/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, 3->3, 4->4 }, it remains to prove termination of the 99-rule system { 0 0 0 1 2 2 3 3 2 3 0 0 2 1 1 4 0 2 4 2 -> 4 4 1 1 0 1 4 4 3 3 1 1 0 1 0 1 1 1 1 2 , 0 0 0 3 1 1 4 2 2 0 1 2 1 4 3 0 4 0 3 0 -> 0 2 2 4 0 1 3 2 0 1 1 4 0 4 2 0 1 4 4 4 , 0 0 3 2 0 1 0 3 3 3 3 3 0 2 0 2 2 4 2 0 -> 0 0 3 3 4 1 1 1 2 0 2 2 0 4 2 4 0 1 4 0 , 0 1 0 0 1 1 3 3 4 4 2 3 0 0 3 4 4 2 1 4 -> 1 0 2 4 1 3 1 4 1 1 3 4 1 4 2 1 0 1 4 4 , 0 1 2 0 1 4 3 4 3 0 3 0 2 2 1 3 1 4 2 4 -> 1 0 1 2 4 1 3 0 3 1 1 1 2 0 1 0 0 2 0 1 , 0 1 3 0 0 4 1 1 4 3 2 4 1 3 4 0 2 4 1 4 -> 0 2 0 0 2 2 0 4 1 0 0 4 4 2 2 2 4 4 0 0 , 0 1 4 1 2 0 0 3 4 2 3 1 4 0 4 1 0 4 4 2 -> 4 1 3 0 0 1 0 0 0 4 0 4 2 0 1 3 2 4 0 2 , 0 2 0 0 3 3 4 2 1 1 4 4 2 2 1 1 4 2 0 1 -> 0 0 0 1 4 4 2 0 1 1 0 2 0 2 2 4 4 1 4 4 , 0 2 1 2 2 2 4 3 3 4 2 3 2 2 3 1 0 2 1 3 -> 1 2 1 1 4 2 4 3 0 4 1 1 2 0 4 0 2 1 0 0 , 0 2 1 3 1 1 3 0 3 1 4 2 3 3 0 4 2 2 2 3 -> 1 2 3 0 1 2 3 0 0 4 3 0 0 4 0 0 0 4 4 0 , 0 2 2 4 4 3 0 2 1 4 1 4 3 0 4 2 3 1 2 0 -> 3 4 2 2 2 4 0 3 2 2 4 1 0 0 1 4 0 0 0 0 , 0 2 3 4 4 3 3 1 0 1 1 4 4 3 0 2 3 4 0 2 -> 0 4 1 1 0 4 3 1 0 1 2 2 4 3 4 0 0 1 4 3 , 0 3 0 2 3 0 0 0 2 1 4 4 4 2 3 3 3 1 3 4 -> 0 2 0 4 4 4 4 4 2 2 3 2 3 3 3 2 4 4 0 0 , 0 3 2 0 1 3 3 3 2 3 0 1 2 4 1 0 4 0 0 1 -> 4 0 0 2 2 3 1 0 4 0 0 2 2 2 1 1 3 0 4 0 , 0 3 3 0 2 1 3 3 2 1 4 4 2 0 2 4 1 1 4 0 -> 0 0 2 1 3 4 0 1 4 1 3 4 4 0 1 4 4 2 3 3 , 0 3 3 4 3 1 1 2 2 4 2 2 1 2 1 0 1 1 2 3 -> 0 4 2 0 0 0 0 3 0 4 1 2 4 4 4 1 0 2 0 0 , 0 3 4 0 4 4 4 0 4 0 1 4 0 3 4 4 4 4 4 2 -> 0 4 1 3 2 0 3 4 1 0 1 4 1 3 1 2 0 3 1 1 , 0 4 0 3 0 2 0 4 2 4 0 0 0 0 2 0 3 2 2 1 -> 1 2 2 2 4 0 4 1 2 3 1 1 0 4 0 2 3 2 0 1 , 0 4 0 4 0 3 2 0 3 3 0 3 4 2 0 3 4 3 2 2 -> 2 0 4 0 4 2 2 3 4 0 1 2 2 0 4 1 1 3 1 1 , 0 4 1 2 1 2 0 0 2 3 2 2 4 2 2 3 4 4 0 0 -> 2 2 2 4 1 0 2 0 0 0 4 0 2 2 2 2 1 1 0 0 , 0 4 2 3 2 3 3 0 4 3 1 3 0 4 2 3 1 3 4 2 -> 3 2 4 1 3 3 3 2 0 2 1 4 0 1 2 4 0 0 2 2 , 1 0 0 2 3 3 0 2 1 2 4 1 1 0 1 1 4 4 4 3 -> 0 4 0 2 2 4 1 0 2 4 0 0 1 0 2 4 3 1 1 1 , 1 0 1 3 3 0 0 2 4 3 4 3 4 1 1 3 2 2 2 3 -> 0 0 4 4 0 3 1 0 3 1 4 1 4 2 3 3 1 1 2 3 , 1 0 2 4 0 3 1 3 4 0 2 4 4 4 4 2 0 3 0 4 -> 3 3 2 3 0 0 0 1 1 4 4 3 1 4 1 2 2 4 0 1 , 1 0 3 0 3 4 4 2 4 3 4 4 2 1 1 2 4 1 1 4 -> 3 3 4 1 2 4 4 4 4 0 2 2 3 4 0 4 2 2 3 4 , 1 0 3 3 2 0 1 1 2 0 4 4 4 4 2 0 4 3 4 3 -> 1 2 4 0 0 3 2 1 2 4 0 2 1 3 1 2 2 4 3 1 , 1 1 0 1 2 0 1 4 2 3 0 3 4 2 2 1 4 0 0 3 -> 1 4 1 3 0 3 0 4 0 2 2 2 0 1 0 0 1 1 0 1 , 1 1 2 1 4 4 3 1 1 4 0 1 2 4 4 2 0 1 4 4 -> 1 3 0 2 2 4 2 4 0 1 0 0 2 4 0 2 1 0 1 4 , 1 1 3 2 4 1 3 3 2 1 4 2 2 4 4 2 2 3 2 2 -> 0 1 2 2 2 3 3 2 0 3 2 2 0 1 2 2 1 1 3 2 , 1 1 3 3 2 2 2 1 2 1 4 0 0 3 2 1 1 3 0 1 -> 1 2 2 2 3 1 0 1 1 2 1 0 0 1 3 4 2 2 0 2 , 1 1 3 4 1 3 2 0 2 0 3 0 3 0 1 1 1 2 4 0 -> 4 1 2 0 4 2 4 1 2 2 0 0 1 2 2 1 2 1 4 1 , 1 1 4 0 3 2 1 3 4 4 1 0 4 2 3 2 3 2 4 1 -> 0 1 1 4 4 3 1 1 0 3 1 1 2 4 1 3 0 1 4 3 , 1 1 4 3 1 1 4 1 2 3 1 4 2 2 3 3 0 3 4 4 -> 4 1 2 3 3 2 2 0 0 2 2 1 0 4 0 2 1 1 2 1 , 1 2 1 3 1 2 1 3 0 3 4 2 4 4 0 2 0 1 3 4 -> 0 2 1 1 1 4 4 4 3 2 1 4 0 0 1 3 0 4 4 1 , 1 2 1 4 0 2 0 2 2 0 2 1 3 4 1 4 3 0 0 3 -> 1 3 1 1 1 1 3 1 1 1 3 0 0 4 2 2 4 2 4 1 , 1 2 2 4 0 1 2 1 1 1 1 3 4 1 3 3 1 3 3 3 -> 4 1 0 3 4 2 4 1 4 0 4 0 2 4 0 1 2 0 2 4 , 1 2 3 1 4 3 4 4 1 0 1 4 0 4 1 4 2 3 3 0 -> 2 4 0 0 0 3 4 4 1 0 3 3 0 4 0 4 0 1 1 0 , 1 2 4 0 2 1 4 0 4 4 1 4 1 0 4 4 2 2 4 3 -> 1 2 2 2 0 1 0 4 0 4 3 0 4 2 4 0 1 1 2 4 , 1 3 3 1 1 0 0 3 2 0 1 4 4 1 4 2 4 0 3 0 -> 3 1 0 0 0 0 0 2 4 1 4 0 1 0 1 4 0 3 4 4 , 1 3 3 1 2 2 4 0 1 1 2 2 1 3 4 3 1 4 2 1 -> 2 4 0 4 1 2 4 0 3 1 4 4 4 0 1 3 0 2 2 0 , 1 4 0 3 2 4 3 2 0 1 0 3 0 4 1 2 1 1 0 3 -> 1 4 4 0 1 2 2 1 3 3 1 0 2 0 1 1 0 3 4 4 , 1 4 0 4 0 4 4 0 4 4 2 1 4 4 2 0 4 4 4 0 -> 0 2 0 4 2 2 0 4 1 4 1 0 1 2 1 0 0 0 3 3 , 1 4 1 2 0 2 1 2 2 1 4 1 4 3 4 0 4 0 3 1 -> 3 3 3 1 4 2 4 0 2 0 4 0 1 4 0 1 0 0 0 0 , 1 4 1 2 4 3 4 3 4 1 2 1 1 2 3 3 0 2 4 2 -> 0 2 1 2 2 2 4 0 4 1 1 0 0 4 4 4 4 4 4 0 , 1 4 3 2 2 1 3 4 1 1 1 3 2 4 1 4 0 4 3 0 -> 4 1 2 3 0 1 1 4 3 0 1 2 4 0 2 4 2 2 3 4 , 1 4 4 0 1 2 2 1 1 4 1 3 0 4 3 2 4 0 4 0 -> 0 0 2 1 2 0 4 0 1 1 4 1 0 0 1 2 2 2 4 1 , 1 4 4 2 0 1 3 3 1 4 4 4 1 2 1 1 3 4 4 1 -> 3 0 1 0 0 3 4 0 2 2 1 0 4 0 4 4 3 0 1 0 , 2 0 1 0 1 2 0 0 2 0 2 2 4 4 3 1 0 2 3 2 -> 0 1 1 3 2 2 2 4 0 0 0 0 1 3 4 2 2 0 1 2 , 2 0 2 2 4 1 2 3 4 4 1 1 0 2 4 2 3 0 0 4 -> 1 4 1 0 1 1 2 3 0 0 2 2 2 2 0 1 1 1 2 2 , 2 0 3 3 0 3 3 3 3 3 4 3 3 1 0 2 2 3 2 2 -> 4 1 3 3 0 2 0 3 1 3 4 0 3 1 4 2 1 4 1 4 , 2 1 0 4 3 2 4 0 3 3 3 2 2 4 4 4 2 3 2 4 -> 1 0 4 0 0 3 3 0 1 3 0 4 2 2 4 4 0 1 0 0 , 2 1 4 1 4 3 0 4 0 1 4 3 2 0 2 3 3 0 4 4 -> 4 0 1 2 4 3 1 1 1 2 0 4 2 0 1 1 3 4 1 3 , 2 2 2 1 4 4 3 0 4 1 3 2 3 1 0 1 0 3 4 0 -> 1 2 0 0 2 3 0 4 1 1 2 0 2 0 1 0 4 0 2 0 , 2 2 3 3 1 3 1 2 0 1 3 0 0 3 0 0 0 4 3 4 -> 0 4 1 4 3 1 4 0 1 2 0 3 1 2 4 2 2 2 2 1 , 2 3 0 2 3 1 2 4 0 3 2 0 0 3 1 3 4 4 1 1 -> 4 4 4 4 0 1 0 4 0 0 4 1 4 4 0 1 2 2 0 4 , 2 3 3 3 3 0 4 0 4 4 2 2 0 3 2 1 3 3 1 4 -> 4 3 2 0 4 4 4 1 4 1 1 4 1 2 2 4 4 4 1 3 , 2 4 0 1 4 4 1 4 3 1 3 0 0 4 3 3 1 3 1 3 -> 0 3 1 1 1 2 3 3 1 0 2 2 0 2 3 1 1 1 1 1 , 2 4 0 2 1 3 0 4 4 4 1 1 4 4 1 1 1 1 3 2 -> 0 1 1 4 0 0 2 0 3 0 0 2 0 1 2 0 1 3 3 1 , 2 4 1 4 3 3 1 1 4 3 0 0 1 0 0 2 3 1 1 1 -> 2 2 4 1 2 1 4 2 2 4 0 0 1 4 2 2 0 2 1 1 , 2 4 2 0 3 4 4 1 1 1 4 1 1 2 3 2 3 3 3 3 -> 0 3 3 0 1 3 3 3 0 1 2 2 2 1 3 1 0 1 0 3 , 2 4 2 1 1 4 2 2 1 0 3 2 3 4 1 0 3 2 3 4 -> 1 0 1 4 0 1 1 4 3 4 4 1 3 0 0 3 4 0 0 4 , 2 4 2 3 3 3 2 2 3 3 3 0 4 1 0 0 1 4 0 1 -> 3 2 3 2 4 0 2 1 1 2 2 0 1 1 1 0 3 2 2 0 , 2 4 2 4 4 4 1 3 0 1 1 1 4 1 1 0 2 2 3 2 -> 4 0 2 0 1 1 1 2 2 1 4 0 1 0 0 3 3 0 4 0 , 2 4 3 0 1 3 4 1 0 2 4 4 4 1 3 1 0 3 0 4 -> 0 3 0 4 4 1 0 3 1 0 0 0 0 1 0 0 0 1 3 2 , 2 4 3 3 0 4 4 4 4 4 3 3 4 0 2 3 0 1 4 4 -> 3 1 2 0 1 1 2 0 3 3 1 4 0 2 2 4 2 3 4 1 , 2 4 3 4 4 0 0 4 2 1 1 3 1 3 1 1 2 3 4 0 -> 0 3 0 4 1 1 4 1 4 0 3 2 2 0 0 2 4 0 1 4 , 2 4 4 2 3 0 0 1 4 2 2 4 4 4 3 1 2 2 1 4 -> 3 1 1 4 1 2 1 4 2 0 1 4 1 4 2 2 1 1 4 4 , 3 0 3 1 0 3 2 4 4 4 0 1 1 1 2 1 1 0 1 3 -> 4 3 4 1 3 0 1 4 1 1 1 2 3 4 1 2 1 0 0 0 , 3 1 1 0 3 4 4 2 4 1 1 2 0 0 4 4 2 3 4 1 -> 1 3 4 0 1 3 0 1 1 2 2 4 0 0 2 0 1 3 3 4 , 3 1 1 2 1 3 2 1 1 2 0 2 3 0 0 0 0 4 0 3 -> 0 4 0 0 0 2 0 4 0 1 4 0 2 1 0 1 3 3 4 3 , 3 1 3 0 2 0 3 1 1 0 0 0 0 3 3 2 4 3 1 2 -> 1 4 3 2 0 0 1 2 1 1 4 4 1 4 1 4 1 2 0 0 , 3 1 3 1 2 1 1 3 1 1 1 2 2 0 4 4 2 2 3 4 -> 2 1 3 4 4 0 0 4 0 0 1 1 4 0 1 4 2 2 4 1 , 3 1 4 0 1 2 4 2 1 4 1 3 1 3 0 1 2 4 3 3 -> 1 4 3 1 1 0 4 3 3 4 2 4 0 3 0 2 2 2 3 0 , 3 1 4 0 4 1 0 3 1 3 0 1 1 2 4 4 2 2 0 1 -> 1 3 0 1 4 1 1 2 1 0 0 0 0 0 1 0 2 2 2 2 , 3 2 0 3 2 0 0 3 3 3 3 4 1 4 3 1 1 2 3 3 -> 1 1 0 4 1 2 2 1 4 2 4 3 3 1 3 2 1 1 2 1 , 3 2 0 4 1 3 2 1 4 3 2 4 4 1 0 2 4 2 2 3 -> 4 2 0 1 1 1 1 3 2 0 2 4 2 2 3 1 4 1 4 2 , 3 2 2 3 0 2 2 0 2 1 2 4 3 4 2 1 1 3 3 0 -> 4 3 0 3 4 4 4 1 4 3 1 4 3 0 1 0 3 4 3 1 , 3 3 2 4 1 2 1 4 0 2 1 4 2 2 1 4 2 1 1 0 -> 3 2 1 2 2 0 2 0 0 3 2 0 2 1 1 4 1 2 2 4 , 3 3 3 4 0 1 4 0 0 2 3 0 3 0 0 1 0 3 1 0 -> 4 4 3 1 0 0 3 1 1 4 0 0 2 3 2 1 2 2 2 1 , 3 3 4 2 1 4 4 2 0 1 0 1 4 1 1 2 0 0 1 4 -> 4 1 4 4 0 2 1 1 2 2 3 1 1 0 1 0 2 3 4 0 , 3 4 0 1 4 1 4 3 3 4 0 0 4 1 0 3 2 3 2 4 -> 4 2 3 1 4 0 4 4 0 1 3 2 1 0 4 1 4 0 2 0 , 3 4 3 1 2 3 3 0 2 0 1 0 2 2 0 2 0 4 3 0 -> 4 4 3 2 0 3 4 1 2 1 2 0 1 4 4 2 4 0 0 0 , 3 4 4 0 2 0 2 3 0 1 4 2 2 2 3 3 0 4 0 0 -> 3 0 2 2 0 1 2 4 3 3 1 2 4 1 2 2 1 3 0 0 , 3 4 4 0 4 2 1 1 3 0 4 4 3 2 4 0 4 1 4 4 -> 3 1 1 1 0 2 1 4 2 2 2 0 1 3 0 2 3 3 3 3 , 4 0 0 0 3 1 4 2 3 3 3 3 3 3 1 4 3 2 0 2 -> 3 3 4 1 1 4 2 4 1 0 0 4 0 3 1 4 2 0 4 4 , 4 0 2 0 3 3 1 4 2 4 2 3 1 3 4 0 4 4 3 1 -> 3 1 0 2 4 0 3 3 1 4 0 1 4 4 0 0 2 1 4 3 , 4 0 3 2 3 1 2 1 3 1 0 4 4 1 2 3 2 3 1 4 -> 2 2 3 1 1 3 1 0 0 1 4 4 2 4 0 3 1 2 0 3 , 4 0 4 0 1 3 2 3 1 2 3 3 1 1 1 4 2 0 3 2 -> 0 0 4 1 0 2 3 0 1 2 1 2 3 0 0 0 1 1 0 0 , 4 1 0 3 2 4 1 3 0 3 4 3 4 2 2 3 2 0 0 1 -> 4 3 0 0 3 4 0 3 4 4 4 4 2 2 1 2 2 3 1 1 , 4 1 2 2 2 3 1 2 2 4 3 4 1 2 1 2 2 0 0 3 -> 3 1 1 0 3 1 0 4 1 0 4 0 3 0 0 1 0 4 4 0 , 4 1 4 2 3 0 3 2 2 3 1 1 4 3 0 3 0 4 0 4 -> 1 2 0 4 1 4 4 3 1 1 4 1 0 2 2 0 0 3 4 3 , 4 2 0 4 4 0 3 1 1 2 4 3 0 3 2 3 2 0 1 3 -> 3 3 4 3 4 0 2 2 0 1 0 1 3 4 1 3 2 0 4 4 , 4 2 2 0 2 2 2 1 1 3 2 0 0 2 4 4 1 4 2 1 -> 2 0 3 4 4 3 3 0 0 1 1 2 2 4 1 0 0 4 0 0 , 4 2 2 1 0 2 3 0 3 3 3 1 4 4 2 4 4 0 1 1 -> 1 1 4 0 4 2 2 3 4 3 4 2 4 1 4 1 3 3 1 1 , 4 2 2 4 3 1 4 1 1 2 1 2 0 4 2 1 1 4 1 0 -> 1 1 1 0 3 4 4 1 0 2 4 1 2 0 0 4 0 1 3 0 , 4 3 1 0 1 1 2 2 0 0 4 2 1 3 1 3 1 2 2 4 -> 1 2 2 1 2 0 0 4 1 1 4 0 0 2 0 3 1 0 1 0 , 4 3 4 4 4 4 2 1 2 0 0 3 3 3 1 2 0 2 4 0 -> 2 1 1 3 3 2 0 0 2 1 1 2 1 4 1 0 0 1 3 0 , 4 4 0 2 1 4 2 1 4 0 2 2 1 4 3 4 2 1 1 1 -> 4 3 4 1 4 2 0 3 4 3 1 1 2 1 1 4 3 1 1 1 , 4 4 2 0 4 2 4 1 4 3 3 2 3 4 1 4 0 0 2 4 -> 3 0 4 0 4 0 3 0 0 2 1 4 0 0 0 0 3 4 4 0 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,2)->3, (2,3)->4, (3,3)->5, (3,2)->6, (3,0)->7, (0,2)->8, (2,1)->9, (1,1)->10, (1,4)->11, (4,0)->12, (2,4)->13, (4,2)->14, (2,0)->15, (0,4)->16, (4,4)->17, (4,1)->18, (1,0)->19, (4,3)->20, (3,1)->21, (2,6)->22, (3,4)->23, (5,0)->24, (5,4)->25, (0,3)->26, (1,3)->27, (0,6)->28, (4,6)->29, (5,1)->30, (1,6)->31, (3,6)->32, (5,3)->33, (5,2)->34 }, it remains to prove termination of the 3564-rule system { 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 0 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 16 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 19 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 11 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 15 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 13 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 7 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 23 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 12 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 17 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 15 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 15 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 9 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 9 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 3 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 3 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 4 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 4 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 13 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 13 , 24 0 0 1 2 3 4 5 6 4 7 0 8 9 10 11 12 8 13 14 22 -> 25 17 18 10 19 1 11 17 20 5 21 10 19 1 19 1 10 10 10 2 22 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 0 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 0 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 19 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 19 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 15 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 15 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 7 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 7 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 12 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 12 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 0 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 12 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 1 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 18 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 8 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 14 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 26 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 20 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 16 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 17 , 24 0 0 26 21 10 11 14 3 15 1 2 9 11 20 7 16 12 26 7 28 -> 24 8 3 13 12 1 27 6 15 1 10 11 12 16 14 15 1 11 17 17 29 , 0 0 26 6 15 1 19 26 5 5 5 5 7 8 15 8 3 13 14 15 0 -> 0 0 26 5 23 18 10 10 2 15 8 3 15 16 14 13 12 1 11 12 0 , 0 0 26 6 15 1 19 26 5 5 5 5 7 8 15 8 3 13 14 15 1 -> 0 0 26 5 23 18 10 10 2 15 8 3 15 16 14 13 12 1 11 12 1 , 0 0 26 6 15 1 19 26 5 5 5 5 7 8 15 8 3 13 14 15 8 -> 0 0 26 5 23 18 10 10 2 15 8 3 15 16 14 13 12 1 11 12 8 , 0 0 26 6 15 1 19 26 5 5 5 5 7 8 15 8 3 13 14 15 26 -> 0 0 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19 0 1 27 7 1 , 25 20 23 17 17 17 14 9 2 15 0 26 5 5 21 2 15 8 13 12 8 -> 34 9 10 27 5 6 15 0 8 9 10 2 9 11 18 19 0 1 27 7 8 , 25 20 23 17 17 17 14 9 2 15 0 26 5 5 21 2 15 8 13 12 26 -> 34 9 10 27 5 6 15 0 8 9 10 2 9 11 18 19 0 1 27 7 26 , 25 20 23 17 17 17 14 9 2 15 0 26 5 5 21 2 15 8 13 12 16 -> 34 9 10 27 5 6 15 0 8 9 10 2 9 11 18 19 0 1 27 7 16 , 25 20 23 17 17 17 14 9 2 15 0 26 5 5 21 2 15 8 13 12 28 -> 34 9 10 27 5 6 15 0 8 9 10 2 9 11 18 19 0 1 27 7 28 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 16 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 16 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 11 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 11 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 13 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 13 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 23 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 23 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 17 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 17 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 19 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 19 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 10 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 10 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 2 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 2 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 27 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 27 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 11 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 11 , 25 17 12 8 9 11 14 9 11 12 8 3 9 11 20 23 14 9 10 10 31 -> 25 20 23 18 11 14 15 26 23 20 21 10 2 9 10 11 20 21 10 10 31 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 16 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 26 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 11 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 27 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 13 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 4 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 23 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 5 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 17 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 20 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 12 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 0 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 18 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 1 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 14 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 8 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 20 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 26 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 17 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 16 , 25 17 14 15 16 14 13 18 11 20 5 6 4 23 18 11 12 0 8 13 29 -> 33 7 16 12 16 12 26 7 0 8 9 11 12 0 0 0 26 23 17 12 28 } 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 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 3 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 3 | | 0 1 | \ / 5 is interpreted by / \ | 1 7 | | 0 1 | \ / 6 is interpreted by / \ | 1 9 | | 0 1 | \ / 7 is interpreted by / \ | 1 4 | | 0 1 | \ / 8 is interpreted by / \ | 1 4 | | 0 1 | \ / 9 is interpreted by / \ | 1 4 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 2 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 8 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 3 | | 0 1 | \ / 17 is interpreted by / \ | 1 4 | | 0 1 | \ / 18 is interpreted by / \ | 1 1 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 5 | | 0 1 | \ / 21 is interpreted by / \ | 1 3 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 4 | | 0 1 | \ / 24 is interpreted by / \ | 1 0 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 5 | | 0 1 | \ / 27 is interpreted by / \ | 1 5 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 is interpreted by / \ | 1 0 | | 0 1 | \ / 30 is interpreted by / \ | 1 1 | | 0 1 | \ / 31 is interpreted by / \ | 1 0 | | 0 1 | \ / 32 is interpreted by / \ | 1 0 | | 0 1 | \ / 33 is interpreted by / \ | 1 1 | | 0 1 | \ / 34 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 26->1, 21->2, 10->3, 11->4, 14->5, 3->6, 15->7, 1->8, 2->9, 9->10, 20->11, 7->12, 16->13, 12->14, 8->15, 13->16, 27->17, 6->18, 17->19, 19->20, 24->21, 4->22, 18->23, 5->24, 32->25, 23->26, 28->27 }, it remains to prove termination of the 7-rule system { 0 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 0 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 20 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 20 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 7 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 7 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 12 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 12 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 14 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 14 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 21 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 21 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 22 2 4 14 8 9 16 5 10 4 23 17 2 17 12 8 9 16 11 24 25 -> 10 4 11 2 3 20 13 11 24 26 5 16 14 1 12 15 6 6 22 12 27 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, it remains to prove termination of the 6-rule system { 0 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 0 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 20 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 20 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 7 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 7 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 12 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 12 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 14 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 14 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 , 21 0 0 1 2 3 4 5 6 7 8 9 10 4 11 12 13 14 1 12 15 -> 21 15 6 16 14 8 17 18 7 8 3 4 14 13 5 7 8 4 19 19 5 } 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 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 1 | | 0 1 | \ / 10 is interpreted by / \ | 1 1 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.