/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 19-rule system { 0 0 0 1 0 2 0 2 1 2 0 2 2 -> 0 0 1 0 1 1 0 2 1 0 0 0 1 0 1 1 0 , 0 0 0 1 1 2 1 2 1 1 0 0 0 -> 1 0 0 2 2 2 2 1 1 2 0 2 0 0 2 1 0 , 0 1 0 1 0 0 1 0 0 2 1 2 0 -> 0 1 0 2 0 0 2 1 0 0 0 0 0 1 0 0 0 , 0 1 2 0 2 0 1 1 1 1 0 0 2 -> 0 0 0 0 0 2 0 2 2 0 2 2 2 0 0 0 0 , 0 1 2 1 1 0 0 2 2 1 0 2 2 -> 1 0 0 2 1 0 0 2 0 0 0 2 0 2 2 2 2 , 0 1 2 2 0 0 2 0 0 0 2 0 2 -> 2 1 0 0 0 2 1 1 0 2 0 1 0 2 1 0 2 , 0 2 0 1 0 1 1 0 1 2 0 0 1 -> 0 1 1 0 0 0 2 1 1 1 0 2 0 0 2 0 1 , 1 0 0 1 0 2 2 0 0 1 2 0 0 -> 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 2 0 , 1 0 1 1 1 2 2 2 2 1 0 0 0 -> 2 1 0 0 1 0 1 0 2 2 1 1 0 0 2 2 2 , 1 1 0 0 1 0 0 0 0 1 1 1 2 -> 1 1 0 2 1 0 0 2 1 0 1 0 0 2 0 1 2 , 1 1 2 0 1 0 2 1 2 0 1 0 2 -> 1 1 2 1 0 1 0 2 1 1 1 0 1 0 2 0 2 , 1 1 2 2 1 1 2 1 0 0 1 0 2 -> 0 0 2 0 2 0 0 0 2 0 0 2 0 0 2 2 2 , 2 0 0 0 1 1 2 1 0 2 2 0 0 -> 1 1 0 2 0 1 0 2 2 1 1 1 0 2 2 0 0 , 2 0 0 1 1 2 2 1 0 2 2 2 2 -> 1 0 2 2 1 0 1 2 1 0 1 0 0 2 0 2 0 , 2 0 0 2 1 2 1 1 0 1 0 0 2 -> 2 1 1 1 1 0 2 0 1 0 1 0 2 1 0 0 2 , 2 1 1 2 2 0 2 1 0 0 0 1 0 -> 1 1 2 0 0 2 0 0 1 0 0 2 0 0 0 1 0 , 2 1 2 1 1 2 1 0 0 1 0 1 0 -> 2 2 1 1 1 0 0 0 0 1 0 0 2 2 0 1 0 , 2 1 2 2 0 2 1 0 2 0 2 1 0 -> 1 0 1 2 0 0 2 0 0 2 1 0 2 1 0 0 0 , 2 2 0 1 1 1 1 0 1 0 1 2 0 -> 0 1 1 0 1 1 0 0 2 2 0 1 1 0 1 0 0 } The system was reversed. After renaming modulo { 2->0, 0->1, 1->2 }, it remains to prove termination of the 19-rule system { 0 0 1 0 2 0 1 0 1 2 1 1 1 -> 1 2 2 1 2 1 1 1 2 0 1 2 2 1 2 1 1 , 1 1 1 2 2 0 2 0 2 2 1 1 1 -> 1 2 0 1 1 0 1 0 2 2 0 0 0 0 1 1 2 , 1 0 2 0 1 1 2 1 1 2 1 2 1 -> 1 1 1 2 1 1 1 1 1 2 0 1 1 0 1 2 1 , 0 1 1 2 2 2 2 1 0 1 0 2 1 -> 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 , 0 0 1 2 0 0 1 1 2 2 0 2 1 -> 0 0 0 0 1 0 1 1 1 0 1 1 2 0 1 1 2 , 0 1 0 1 1 1 0 1 1 0 0 2 1 -> 0 1 2 0 1 2 1 0 1 2 2 0 1 1 1 2 0 , 2 1 1 0 2 1 2 2 1 2 1 0 1 -> 2 1 0 1 1 0 1 2 2 2 0 1 1 1 2 2 1 , 1 1 0 2 1 1 0 0 1 2 1 1 2 -> 1 0 1 1 2 1 2 2 1 2 1 2 1 1 1 1 1 , 1 1 1 2 0 0 0 0 2 2 2 1 2 -> 0 0 0 1 1 2 2 0 0 1 2 1 2 1 1 2 0 , 0 2 2 2 1 1 1 1 2 1 1 2 2 -> 0 2 1 0 1 1 2 1 2 0 1 1 2 0 1 2 2 , 0 1 2 1 0 2 0 1 2 1 0 2 2 -> 0 1 0 1 2 1 2 2 2 0 1 2 1 2 0 2 2 , 0 1 2 1 1 2 0 2 2 0 0 2 2 -> 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 , 1 1 0 0 1 2 0 2 2 1 1 1 0 -> 1 1 0 0 1 2 2 2 0 0 1 2 1 0 1 2 2 , 0 0 0 0 1 2 0 0 2 2 1 1 0 -> 1 0 1 0 1 1 2 1 2 0 2 1 2 0 0 1 2 , 0 1 1 2 1 2 2 0 2 0 1 1 0 -> 0 1 1 2 0 1 2 1 2 1 0 1 2 2 2 2 0 , 1 2 1 1 1 2 0 1 0 0 2 2 0 -> 1 2 1 1 1 0 1 1 2 1 1 0 1 1 0 2 2 , 1 2 1 2 1 1 2 0 2 2 0 2 0 -> 1 2 1 0 0 1 1 2 1 1 1 1 2 2 2 0 0 , 1 2 0 1 0 1 2 0 1 0 0 2 0 -> 1 1 1 2 0 1 2 0 1 1 0 1 1 0 2 1 2 , 1 0 2 1 2 1 2 2 2 2 1 0 0 -> 1 1 2 1 2 2 1 0 0 1 1 2 2 1 2 2 1 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (0,2)->3, (2,0)->4, (1,2)->5, (2,1)->6, (1,1)->7, (2,2)->8, (1,4)->9, (3,0)->10, (3,1)->11, (2,4)->12, (0,4)->13, (3,2)->14 }, it remains to prove termination of the 304-rule system { 0 0 1 2 3 4 1 2 1 5 6 7 7 2 -> 1 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 2 , 0 0 1 2 3 4 1 2 1 5 6 7 7 7 -> 1 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 7 , 0 0 1 2 3 4 1 2 1 5 6 7 7 5 -> 1 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 5 , 0 0 1 2 3 4 1 2 1 5 6 7 7 9 -> 1 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 9 , 2 0 1 2 3 4 1 2 1 5 6 7 7 2 -> 7 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 2 , 2 0 1 2 3 4 1 2 1 5 6 7 7 7 -> 7 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 7 , 2 0 1 2 3 4 1 2 1 5 6 7 7 5 -> 7 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 5 , 2 0 1 2 3 4 1 2 1 5 6 7 7 9 -> 7 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 9 , 4 0 1 2 3 4 1 2 1 5 6 7 7 2 -> 6 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 2 , 4 0 1 2 3 4 1 2 1 5 6 7 7 7 -> 6 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 7 , 4 0 1 2 3 4 1 2 1 5 6 7 7 5 -> 6 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 5 , 4 0 1 2 3 4 1 2 1 5 6 7 7 9 -> 6 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 9 , 10 0 1 2 3 4 1 2 1 5 6 7 7 2 -> 11 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 2 , 10 0 1 2 3 4 1 2 1 5 6 7 7 7 -> 11 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 7 , 10 0 1 2 3 4 1 2 1 5 6 7 7 5 -> 11 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 5 , 10 0 1 2 3 4 1 2 1 5 6 7 7 9 -> 11 5 8 6 5 6 7 7 5 4 1 5 8 6 5 6 7 9 , 1 7 7 5 8 4 3 4 3 8 6 7 7 2 -> 1 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 4 , 1 7 7 5 8 4 3 4 3 8 6 7 7 7 -> 1 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 6 , 1 7 7 5 8 4 3 4 3 8 6 7 7 5 -> 1 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 8 , 1 7 7 5 8 4 3 4 3 8 6 7 7 9 -> 1 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 12 , 7 7 7 5 8 4 3 4 3 8 6 7 7 2 -> 7 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 4 , 7 7 7 5 8 4 3 4 3 8 6 7 7 7 -> 7 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 6 , 7 7 7 5 8 4 3 4 3 8 6 7 7 5 -> 7 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 8 , 7 7 7 5 8 4 3 4 3 8 6 7 7 9 -> 7 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 12 , 6 7 7 5 8 4 3 4 3 8 6 7 7 2 -> 6 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 4 , 6 7 7 5 8 4 3 4 3 8 6 7 7 7 -> 6 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 6 , 6 7 7 5 8 4 3 4 3 8 6 7 7 5 -> 6 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 8 , 6 7 7 5 8 4 3 4 3 8 6 7 7 9 -> 6 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 12 , 11 7 7 5 8 4 3 4 3 8 6 7 7 2 -> 11 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 4 , 11 7 7 5 8 4 3 4 3 8 6 7 7 7 -> 11 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 6 , 11 7 7 5 8 4 3 4 3 8 6 7 7 5 -> 11 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 8 , 11 7 7 5 8 4 3 4 3 8 6 7 7 9 -> 11 5 4 1 7 2 1 2 3 8 4 0 0 0 1 7 5 12 , 1 2 3 4 1 7 5 6 7 5 6 5 6 2 -> 1 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 2 , 1 2 3 4 1 7 5 6 7 5 6 5 6 7 -> 1 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 7 , 1 2 3 4 1 7 5 6 7 5 6 5 6 5 -> 1 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 5 , 1 2 3 4 1 7 5 6 7 5 6 5 6 9 -> 1 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 9 , 7 2 3 4 1 7 5 6 7 5 6 5 6 2 -> 7 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 2 , 7 2 3 4 1 7 5 6 7 5 6 5 6 7 -> 7 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 7 , 7 2 3 4 1 7 5 6 7 5 6 5 6 5 -> 7 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 5 , 7 2 3 4 1 7 5 6 7 5 6 5 6 9 -> 7 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 9 , 6 2 3 4 1 7 5 6 7 5 6 5 6 2 -> 6 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 2 , 6 2 3 4 1 7 5 6 7 5 6 5 6 7 -> 6 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 7 , 6 2 3 4 1 7 5 6 7 5 6 5 6 5 -> 6 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 5 , 6 2 3 4 1 7 5 6 7 5 6 5 6 9 -> 6 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 9 , 11 2 3 4 1 7 5 6 7 5 6 5 6 2 -> 11 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 2 , 11 2 3 4 1 7 5 6 7 5 6 5 6 7 -> 11 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 7 , 11 2 3 4 1 7 5 6 7 5 6 5 6 5 -> 11 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 5 , 11 2 3 4 1 7 5 6 7 5 6 5 6 9 -> 11 7 7 5 6 7 7 7 7 5 4 1 7 2 1 5 6 9 , 0 1 7 5 8 8 8 6 2 1 2 3 6 2 -> 1 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 2 , 0 1 7 5 8 8 8 6 2 1 2 3 6 7 -> 1 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 7 , 0 1 7 5 8 8 8 6 2 1 2 3 6 5 -> 1 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 5 , 0 1 7 5 8 8 8 6 2 1 2 3 6 9 -> 1 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 9 , 2 1 7 5 8 8 8 6 2 1 2 3 6 2 -> 7 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 2 , 2 1 7 5 8 8 8 6 2 1 2 3 6 7 -> 7 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 7 , 2 1 7 5 8 8 8 6 2 1 2 3 6 5 -> 7 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 5 , 2 1 7 5 8 8 8 6 2 1 2 3 6 9 -> 7 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 9 , 4 1 7 5 8 8 8 6 2 1 2 3 6 2 -> 6 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 2 , 4 1 7 5 8 8 8 6 2 1 2 3 6 7 -> 6 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 7 , 4 1 7 5 8 8 8 6 2 1 2 3 6 5 -> 6 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 5 , 4 1 7 5 8 8 8 6 2 1 2 3 6 9 -> 6 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 9 , 10 1 7 5 8 8 8 6 2 1 2 3 6 2 -> 11 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 2 , 10 1 7 5 8 8 8 6 2 1 2 3 6 7 -> 11 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 7 , 10 1 7 5 8 8 8 6 2 1 2 3 6 5 -> 11 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 5 , 10 1 7 5 8 8 8 6 2 1 2 3 6 9 -> 11 7 7 7 2 0 0 1 2 0 1 2 1 7 7 7 7 9 , 0 0 1 5 4 0 1 7 5 8 4 3 6 2 -> 0 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 4 , 0 0 1 5 4 0 1 7 5 8 4 3 6 7 -> 0 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 6 , 0 0 1 5 4 0 1 7 5 8 4 3 6 5 -> 0 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 8 , 0 0 1 5 4 0 1 7 5 8 4 3 6 9 -> 0 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 12 , 2 0 1 5 4 0 1 7 5 8 4 3 6 2 -> 2 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 4 , 2 0 1 5 4 0 1 7 5 8 4 3 6 7 -> 2 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 6 , 2 0 1 5 4 0 1 7 5 8 4 3 6 5 -> 2 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 8 , 2 0 1 5 4 0 1 7 5 8 4 3 6 9 -> 2 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 12 , 4 0 1 5 4 0 1 7 5 8 4 3 6 2 -> 4 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 4 , 4 0 1 5 4 0 1 7 5 8 4 3 6 7 -> 4 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 6 , 4 0 1 5 4 0 1 7 5 8 4 3 6 5 -> 4 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 8 , 4 0 1 5 4 0 1 7 5 8 4 3 6 9 -> 4 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 12 , 10 0 1 5 4 0 1 7 5 8 4 3 6 2 -> 10 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 4 , 10 0 1 5 4 0 1 7 5 8 4 3 6 7 -> 10 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 6 , 10 0 1 5 4 0 1 7 5 8 4 3 6 5 -> 10 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 8 , 10 0 1 5 4 0 1 7 5 8 4 3 6 9 -> 10 0 0 0 1 2 1 7 7 2 1 7 5 4 1 7 5 12 , 0 1 2 1 7 7 2 1 7 2 0 3 6 2 -> 0 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 0 , 0 1 2 1 7 7 2 1 7 2 0 3 6 7 -> 0 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 1 , 0 1 2 1 7 7 2 1 7 2 0 3 6 5 -> 0 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 3 , 0 1 2 1 7 7 2 1 7 2 0 3 6 9 -> 0 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 13 , 2 1 2 1 7 7 2 1 7 2 0 3 6 2 -> 2 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 0 , 2 1 2 1 7 7 2 1 7 2 0 3 6 7 -> 2 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 1 , 2 1 2 1 7 7 2 1 7 2 0 3 6 5 -> 2 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 3 , 2 1 2 1 7 7 2 1 7 2 0 3 6 9 -> 2 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 13 , 4 1 2 1 7 7 2 1 7 2 0 3 6 2 -> 4 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 0 , 4 1 2 1 7 7 2 1 7 2 0 3 6 7 -> 4 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 1 , 4 1 2 1 7 7 2 1 7 2 0 3 6 5 -> 4 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 3 , 4 1 2 1 7 7 2 1 7 2 0 3 6 9 -> 4 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 13 , 10 1 2 1 7 7 2 1 7 2 0 3 6 2 -> 10 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 0 , 10 1 2 1 7 7 2 1 7 2 0 3 6 7 -> 10 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 1 , 10 1 2 1 7 7 2 1 7 2 0 3 6 5 -> 10 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 3 , 10 1 2 1 7 7 2 1 7 2 0 3 6 9 -> 10 1 5 4 1 5 6 2 1 5 8 4 1 7 7 5 4 13 , 3 6 7 2 3 6 5 8 6 5 6 2 1 2 -> 3 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 2 , 3 6 7 2 3 6 5 8 6 5 6 2 1 7 -> 3 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 7 , 3 6 7 2 3 6 5 8 6 5 6 2 1 5 -> 3 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 5 , 3 6 7 2 3 6 5 8 6 5 6 2 1 9 -> 3 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 9 , 5 6 7 2 3 6 5 8 6 5 6 2 1 2 -> 5 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 2 , 5 6 7 2 3 6 5 8 6 5 6 2 1 7 -> 5 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 7 , 5 6 7 2 3 6 5 8 6 5 6 2 1 5 -> 5 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 5 , 5 6 7 2 3 6 5 8 6 5 6 2 1 9 -> 5 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 9 , 8 6 7 2 3 6 5 8 6 5 6 2 1 2 -> 8 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 2 , 8 6 7 2 3 6 5 8 6 5 6 2 1 7 -> 8 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 7 , 8 6 7 2 3 6 5 8 6 5 6 2 1 5 -> 8 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 5 , 8 6 7 2 3 6 5 8 6 5 6 2 1 9 -> 8 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 9 , 14 6 7 2 3 6 5 8 6 5 6 2 1 2 -> 14 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 2 , 14 6 7 2 3 6 5 8 6 5 6 2 1 7 -> 14 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 7 , 14 6 7 2 3 6 5 8 6 5 6 2 1 5 -> 14 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 5 , 14 6 7 2 3 6 5 8 6 5 6 2 1 9 -> 14 6 2 1 7 2 1 5 8 8 4 1 7 7 5 8 6 9 , 1 7 2 3 6 7 2 0 1 5 6 7 5 4 -> 1 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 2 , 1 7 2 3 6 7 2 0 1 5 6 7 5 6 -> 1 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 7 , 1 7 2 3 6 7 2 0 1 5 6 7 5 8 -> 1 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 5 , 1 7 2 3 6 7 2 0 1 5 6 7 5 12 -> 1 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 9 , 7 7 2 3 6 7 2 0 1 5 6 7 5 4 -> 7 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 2 , 7 7 2 3 6 7 2 0 1 5 6 7 5 6 -> 7 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 7 , 7 7 2 3 6 7 2 0 1 5 6 7 5 8 -> 7 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 5 , 7 7 2 3 6 7 2 0 1 5 6 7 5 12 -> 7 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 9 , 6 7 2 3 6 7 2 0 1 5 6 7 5 4 -> 6 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 2 , 6 7 2 3 6 7 2 0 1 5 6 7 5 6 -> 6 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 7 , 6 7 2 3 6 7 2 0 1 5 6 7 5 8 -> 6 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 5 , 6 7 2 3 6 7 2 0 1 5 6 7 5 12 -> 6 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 9 , 11 7 2 3 6 7 2 0 1 5 6 7 5 4 -> 11 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 2 , 11 7 2 3 6 7 2 0 1 5 6 7 5 6 -> 11 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 7 , 11 7 2 3 6 7 2 0 1 5 6 7 5 8 -> 11 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 5 , 11 7 2 3 6 7 2 0 1 5 6 7 5 12 -> 11 2 1 7 5 6 5 8 6 5 6 5 6 7 7 7 7 9 , 1 7 7 5 4 0 0 0 3 8 8 6 5 4 -> 0 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 0 , 1 7 7 5 4 0 0 0 3 8 8 6 5 6 -> 0 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 1 , 1 7 7 5 4 0 0 0 3 8 8 6 5 8 -> 0 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 3 , 1 7 7 5 4 0 0 0 3 8 8 6 5 12 -> 0 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 13 , 7 7 7 5 4 0 0 0 3 8 8 6 5 4 -> 2 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 0 , 7 7 7 5 4 0 0 0 3 8 8 6 5 6 -> 2 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 1 , 7 7 7 5 4 0 0 0 3 8 8 6 5 8 -> 2 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 3 , 7 7 7 5 4 0 0 0 3 8 8 6 5 12 -> 2 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 13 , 6 7 7 5 4 0 0 0 3 8 8 6 5 4 -> 4 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 0 , 6 7 7 5 4 0 0 0 3 8 8 6 5 6 -> 4 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 1 , 6 7 7 5 4 0 0 0 3 8 8 6 5 8 -> 4 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 3 , 6 7 7 5 4 0 0 0 3 8 8 6 5 12 -> 4 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 13 , 11 7 7 5 4 0 0 0 3 8 8 6 5 4 -> 10 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 0 , 11 7 7 5 4 0 0 0 3 8 8 6 5 6 -> 10 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 1 , 11 7 7 5 4 0 0 0 3 8 8 6 5 8 -> 10 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 3 , 11 7 7 5 4 0 0 0 3 8 8 6 5 12 -> 10 0 0 1 7 5 8 4 0 1 5 6 5 6 7 5 4 13 , 0 3 8 8 6 7 7 7 5 6 7 5 8 4 -> 0 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 4 , 0 3 8 8 6 7 7 7 5 6 7 5 8 6 -> 0 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 6 , 0 3 8 8 6 7 7 7 5 6 7 5 8 8 -> 0 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 8 , 0 3 8 8 6 7 7 7 5 6 7 5 8 12 -> 0 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 12 , 2 3 8 8 6 7 7 7 5 6 7 5 8 4 -> 2 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 4 , 2 3 8 8 6 7 7 7 5 6 7 5 8 6 -> 2 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 6 , 2 3 8 8 6 7 7 7 5 6 7 5 8 8 -> 2 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 8 , 2 3 8 8 6 7 7 7 5 6 7 5 8 12 -> 2 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 12 , 4 3 8 8 6 7 7 7 5 6 7 5 8 4 -> 4 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 4 , 4 3 8 8 6 7 7 7 5 6 7 5 8 6 -> 4 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 6 , 4 3 8 8 6 7 7 7 5 6 7 5 8 8 -> 4 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 8 , 4 3 8 8 6 7 7 7 5 6 7 5 8 12 -> 4 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 12 , 10 3 8 8 6 7 7 7 5 6 7 5 8 4 -> 10 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 4 , 10 3 8 8 6 7 7 7 5 6 7 5 8 6 -> 10 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 6 , 10 3 8 8 6 7 7 7 5 6 7 5 8 8 -> 10 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 8 , 10 3 8 8 6 7 7 7 5 6 7 5 8 12 -> 10 3 6 2 1 7 5 6 5 4 1 7 5 4 1 5 8 12 , 0 1 5 6 2 3 4 1 5 6 2 3 8 4 -> 0 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 4 , 0 1 5 6 2 3 4 1 5 6 2 3 8 6 -> 0 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 6 , 0 1 5 6 2 3 4 1 5 6 2 3 8 8 -> 0 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 8 , 0 1 5 6 2 3 4 1 5 6 2 3 8 12 -> 0 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 12 , 2 1 5 6 2 3 4 1 5 6 2 3 8 4 -> 2 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 4 , 2 1 5 6 2 3 4 1 5 6 2 3 8 6 -> 2 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 6 , 2 1 5 6 2 3 4 1 5 6 2 3 8 8 -> 2 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 8 , 2 1 5 6 2 3 4 1 5 6 2 3 8 12 -> 2 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 12 , 4 1 5 6 2 3 4 1 5 6 2 3 8 4 -> 4 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 4 , 4 1 5 6 2 3 4 1 5 6 2 3 8 6 -> 4 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 6 , 4 1 5 6 2 3 4 1 5 6 2 3 8 8 -> 4 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 8 , 4 1 5 6 2 3 4 1 5 6 2 3 8 12 -> 4 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 12 , 10 1 5 6 2 3 4 1 5 6 2 3 8 4 -> 10 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 4 , 10 1 5 6 2 3 4 1 5 6 2 3 8 6 -> 10 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 6 , 10 1 5 6 2 3 4 1 5 6 2 3 8 8 -> 10 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 8 , 10 1 5 6 2 3 4 1 5 6 2 3 8 12 -> 10 1 2 1 5 6 5 8 8 4 1 5 6 5 4 3 8 12 , 0 1 5 6 7 5 4 3 8 4 0 3 8 4 -> 0 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 2 , 0 1 5 6 7 5 4 3 8 4 0 3 8 6 -> 0 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 7 , 0 1 5 6 7 5 4 3 8 4 0 3 8 8 -> 0 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 5 , 0 1 5 6 7 5 4 3 8 4 0 3 8 12 -> 0 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 9 , 2 1 5 6 7 5 4 3 8 4 0 3 8 4 -> 2 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 2 , 2 1 5 6 7 5 4 3 8 4 0 3 8 6 -> 2 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 7 , 2 1 5 6 7 5 4 3 8 4 0 3 8 8 -> 2 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 5 , 2 1 5 6 7 5 4 3 8 4 0 3 8 12 -> 2 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 9 , 4 1 5 6 7 5 4 3 8 4 0 3 8 4 -> 4 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 2 , 4 1 5 6 7 5 4 3 8 4 0 3 8 6 -> 4 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 7 , 4 1 5 6 7 5 4 3 8 4 0 3 8 8 -> 4 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 5 , 4 1 5 6 7 5 4 3 8 4 0 3 8 12 -> 4 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 9 , 10 1 5 6 7 5 4 3 8 4 0 3 8 4 -> 10 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 2 , 10 1 5 6 7 5 4 3 8 4 0 3 8 6 -> 10 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 7 , 10 1 5 6 7 5 4 3 8 4 0 3 8 8 -> 10 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 5 , 10 1 5 6 7 5 4 3 8 4 0 3 8 12 -> 10 0 0 1 7 2 1 7 2 1 7 7 2 1 2 1 7 9 , 1 7 2 0 1 5 4 3 8 6 7 7 2 0 -> 1 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 4 , 1 7 2 0 1 5 4 3 8 6 7 7 2 1 -> 1 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 6 , 1 7 2 0 1 5 4 3 8 6 7 7 2 3 -> 1 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 8 , 1 7 2 0 1 5 4 3 8 6 7 7 2 13 -> 1 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 12 , 7 7 2 0 1 5 4 3 8 6 7 7 2 0 -> 7 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 4 , 7 7 2 0 1 5 4 3 8 6 7 7 2 1 -> 7 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 6 , 7 7 2 0 1 5 4 3 8 6 7 7 2 3 -> 7 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 8 , 7 7 2 0 1 5 4 3 8 6 7 7 2 13 -> 7 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 12 , 6 7 2 0 1 5 4 3 8 6 7 7 2 0 -> 6 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 4 , 6 7 2 0 1 5 4 3 8 6 7 7 2 1 -> 6 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 6 , 6 7 2 0 1 5 4 3 8 6 7 7 2 3 -> 6 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 8 , 6 7 2 0 1 5 4 3 8 6 7 7 2 13 -> 6 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 12 , 11 7 2 0 1 5 4 3 8 6 7 7 2 0 -> 11 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 4 , 11 7 2 0 1 5 4 3 8 6 7 7 2 1 -> 11 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 6 , 11 7 2 0 1 5 4 3 8 6 7 7 2 3 -> 11 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 8 , 11 7 2 0 1 5 4 3 8 6 7 7 2 13 -> 11 7 2 0 1 5 8 8 4 0 1 5 6 2 1 5 8 12 , 0 0 0 0 1 5 4 0 3 8 6 7 2 0 -> 1 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 4 , 0 0 0 0 1 5 4 0 3 8 6 7 2 1 -> 1 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 6 , 0 0 0 0 1 5 4 0 3 8 6 7 2 3 -> 1 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 8 , 0 0 0 0 1 5 4 0 3 8 6 7 2 13 -> 1 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 12 , 2 0 0 0 1 5 4 0 3 8 6 7 2 0 -> 7 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 4 , 2 0 0 0 1 5 4 0 3 8 6 7 2 1 -> 7 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 6 , 2 0 0 0 1 5 4 0 3 8 6 7 2 3 -> 7 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 8 , 2 0 0 0 1 5 4 0 3 8 6 7 2 13 -> 7 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 12 , 4 0 0 0 1 5 4 0 3 8 6 7 2 0 -> 6 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 4 , 4 0 0 0 1 5 4 0 3 8 6 7 2 1 -> 6 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 6 , 4 0 0 0 1 5 4 0 3 8 6 7 2 3 -> 6 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 8 , 4 0 0 0 1 5 4 0 3 8 6 7 2 13 -> 6 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 12 , 10 0 0 0 1 5 4 0 3 8 6 7 2 0 -> 11 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 4 , 10 0 0 0 1 5 4 0 3 8 6 7 2 1 -> 11 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 6 , 10 0 0 0 1 5 4 0 3 8 6 7 2 3 -> 11 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 8 , 10 0 0 0 1 5 4 0 3 8 6 7 2 13 -> 11 2 1 2 1 7 5 6 5 4 3 6 5 4 0 1 5 12 , 0 1 7 5 6 5 8 4 3 4 1 7 2 0 -> 0 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 0 , 0 1 7 5 6 5 8 4 3 4 1 7 2 1 -> 0 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 1 , 0 1 7 5 6 5 8 4 3 4 1 7 2 3 -> 0 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 3 , 0 1 7 5 6 5 8 4 3 4 1 7 2 13 -> 0 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 13 , 2 1 7 5 6 5 8 4 3 4 1 7 2 0 -> 2 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 0 , 2 1 7 5 6 5 8 4 3 4 1 7 2 1 -> 2 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 1 , 2 1 7 5 6 5 8 4 3 4 1 7 2 3 -> 2 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 3 , 2 1 7 5 6 5 8 4 3 4 1 7 2 13 -> 2 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 13 , 4 1 7 5 6 5 8 4 3 4 1 7 2 0 -> 4 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 0 , 4 1 7 5 6 5 8 4 3 4 1 7 2 1 -> 4 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 1 , 4 1 7 5 6 5 8 4 3 4 1 7 2 3 -> 4 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 3 , 4 1 7 5 6 5 8 4 3 4 1 7 2 13 -> 4 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 13 , 10 1 7 5 6 5 8 4 3 4 1 7 2 0 -> 10 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 0 , 10 1 7 5 6 5 8 4 3 4 1 7 2 1 -> 10 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 1 , 10 1 7 5 6 5 8 4 3 4 1 7 2 3 -> 10 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 3 , 10 1 7 5 6 5 8 4 3 4 1 7 2 13 -> 10 1 7 5 4 1 5 6 5 6 2 1 5 8 8 8 4 13 , 1 5 6 7 7 5 4 1 2 0 3 8 4 0 -> 1 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 4 , 1 5 6 7 7 5 4 1 2 0 3 8 4 1 -> 1 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 6 , 1 5 6 7 7 5 4 1 2 0 3 8 4 3 -> 1 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 8 , 1 5 6 7 7 5 4 1 2 0 3 8 4 13 -> 1 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 12 , 7 5 6 7 7 5 4 1 2 0 3 8 4 0 -> 7 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 4 , 7 5 6 7 7 5 4 1 2 0 3 8 4 1 -> 7 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 6 , 7 5 6 7 7 5 4 1 2 0 3 8 4 3 -> 7 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 8 , 7 5 6 7 7 5 4 1 2 0 3 8 4 13 -> 7 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 12 , 6 5 6 7 7 5 4 1 2 0 3 8 4 0 -> 6 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 4 , 6 5 6 7 7 5 4 1 2 0 3 8 4 1 -> 6 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 6 , 6 5 6 7 7 5 4 1 2 0 3 8 4 3 -> 6 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 8 , 6 5 6 7 7 5 4 1 2 0 3 8 4 13 -> 6 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 12 , 11 5 6 7 7 5 4 1 2 0 3 8 4 0 -> 11 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 4 , 11 5 6 7 7 5 4 1 2 0 3 8 4 1 -> 11 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 6 , 11 5 6 7 7 5 4 1 2 0 3 8 4 3 -> 11 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 8 , 11 5 6 7 7 5 4 1 2 0 3 8 4 13 -> 11 5 6 7 7 2 1 7 5 6 7 2 1 7 2 3 8 12 , 1 5 6 5 6 7 5 4 3 8 4 3 4 0 -> 1 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 0 , 1 5 6 5 6 7 5 4 3 8 4 3 4 1 -> 1 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 1 , 1 5 6 5 6 7 5 4 3 8 4 3 4 3 -> 1 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 3 , 1 5 6 5 6 7 5 4 3 8 4 3 4 13 -> 1 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 13 , 7 5 6 5 6 7 5 4 3 8 4 3 4 0 -> 7 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 0 , 7 5 6 5 6 7 5 4 3 8 4 3 4 1 -> 7 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 1 , 7 5 6 5 6 7 5 4 3 8 4 3 4 3 -> 7 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 3 , 7 5 6 5 6 7 5 4 3 8 4 3 4 13 -> 7 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 13 , 6 5 6 5 6 7 5 4 3 8 4 3 4 0 -> 6 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 0 , 6 5 6 5 6 7 5 4 3 8 4 3 4 1 -> 6 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 1 , 6 5 6 5 6 7 5 4 3 8 4 3 4 3 -> 6 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 3 , 6 5 6 5 6 7 5 4 3 8 4 3 4 13 -> 6 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 13 , 11 5 6 5 6 7 5 4 3 8 4 3 4 0 -> 11 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 0 , 11 5 6 5 6 7 5 4 3 8 4 3 4 1 -> 11 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 1 , 11 5 6 5 6 7 5 4 3 8 4 3 4 3 -> 11 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 3 , 11 5 6 5 6 7 5 4 3 8 4 3 4 13 -> 11 5 6 2 0 1 7 5 6 7 7 7 5 8 8 4 0 13 , 1 5 4 1 2 1 5 4 1 2 0 3 4 0 -> 1 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 4 , 1 5 4 1 2 1 5 4 1 2 0 3 4 1 -> 1 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 6 , 1 5 4 1 2 1 5 4 1 2 0 3 4 3 -> 1 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 8 , 1 5 4 1 2 1 5 4 1 2 0 3 4 13 -> 1 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 12 , 7 5 4 1 2 1 5 4 1 2 0 3 4 0 -> 7 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 4 , 7 5 4 1 2 1 5 4 1 2 0 3 4 1 -> 7 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 6 , 7 5 4 1 2 1 5 4 1 2 0 3 4 3 -> 7 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 8 , 7 5 4 1 2 1 5 4 1 2 0 3 4 13 -> 7 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 12 , 6 5 4 1 2 1 5 4 1 2 0 3 4 0 -> 6 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 4 , 6 5 4 1 2 1 5 4 1 2 0 3 4 1 -> 6 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 6 , 6 5 4 1 2 1 5 4 1 2 0 3 4 3 -> 6 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 8 , 6 5 4 1 2 1 5 4 1 2 0 3 4 13 -> 6 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 12 , 11 5 4 1 2 1 5 4 1 2 0 3 4 0 -> 11 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 4 , 11 5 4 1 2 1 5 4 1 2 0 3 4 1 -> 11 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 6 , 11 5 4 1 2 1 5 4 1 2 0 3 4 3 -> 11 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 8 , 11 5 4 1 2 1 5 4 1 2 0 3 4 13 -> 11 7 7 5 4 1 5 4 1 7 2 1 7 2 3 6 5 12 , 1 2 3 6 5 6 5 8 8 8 6 2 0 0 -> 1 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 2 , 1 2 3 6 5 6 5 8 8 8 6 2 0 1 -> 1 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 7 , 1 2 3 6 5 6 5 8 8 8 6 2 0 3 -> 1 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 5 , 1 2 3 6 5 6 5 8 8 8 6 2 0 13 -> 1 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 9 , 7 2 3 6 5 6 5 8 8 8 6 2 0 0 -> 7 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 2 , 7 2 3 6 5 6 5 8 8 8 6 2 0 1 -> 7 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 7 , 7 2 3 6 5 6 5 8 8 8 6 2 0 3 -> 7 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 5 , 7 2 3 6 5 6 5 8 8 8 6 2 0 13 -> 7 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 9 , 6 2 3 6 5 6 5 8 8 8 6 2 0 0 -> 6 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 2 , 6 2 3 6 5 6 5 8 8 8 6 2 0 1 -> 6 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 7 , 6 2 3 6 5 6 5 8 8 8 6 2 0 3 -> 6 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 5 , 6 2 3 6 5 6 5 8 8 8 6 2 0 13 -> 6 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 9 , 11 2 3 6 5 6 5 8 8 8 6 2 0 0 -> 11 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 2 , 11 2 3 6 5 6 5 8 8 8 6 2 0 1 -> 11 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 7 , 11 2 3 6 5 6 5 8 8 8 6 2 0 3 -> 11 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 5 , 11 2 3 6 5 6 5 8 8 8 6 2 0 13 -> 11 7 5 6 5 8 6 2 0 1 7 5 8 6 5 8 6 9 } 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 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 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 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 7->3, 3->4, 6->5, 5->6, 4->7, 8->8, 10->9, 11->10, 12->11, 13->12 }, it remains to prove termination of the 60-rule system { 0 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 0 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 2 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 2 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 7 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 7 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 9 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 9 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 1 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 0 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 3 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 2 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 5 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 7 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 10 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 9 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 0 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 0 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 0 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 0 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 2 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 2 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 2 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 2 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 7 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 7 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 7 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 7 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 9 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 9 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 9 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 9 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 0 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 1 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 0 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 1 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 0 0 0 0 1 6 7 0 4 8 5 3 2 12 -> 1 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 11 , 2 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 3 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 2 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 3 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 2 0 0 0 1 6 7 0 4 8 5 3 2 12 -> 3 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 11 , 7 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 5 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 7 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 5 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 7 0 0 0 1 6 7 0 4 8 5 3 2 12 -> 5 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 11 , 9 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 10 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 9 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 10 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 9 0 0 0 1 6 7 0 4 8 5 3 2 12 -> 10 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 11 , 1 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 1 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 1 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 1 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 1 6 5 3 3 6 7 1 2 0 4 8 7 12 -> 1 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 11 , 3 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 3 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 3 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 3 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 3 6 5 3 3 6 7 1 2 0 4 8 7 12 -> 3 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 11 , 5 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 5 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 5 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 5 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 5 6 5 3 3 6 7 1 2 0 4 8 7 12 -> 5 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 11 , 10 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 10 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 10 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 10 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 10 6 5 3 3 6 7 1 2 0 4 8 7 12 -> 10 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 11 , 1 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 1 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 1 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 1 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 1 6 7 1 2 1 6 7 1 2 0 4 7 12 -> 1 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 11 , 3 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 3 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 3 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 3 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 3 6 7 1 2 1 6 7 1 2 0 4 7 12 -> 3 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 11 , 5 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 5 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 5 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 5 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 5 6 7 1 2 1 6 7 1 2 0 4 7 12 -> 5 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 11 , 10 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 10 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 10 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 10 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 10 6 7 1 2 1 6 7 1 2 0 4 7 12 -> 10 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 11 } 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 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 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 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 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 }, it remains to prove termination of the 48-rule system { 0 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 0 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 2 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 2 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 7 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 7 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 9 1 2 1 3 3 2 1 3 2 0 4 5 6 -> 9 1 6 7 1 6 5 2 1 6 8 7 1 3 3 6 7 4 , 1 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 0 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 3 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 2 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 5 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 7 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 10 3 3 6 7 0 0 0 4 8 8 5 6 8 -> 9 0 0 1 3 6 8 7 0 1 6 5 6 5 3 6 7 4 , 0 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 0 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 0 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 0 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 0 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 2 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 2 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 2 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 2 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 2 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 7 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 7 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 7 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 7 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 7 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 9 4 8 8 5 3 3 3 6 5 3 6 8 7 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 7 , 9 4 8 8 5 3 3 3 6 5 3 6 8 5 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 5 , 9 4 8 8 5 3 3 3 6 5 3 6 8 8 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 8 , 9 4 8 8 5 3 3 3 6 5 3 6 8 11 -> 9 4 5 2 1 3 6 5 6 7 1 3 6 7 1 6 8 11 , 0 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 1 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 0 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 1 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 2 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 3 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 2 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 3 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 7 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 5 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 7 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 5 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 9 0 0 0 1 6 7 0 4 8 5 3 2 0 -> 10 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 7 , 9 0 0 0 1 6 7 0 4 8 5 3 2 1 -> 10 2 1 2 1 3 6 5 6 7 4 5 6 7 0 1 6 5 , 1 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 1 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 1 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 1 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 3 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 3 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 3 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 3 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 5 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 5 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 5 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 5 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 10 6 5 3 3 6 7 1 2 0 4 8 7 0 -> 10 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 7 , 10 6 5 3 3 6 7 1 2 0 4 8 7 1 -> 10 6 5 3 3 2 1 3 6 5 3 2 1 3 2 4 8 5 , 1 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 1 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 1 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 1 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 3 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 3 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 3 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 3 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 5 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 5 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 5 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 5 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 5 , 10 6 7 1 2 1 6 7 1 2 0 4 7 0 -> 10 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 7 , 10 6 7 1 2 1 6 7 1 2 0 4 7 1 -> 10 3 3 6 7 1 6 7 1 3 2 1 3 2 4 5 6 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 5 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 2 | | 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 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 4 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 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.