1 8 1 5 5 5 5 5 2 6 0 1 8 0 0 0 1 8 , 1 2 6 0 7 3 4 5 5 8 1 2 4 8 -> 1 5 5 5 5 5 8 1 5 5 5 5 8 0 1 5 2 6 , 0 1 5 2 4 8 0 7 6 7 4 2 4 8 -> 7 6 0 0 7 4 2 6 0 0 0 0 0 7 3 4 5 8 , 0 7 4 2 4 5 5 5 2 4 5 2 4 8 -> 0 0 0 0 0 0 0 0 7 6 0 0 0 1 8 0 1 8 , 0 0 7 4 5 8 7 4 2 6 0 1 5 8 -> 0 1 5 8 1 5 8 1 5 8 1 5 5 5 5 5 5 8 , 0 1 2 6 1 2 4 2 4 8 0 1 5 8 -> 7 4 8 0 7 6 0 0 0 7 6 1 5 5 5 5 5 8 , 0 7 6 7 4 2 3 6 1 5 8 1 5 8 -> 7 6 0 1 8 0 7 4 5 5 5 5 5 5 5 5 5 8 , 0 1 8 1 5 2 4 2 4 5 8 1 5 8 -> 7 6 0 0 7 6 1 5 8 1 5 5 8 1 5 5 5 8 , 7 6 7 6 1 5 2 3 4 8 7 4 5 8 -> 1 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 8 , 1 8 0 1 2 3 6 7 4 2 3 4 5 8 -> 1 5 5 5 5 8 0 0 1 2 6 0 0 0 1 5 5 8 , 0 7 4 8 0 1 8 1 2 4 5 2 4 8 ->= 0 1 2 4 5 5 5 5 5 8 1 5 5 8 1 2 3 6 , 0 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 7 4 8 1 2 3 4 8 7 4 8 0 0 1 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 0 7 3 6 1 5 8 7 4 5 8 0 0 1 -> 7 3 4 8 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 7 6 7 4 8 1 8 0 7 6 7 6 0 1 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 1 2 4 8 1 2 4 8 7 3 3 6 0 1 -> 7 4 2 4 8 1 5 2 6 0 0 0 0 7 6 0 0 1 , 1 5 8 7 3 4 8 7 3 6 1 8 0 1 -> 1 8 1 5 8 7 4 5 5 5 5 5 8 1 8 0 0 1 , 0 0 7 4 5 8 7 4 2 3 4 8 0 1 -> 0 1 5 5 5 5 8 1 5 5 2 6 0 0 0 0 7 4 , 0 0 1 8 7 4 5 8 0 1 5 8 0 1 -> 0 0 1 5 2 6 0 0 0 0 0 0 0 0 7 6 1 5 , 7 3 6 7 4 2 3 3 3 6 0 7 6 1 -> 0 0 1 5 5 5 8 1 5 8 0 0 7 3 6 7 6 1 , 1 2 6 0 7 3 3 3 6 7 6 7 6 1 -> 1 5 5 2 6 0 0 7 4 8 1 5 5 5 5 8 0 1 , 1 8 7 4 5 8 1 8 7 3 6 7 6 1 -> 1 5 5 8 1 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1 8 7 6 0 0 0 0 0 0 0 0 0 0 0 , 6 7 3 6 1 8 1 5 2 4 2 4 8 0 -> 6 1 8 0 0 0 0 0 0 1 2 6 0 0 7 6 1 8 , 3 6 0 7 6 7 3 3 3 6 0 0 7 6 -> 6 1 2 6 0 0 0 0 0 0 0 0 0 7 6 1 5 8 , 6 1 2 6 7 4 2 4 8 7 6 0 7 6 -> 6 1 5 8 0 0 0 0 7 6 0 0 0 0 1 8 0 0 , 3 3 3 4 2 4 5 8 0 1 8 0 7 6 -> 6 0 1 8 1 2 6 0 0 0 0 0 7 4 8 7 6 0 , 4 2 6 0 7 4 5 2 6 1 8 0 7 6 -> 4 8 0 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 , 3 4 8 0 1 2 6 7 3 4 8 0 7 6 -> 3 6 1 5 5 8 1 5 5 2 6 0 0 1 8 0 7 6 , 3 3 4 8 7 3 6 0 1 5 8 0 7 6 -> 3 6 0 1 8 1 5 8 1 5 5 5 5 5 8 1 2 6 , 6 7 4 2 6 1 8 1 2 4 2 6 7 6 -> 6 1 2 4 5 5 5 2 6 0 0 0 0 7 6 0 1 8 , 3 6 7 6 0 0 7 3 3 6 1 8 7 6 -> 6 1 2 4 5 2 6 0 0 0 0 7 6 0 0 0 7 6 , 3 3 3 3 3 6 7 6 1 8 1 8 7 6 -> 3 6 0 7 4 8 1 8 1 5 5 5 5 5 8 7 3 6 , 3 6 1 8 7 4 8 0 7 3 4 8 7 6 -> 3 3 3 4 5 2 3 6 0 0 0 0 0 0 0 7 6 0 , 6 7 4 8 0 7 6 7 4 2 4 8 7 6 -> 6 0 1 8 0 7 4 5 5 2 6 0 0 0 0 7 4 8 , 4 2 6 1 8 7 3 3 4 2 4 8 7 6 -> 4 8 1 8 0 1 8 0 0 0 7 6 0 0 0 7 3 6 , 6 1 5 2 6 0 0 1 5 2 4 8 7 6 -> 4 8 7 6 1 5 5 5 5 5 5 5 5 5 5 8 0 0 , 4 2 6 7 4 2 3 6 7 6 0 7 3 6 -> 4 8 1 8 7 6 0 1 5 2 6 0 0 0 0 0 7 6 , 6 0 1 8 7 4 5 8 7 3 6 7 3 6 -> 3 6 0 0 1 2 4 5 5 5 2 6 0 0 0 7 6 0 , 4 2 4 8 7 4 8 7 6 1 8 7 3 6 -> 4 2 4 5 5 5 5 5 2 3 4 5 5 5 5 5 2 6 , 4 2 4 5 8 0 7 3 6 1 8 7 3 6 -> 4 8 0 0 0 0 1 5 2 6 0 0 0 0 7 4 8 0 , 4 8 7 3 6 7 3 6 0 0 7 3 3 6 -> 4 2 4 5 5 8 1 5 8 1 5 5 5 5 8 0 0 0 , 4 8 1 8 7 4 8 1 8 0 7 3 3 6 -> 4 5 5 5 8 1 5 8 1 5 5 5 2 6 1 8 7 6 , 4 2 4 8 0 7 4 5 5 5 2 3 3 6 -> 4 2 3 4 5 2 6 0 0 0 7 6 0 0 0 0 0 0 , 6 1 8 0 7 6 1 8 1 8 1 2 3 6 -> 3 4 5 5 5 8 1 5 5 2 6 0 0 0 7 6 1 8 , 4 5 8 1 8 7 6 0 0 7 4 2 3 6 -> 4 5 5 5 5 2 6 0 0 0 0 0 0 7 4 8 7 6 , 6 7 3 3 3 6 1 8 0 1 5 2 3 6 -> 6 0 7 4 5 5 5 2 6 7 4 2 6 0 0 0 1 8 , 6 0 1 5 2 4 5 2 3 6 0 1 2 6 -> 4 5 2 6 0 0 0 0 0 0 0 0 1 8 1 8 7 6 , 3 6 0 1 5 5 8 7 4 8 0 1 2 6 -> 3 6 7 4 5 8 1 8 1 5 5 2 6 0 0 0 0 0 , 3 3 6 7 3 3 3 6 0 7 6 1 2 6 -> 6 7 3 4 2 6 0 0 0 0 7 6 1 8 0 0 0 0 , 6 0 7 6 7 4 5 2 4 2 6 1 2 6 -> 6 0 7 6 7 4 5 5 5 5 8 1 2 6 0 0 7 6 , 3 6 0 7 4 5 8 0 1 2 3 4 2 6 -> 6 1 5 5 5 2 6 0 7 6 0 0 0 0 0 7 3 6 , 3 6 0 7 4 8 1 2 6 0 1 5 2 6 -> 4 5 5 5 5 5 5 5 8 1 5 5 5 5 8 7 6 0 , 3 3 4 2 6 1 5 5 2 6 1 5 2 6 -> 3 6 0 0 1 2 4 5 8 1 5 5 5 5 8 0 0 0 , 4 8 7 6 0 1 2 3 6 0 0 0 1 8 -> 4 5 5 5 8 1 8 1 5 5 5 2 6 0 0 7 6 0 , 3 3 3 6 7 6 7 4 2 4 8 0 1 8 -> 6 0 1 8 1 5 5 2 3 6 0 0 0 0 0 0 7 6 , 3 4 2 6 1 8 0 0 7 6 7 6 1 8 -> 6 0 0 0 0 0 0 0 7 6 0 7 6 0 7 6 1 8 , 4 8 7 3 4 8 0 7 3 6 1 8 1 8 -> 4 8 7 6 0 0 7 6 0 0 0 7 6 0 0 1 5 8 , 3 6 1 2 4 8 1 5 8 1 5 8 1 8 -> 6 1 5 2 6 0 0 0 0 0 0 0 0 1 5 5 5 8 , 3 4 5 5 2 4 2 4 2 4 8 7 4 8 -> 3 4 2 6 0 0 0 0 1 8 1 2 6 0 0 7 4 8 , 4 8 7 6 7 6 1 2 3 4 2 3 4 8 -> 4 2 4 5 5 5 5 5 8 1 2 6 0 1 8 1 5 8 , 6 7 6 1 8 0 1 8 1 5 2 3 4 8 -> 6 0 1 5 8 1 5 5 5 5 5 5 2 6 7 6 1 8 , 4 5 2 6 1 8 1 5 8 0 1 2 4 8 -> 4 8 1 5 5 5 5 5 2 6 0 1 8 0 0 0 1 8 , 4 2 6 0 7 3 4 5 5 8 1 2 4 8 -> 4 5 5 5 5 5 8 1 5 5 5 5 8 0 1 5 2 6 , 6 1 5 2 4 8 0 7 6 7 4 2 4 8 -> 3 6 0 0 7 4 2 6 0 0 0 0 0 7 3 4 5 8 , 6 7 4 2 4 5 5 5 2 4 5 2 4 8 -> 6 0 0 0 0 0 0 0 7 6 0 0 0 1 8 0 1 8 , 6 0 7 4 5 8 7 4 2 6 0 1 5 8 -> 6 1 5 8 1 5 8 1 5 8 1 5 5 5 5 5 5 8 , 6 1 2 6 1 2 4 2 4 8 0 1 5 8 -> 3 4 8 0 7 6 0 0 0 7 6 1 5 5 5 5 5 8 , 6 7 6 7 4 2 3 6 1 5 8 1 5 8 -> 3 6 0 1 8 0 7 4 5 5 5 5 5 5 5 5 5 8 , 6 1 8 1 5 2 4 2 4 5 8 1 5 8 -> 3 6 0 0 7 6 1 5 8 1 5 5 8 1 5 5 5 8 , 3 6 7 6 1 5 2 3 4 8 7 4 5 8 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 8 , 4 8 0 1 2 3 6 7 4 2 3 4 5 8 -> 4 5 5 5 5 8 0 0 1 2 6 0 0 0 1 5 5 8 , 6 7 4 8 0 1 8 1 2 4 5 2 4 8 ->= 6 1 2 4 5 5 5 5 5 8 1 5 5 8 1 2 3 6 , 6 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 3 4 8 1 2 3 4 8 7 4 8 0 0 1 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 6 7 3 6 1 5 8 7 4 5 8 0 0 1 -> 3 3 4 8 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 3 6 7 4 8 1 8 0 7 6 7 6 0 1 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 4 2 4 8 1 2 4 8 7 3 3 6 0 1 -> 3 4 2 4 8 1 5 2 6 0 0 0 0 7 6 0 0 1 , 4 5 8 7 3 4 8 7 3 6 1 8 0 1 -> 4 8 1 5 8 7 4 5 5 5 5 5 8 1 8 0 0 1 , 6 0 7 4 5 8 7 4 2 3 4 8 0 1 -> 6 1 5 5 5 5 8 1 5 5 2 6 0 0 0 0 7 4 , 6 0 1 8 7 4 5 8 0 1 5 8 0 1 -> 6 0 1 5 2 6 0 0 0 0 0 0 0 0 7 6 1 5 , 3 3 6 7 4 2 3 3 3 6 0 7 6 1 -> 6 0 1 5 5 5 8 1 5 8 0 0 7 3 6 7 6 1 , 4 2 6 0 7 3 3 3 6 7 6 7 6 1 -> 4 5 5 2 6 0 0 7 4 8 1 5 5 5 5 8 0 1 , 4 8 7 4 5 8 1 8 7 3 6 7 6 1 -> 4 5 5 8 1 5 5 5 8 1 5 5 5 8 1 5 8 1 , 4 8 7 3 4 5 5 2 3 3 6 7 6 1 -> 6 7 6 0 0 0 0 0 7 4 8 0 0 0 7 6 0 1 , 6 7 6 7 3 6 1 5 2 6 7 3 6 1 -> 6 0 1 2 6 0 0 7 4 5 2 6 0 0 0 0 0 1 , 4 2 3 4 2 6 0 7 4 8 7 3 6 1 -> 4 5 5 5 5 5 5 5 5 8 1 2 6 7 6 0 7 4 , 3 4 5 5 5 2 3 4 5 5 2 3 6 1 -> 4 8 1 5 5 5 5 8 1 5 5 8 1 5 5 5 2 4 , 3 4 2 4 2 6 0 7 6 0 1 2 6 1 -> 4 8 0 7 6 1 5 5 5 5 5 5 8 1 2 6 0 1 , 4 8 1 2 3 4 5 5 2 6 1 2 6 1 -> 4 5 8 0 1 8 1 2 6 0 0 0 0 0 0 0 0 1 , 3 3 3 6 7 4 8 1 8 1 5 2 6 1 -> 3 6 0 0 0 0 0 0 0 0 1 8 1 5 2 6 0 1 , 6 1 5 8 0 7 4 5 8 7 6 1 8 1 -> 6 1 2 6 0 0 0 0 0 0 0 1 2 6 0 0 0 1 , 6 1 5 8 7 4 5 8 7 3 6 1 8 1 -> 3 6 0 0 7 4 5 5 5 5 5 5 5 8 0 0 1 5 , 3 3 6 1 8 7 4 2 3 3 6 1 8 1 -> 6 7 6 0 0 0 7 6 0 7 6 1 5 5 8 1 8 1 , 3 3 6 0 0 7 6 1 2 6 7 4 8 1 -> 6 7 4 8 1 5 8 1 5 5 5 5 5 5 5 2 4 5 , 4 8 0 7 4 5 5 2 4 8 7 4 8 1 -> 4 2 6 1 8 7 6 0 0 0 0 0 0 0 0 0 0 1 , 6 7 3 6 1 8 1 5 2 4 2 4 8 1 -> 6 1 8 0 0 0 0 0 0 1 2 6 0 0 7 6 1 5 , 3 6 0 7 6 7 3 3 3 6 0 0 7 4 -> 6 1 2 6 0 0 0 0 0 0 0 0 0 7 6 1 5 5 , 6 1 2 6 7 4 2 4 8 7 6 0 7 4 -> 6 1 5 8 0 0 0 0 7 6 0 0 0 0 1 8 0 1 , 3 3 3 4 2 4 5 8 0 1 8 0 7 4 -> 6 0 1 8 1 2 6 0 0 0 0 0 7 4 8 7 6 1 , 4 2 6 0 7 4 5 2 6 1 8 0 7 4 -> 4 8 0 1 8 0 0 0 0 0 0 0 0 0 0 0 0 1 , 3 4 8 0 1 2 6 7 3 4 8 0 7 4 -> 3 6 1 5 5 8 1 5 5 2 6 0 0 1 8 0 7 4 , 3 3 4 8 7 3 6 0 1 5 8 0 7 4 -> 3 6 0 1 8 1 5 8 1 5 5 5 5 5 8 1 2 4 , 6 7 4 2 6 1 8 1 2 4 2 6 7 4 -> 6 1 2 4 5 5 5 2 6 0 0 0 0 7 6 0 1 5 , 3 6 7 6 0 0 7 3 3 6 1 8 7 4 -> 6 1 2 4 5 2 6 0 0 0 0 7 6 0 0 0 7 4 , 3 3 3 3 3 6 7 6 1 8 1 8 7 4 -> 3 6 0 7 4 8 1 8 1 5 5 5 5 5 8 7 3 4 , 3 6 1 8 7 4 8 0 7 3 4 8 7 4 -> 3 3 3 4 5 2 3 6 0 0 0 0 0 0 0 7 6 1 , 6 7 4 8 0 7 6 7 4 2 4 8 7 4 -> 6 0 1 8 0 7 4 5 5 2 6 0 0 0 0 7 4 5 , 4 2 6 1 8 7 3 3 4 2 4 8 7 4 -> 4 8 1 8 0 1 8 0 0 0 7 6 0 0 0 7 3 4 , 6 1 5 2 6 0 0 1 5 2 4 8 7 4 -> 4 8 7 6 1 5 5 5 5 5 5 5 5 5 5 8 0 1 , 4 2 6 7 4 2 3 6 7 6 0 7 3 4 -> 4 8 1 8 7 6 0 1 5 2 6 0 0 0 0 0 7 4 , 6 0 1 8 7 4 5 8 7 3 6 7 3 4 -> 3 6 0 0 1 2 4 5 5 5 2 6 0 0 0 7 6 1 , 4 2 4 8 7 4 8 7 6 1 8 7 3 4 -> 4 2 4 5 5 5 5 5 2 3 4 5 5 5 5 5 2 4 , 4 2 4 5 8 0 7 3 6 1 8 7 3 4 -> 4 8 0 0 0 0 1 5 2 6 0 0 0 0 7 4 8 1 , 4 8 7 3 6 7 3 6 0 0 7 3 3 4 -> 4 2 4 5 5 8 1 5 8 1 5 5 5 5 8 0 0 1 , 4 8 1 8 7 4 8 1 8 0 7 3 3 4 -> 4 5 5 5 8 1 5 8 1 5 5 5 2 6 1 8 7 4 , 4 2 4 8 0 7 4 5 5 5 2 3 3 4 -> 4 2 3 4 5 2 6 0 0 0 7 6 0 0 0 0 0 1 , 6 1 8 0 7 6 1 8 1 8 1 2 3 4 -> 3 4 5 5 5 8 1 5 5 2 6 0 0 0 7 6 1 5 , 4 5 8 1 8 7 6 0 0 7 4 2 3 4 -> 4 5 5 5 5 2 6 0 0 0 0 0 0 7 4 8 7 4 , 6 7 3 3 3 6 1 8 0 1 5 2 3 4 -> 6 0 7 4 5 5 5 2 6 7 4 2 6 0 0 0 1 5 , 6 0 1 5 2 4 5 2 3 6 0 1 2 4 -> 4 5 2 6 0 0 0 0 0 0 0 0 1 8 1 8 7 4 , 3 6 0 1 5 5 8 7 4 8 0 1 2 4 -> 3 6 7 4 5 8 1 8 1 5 5 2 6 0 0 0 0 1 , 3 3 6 7 3 3 3 6 0 7 6 1 2 4 -> 6 7 3 4 2 6 0 0 0 0 7 6 1 8 0 0 0 1 , 6 0 7 6 7 4 5 2 4 2 6 1 2 4 -> 6 0 7 6 7 4 5 5 5 5 8 1 2 6 0 0 7 4 , 3 6 0 7 4 5 8 0 1 2 3 4 2 4 -> 6 1 5 5 5 2 6 0 7 6 0 0 0 0 0 7 3 4 , 3 6 0 7 4 8 1 2 6 0 1 5 2 4 -> 4 5 5 5 5 5 5 5 8 1 5 5 5 5 8 7 6 1 , 3 3 4 2 6 1 5 5 2 6 1 5 2 4 -> 3 6 0 0 1 2 4 5 8 1 5 5 5 5 8 0 0 1 , 4 8 7 6 0 1 2 3 6 0 0 0 1 5 -> 4 5 5 5 8 1 8 1 5 5 5 2 6 0 0 7 6 1 , 3 3 3 6 7 6 7 4 2 4 8 0 1 5 -> 6 0 1 8 1 5 5 2 3 6 0 0 0 0 0 0 7 4 , 3 4 2 6 1 8 0 0 7 6 7 6 1 5 -> 6 0 0 0 0 0 0 0 7 6 0 7 6 0 7 6 1 5 , 4 8 7 3 4 8 0 7 3 6 1 8 1 5 -> 4 8 7 6 0 0 7 6 0 0 0 7 6 0 0 1 5 5 , 3 6 1 2 4 8 1 5 8 1 5 8 1 5 -> 6 1 5 2 6 0 0 0 0 0 0 0 0 1 5 5 5 5 , 3 4 5 5 2 4 2 4 2 4 8 7 4 5 -> 3 4 2 6 0 0 0 0 1 8 1 2 6 0 0 7 4 5 , 4 8 7 6 7 6 1 2 3 4 2 3 4 5 -> 4 2 4 5 5 5 5 5 8 1 2 6 0 1 8 1 5 5 , 6 7 6 1 8 0 1 8 1 5 2 3 4 5 -> 6 0 1 5 8 1 5 5 5 5 5 5 2 6 7 6 1 5 , 4 5 2 6 1 8 1 5 8 0 1 2 4 5 -> 4 8 1 5 5 5 5 5 2 6 0 1 8 0 0 0 1 5 , 4 2 6 0 7 3 4 5 5 8 1 2 4 5 -> 4 5 5 5 5 5 8 1 5 5 5 5 8 0 1 5 2 4 , 6 1 5 2 4 8 0 7 6 7 4 2 4 5 -> 3 6 0 0 7 4 2 6 0 0 0 0 0 7 3 4 5 5 , 6 7 4 2 4 5 5 5 2 4 5 2 4 5 -> 6 0 0 0 0 0 0 0 7 6 0 0 0 1 8 0 1 5 , 6 0 7 4 5 8 7 4 2 6 0 1 5 5 -> 6 1 5 8 1 5 8 1 5 8 1 5 5 5 5 5 5 5 , 6 1 2 6 1 2 4 2 4 8 0 1 5 5 -> 3 4 8 0 7 6 0 0 0 7 6 1 5 5 5 5 5 5 , 6 7 6 7 4 2 3 6 1 5 8 1 5 5 -> 3 6 0 1 8 0 7 4 5 5 5 5 5 5 5 5 5 5 , 6 1 8 1 5 2 4 2 4 5 8 1 5 5 -> 3 6 0 0 7 6 1 5 8 1 5 5 8 1 5 5 5 5 , 3 6 7 6 1 5 2 3 4 8 7 4 5 5 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 5 , 4 8 0 1 2 3 6 7 4 2 3 4 5 5 -> 4 5 5 5 5 8 0 0 1 2 6 0 0 0 1 5 5 5 , 6 7 4 8 0 1 8 1 2 4 5 2 4 5 ->= 6 1 2 4 5 5 5 5 5 8 1 5 5 8 1 2 3 4 , 6 1 2 3 4 5 2 4 2 6 0 0 0 7 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 7 , 3 4 8 1 2 3 4 8 7 4 8 0 0 7 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 7 , 6 7 3 6 1 5 8 7 4 5 8 0 0 7 -> 3 3 4 8 0 0 0 0 0 0 0 0 0 0 1 2 6 7 , 3 6 7 4 8 1 8 0 7 6 7 6 0 7 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 7 , 4 2 4 8 1 2 4 8 7 3 3 6 0 7 -> 3 4 2 4 8 1 5 2 6 0 0 0 0 7 6 0 0 7 , 4 5 8 7 3 4 8 7 3 6 1 8 0 7 -> 4 8 1 5 8 7 4 5 5 5 5 5 8 1 8 0 0 7 , 6 0 7 4 5 8 7 4 2 3 4 8 0 7 -> 6 1 5 5 5 5 8 1 5 5 2 6 0 0 0 0 7 3 , 6 0 1 8 7 4 5 8 0 1 5 8 0 7 -> 6 0 1 5 2 6 0 0 0 0 0 0 0 0 7 6 1 2 , 3 3 6 7 4 2 3 3 3 6 0 7 6 7 -> 6 0 1 5 5 5 8 1 5 8 0 0 7 3 6 7 6 7 , 4 2 6 0 7 3 3 3 6 7 6 7 6 7 -> 4 5 5 2 6 0 0 7 4 8 1 5 5 5 5 8 0 7 , 4 8 7 4 5 8 1 8 7 3 6 7 6 7 -> 4 5 5 8 1 5 5 5 8 1 5 5 5 8 1 5 8 7 , 4 8 7 3 4 5 5 2 3 3 6 7 6 7 -> 6 7 6 0 0 0 0 0 7 4 8 0 0 0 7 6 0 7 , 6 7 6 7 3 6 1 5 2 6 7 3 6 7 -> 6 0 1 2 6 0 0 7 4 5 2 6 0 0 0 0 0 7 , 4 2 3 4 2 6 0 7 4 8 7 3 6 7 -> 4 5 5 5 5 5 5 5 5 8 1 2 6 7 6 0 7 3 , 3 4 5 5 5 2 3 4 5 5 2 3 6 7 -> 4 8 1 5 5 5 5 8 1 5 5 8 1 5 5 5 2 3 , 3 4 2 4 2 6 0 7 6 0 1 2 6 7 -> 4 8 0 7 6 1 5 5 5 5 5 5 8 1 2 6 0 7 , 4 8 1 2 3 4 5 5 2 6 1 2 6 7 -> 4 5 8 0 1 8 1 2 6 0 0 0 0 0 0 0 0 7 , 3 3 3 6 7 4 8 1 8 1 5 2 6 7 -> 3 6 0 0 0 0 0 0 0 0 1 8 1 5 2 6 0 7 , 6 1 5 8 0 7 4 5 8 7 6 1 8 7 -> 6 1 2 6 0 0 0 0 0 0 0 1 2 6 0 0 0 7 , 6 1 5 8 7 4 5 8 7 3 6 1 8 7 -> 3 6 0 0 7 4 5 5 5 5 5 5 5 8 0 0 1 2 , 3 3 6 1 8 7 4 2 3 3 6 1 8 7 -> 6 7 6 0 0 0 7 6 0 7 6 1 5 5 8 1 8 7 , 3 3 6 0 0 7 6 1 2 6 7 4 8 7 -> 6 7 4 8 1 5 8 1 5 5 5 5 5 5 5 2 4 2 , 4 8 0 7 4 5 5 2 4 8 7 4 8 7 -> 4 2 6 1 8 7 6 0 0 0 0 0 0 0 0 0 0 7 , 6 7 3 6 1 8 1 5 2 4 2 4 8 7 -> 6 1 8 0 0 0 0 0 0 1 2 6 0 0 7 6 1 2 , 3 6 0 7 6 7 3 3 3 6 0 0 7 3 -> 6 1 2 6 0 0 0 0 0 0 0 0 0 7 6 1 5 2 , 6 1 2 6 7 4 2 4 8 7 6 0 7 3 -> 6 1 5 8 0 0 0 0 7 6 0 0 0 0 1 8 0 7 , 3 3 3 4 2 4 5 8 0 1 8 0 7 3 -> 6 0 1 8 1 2 6 0 0 0 0 0 7 4 8 7 6 7 , 4 2 6 0 7 4 5 2 6 1 8 0 7 3 -> 4 8 0 1 8 0 0 0 0 0 0 0 0 0 0 0 0 7 , 3 4 8 0 1 2 6 7 3 4 8 0 7 3 -> 3 6 1 5 5 8 1 5 5 2 6 0 0 1 8 0 7 3 , 3 3 4 8 7 3 6 0 1 5 8 0 7 3 -> 3 6 0 1 8 1 5 8 1 5 5 5 5 5 8 1 2 3 , 6 7 4 2 6 1 8 1 2 4 2 6 7 3 -> 6 1 2 4 5 5 5 2 6 0 0 0 0 7 6 0 1 2 , 3 6 7 6 0 0 7 3 3 6 1 8 7 3 -> 6 1 2 4 5 2 6 0 0 0 0 7 6 0 0 0 7 3 , 3 3 3 3 3 6 7 6 1 8 1 8 7 3 -> 3 6 0 7 4 8 1 8 1 5 5 5 5 5 8 7 3 3 , 3 6 1 8 7 4 8 0 7 3 4 8 7 3 -> 3 3 3 4 5 2 3 6 0 0 0 0 0 0 0 7 6 7 , 6 7 4 8 0 7 6 7 4 2 4 8 7 3 -> 6 0 1 8 0 7 4 5 5 2 6 0 0 0 0 7 4 2 , 4 2 6 1 8 7 3 3 4 2 4 8 7 3 -> 4 8 1 8 0 1 8 0 0 0 7 6 0 0 0 7 3 3 , 6 1 5 2 6 0 0 1 5 2 4 8 7 3 -> 4 8 7 6 1 5 5 5 5 5 5 5 5 5 5 8 0 7 , 4 2 6 7 4 2 3 6 7 6 0 7 3 3 -> 4 8 1 8 7 6 0 1 5 2 6 0 0 0 0 0 7 3 , 6 0 1 8 7 4 5 8 7 3 6 7 3 3 -> 3 6 0 0 1 2 4 5 5 5 2 6 0 0 0 7 6 7 , 4 2 4 8 7 4 8 7 6 1 8 7 3 3 -> 4 2 4 5 5 5 5 5 2 3 4 5 5 5 5 5 2 3 , 4 2 4 5 8 0 7 3 6 1 8 7 3 3 -> 4 8 0 0 0 0 1 5 2 6 0 0 0 0 7 4 8 7 , 4 8 7 3 6 7 3 6 0 0 7 3 3 3 -> 4 2 4 5 5 8 1 5 8 1 5 5 5 5 8 0 0 7 , 4 8 1 8 7 4 8 1 8 0 7 3 3 3 -> 4 5 5 5 8 1 5 8 1 5 5 5 2 6 1 8 7 3 , 4 2 4 8 0 7 4 5 5 5 2 3 3 3 -> 4 2 3 4 5 2 6 0 0 0 7 6 0 0 0 0 0 7 , 6 1 8 0 7 6 1 8 1 8 1 2 3 3 -> 3 4 5 5 5 8 1 5 5 2 6 0 0 0 7 6 1 2 , 4 5 8 1 8 7 6 0 0 7 4 2 3 3 -> 4 5 5 5 5 2 6 0 0 0 0 0 0 7 4 8 7 3 , 6 7 3 3 3 6 1 8 0 1 5 2 3 3 -> 6 0 7 4 5 5 5 2 6 7 4 2 6 0 0 0 1 2 , 6 0 1 5 2 4 5 2 3 6 0 1 2 3 -> 4 5 2 6 0 0 0 0 0 0 0 0 1 8 1 8 7 3 , 3 6 0 1 5 5 8 7 4 8 0 1 2 3 -> 3 6 7 4 5 8 1 8 1 5 5 2 6 0 0 0 0 7 , 3 3 6 7 3 3 3 6 0 7 6 1 2 3 -> 6 7 3 4 2 6 0 0 0 0 7 6 1 8 0 0 0 7 , 6 0 7 6 7 4 5 2 4 2 6 1 2 3 -> 6 0 7 6 7 4 5 5 5 5 8 1 2 6 0 0 7 3 , 3 6 0 7 4 5 8 0 1 2 3 4 2 3 -> 6 1 5 5 5 2 6 0 7 6 0 0 0 0 0 7 3 3 , 3 6 0 7 4 8 1 2 6 0 1 5 2 3 -> 4 5 5 5 5 5 5 5 8 1 5 5 5 5 8 7 6 7 , 3 3 4 2 6 1 5 5 2 6 1 5 2 3 -> 3 6 0 0 1 2 4 5 8 1 5 5 5 5 8 0 0 7 , 4 8 7 6 0 1 2 3 6 0 0 0 1 2 -> 4 5 5 5 8 1 8 1 5 5 5 2 6 0 0 7 6 7 , 3 3 3 6 7 6 7 4 2 4 8 0 1 2 -> 6 0 1 8 1 5 5 2 3 6 0 0 0 0 0 0 7 3 , 3 4 2 6 1 8 0 0 7 6 7 6 1 2 -> 6 0 0 0 0 0 0 0 7 6 0 7 6 0 7 6 1 2 , 4 8 7 3 4 8 0 7 3 6 1 8 1 2 -> 4 8 7 6 0 0 7 6 0 0 0 7 6 0 0 1 5 2 , 3 6 1 2 4 8 1 5 8 1 5 8 1 2 -> 6 1 5 2 6 0 0 0 0 0 0 0 0 1 5 5 5 2 , 3 4 5 5 2 4 2 4 2 4 8 7 4 2 -> 3 4 2 6 0 0 0 0 1 8 1 2 6 0 0 7 4 2 , 4 8 7 6 7 6 1 2 3 4 2 3 4 2 -> 4 2 4 5 5 5 5 5 8 1 2 6 0 1 8 1 5 2 , 6 7 6 1 8 0 1 8 1 5 2 3 4 2 -> 6 0 1 5 8 1 5 5 5 5 5 5 2 6 7 6 1 2 , 4 5 2 6 1 8 1 5 8 0 1 2 4 2 -> 4 8 1 5 5 5 5 5 2 6 0 1 8 0 0 0 1 2 , 4 2 6 0 7 3 4 5 5 8 1 2 4 2 -> 4 5 5 5 5 5 8 1 5 5 5 5 8 0 1 5 2 3 , 6 1 5 2 4 8 0 7 6 7 4 2 4 2 -> 3 6 0 0 7 4 2 6 0 0 0 0 0 7 3 4 5 2 , 6 7 4 2 4 5 5 5 2 4 5 2 4 2 -> 6 0 0 0 0 0 0 0 7 6 0 0 0 1 8 0 1 2 , 6 0 7 4 5 8 7 4 2 6 0 1 5 2 -> 6 1 5 8 1 5 8 1 5 8 1 5 5 5 5 5 5 2 , 6 1 2 6 1 2 4 2 4 8 0 1 5 2 -> 3 4 8 0 7 6 0 0 0 7 6 1 5 5 5 5 5 2 , 6 7 6 7 4 2 3 6 1 5 8 1 5 2 -> 3 6 0 1 8 0 7 4 5 5 5 5 5 5 5 5 5 2 , 6 1 8 1 5 2 4 2 4 5 8 1 5 2 -> 3 6 0 0 7 6 1 5 8 1 5 5 8 1 5 5 5 2 , 3 6 7 6 1 5 2 3 4 8 7 4 5 2 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 2 , 4 8 0 1 2 3 6 7 4 2 3 4 5 2 -> 4 5 5 5 5 8 0 0 1 2 6 0 0 0 1 5 5 2 , 6 7 4 8 0 1 8 1 2 4 5 2 4 2 ->= 6 1 2 4 5 5 5 5 5 8 1 5 5 8 1 2 3 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 5 | | 0 1 | \ / 3 is interpreted by / \ | 1 5 | | 0 1 | \ / 4 is interpreted by / \ | 1 3 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 3 | | 0 1 | \ / 8 is interpreted by / \ | 1 4 | | 0 1 | \ / After renaming modulo { 7->0, 6->1, 0->2, 1->3, 5->4, 8->5, 4->6, 2->7, 3->8 }, it remains to prove termination of the 3-rule system { 0 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 0 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 , 7 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 7 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 , 8 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 8 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 0->6, 6->7, 8->8 }, it remains to prove termination of the 2-rule system { 0 1 2 3 4 4 5 6 7 5 2 3 0 1 -> 0 1 6 7 4 5 3 5 3 4 4 0 1 2 2 2 2 2 , 8 1 2 3 4 4 5 6 7 5 2 3 0 1 -> 8 1 6 7 4 5 3 5 3 4 4 0 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 8->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 0->8 }, it remains to prove termination of the 1-rule system { 0 1 2 3 4 4 5 6 7 5 2 3 8 1 -> 0 1 6 7 4 5 3 5 3 4 4 8 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.