/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 44-rule system { 0 0 0 1 1 0 0 0 0 1 2 0 1 -> 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 , 0 0 0 1 1 2 2 1 1 0 0 1 1 -> 0 1 1 0 2 0 0 0 1 0 1 1 0 0 0 1 0 , 0 1 0 0 2 1 0 0 1 0 0 1 0 -> 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 , 0 1 0 1 1 0 0 0 0 2 0 1 2 -> 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 2 , 0 1 0 1 1 0 2 1 0 1 0 0 0 -> 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 , 0 1 1 0 0 1 0 2 0 0 0 2 1 -> 0 0 1 1 0 1 0 1 1 0 0 1 1 2 1 1 1 , 0 1 2 1 0 0 0 0 0 2 1 1 1 -> 0 1 0 1 1 2 0 1 0 0 0 1 1 0 0 0 1 , 0 2 0 0 2 1 0 0 0 0 0 0 1 -> 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 , 0 2 1 0 1 2 1 2 2 0 1 1 1 -> 0 2 1 1 0 0 2 1 1 0 0 1 2 1 1 1 1 , 0 2 1 0 2 1 0 1 2 0 0 0 1 -> 0 0 2 1 1 1 1 0 0 1 0 2 0 0 0 1 0 , 0 2 1 1 0 0 0 0 2 1 0 1 1 -> 0 0 1 0 1 0 1 0 2 1 1 1 0 0 0 0 0 , 0 2 2 0 0 1 1 0 1 0 1 0 1 -> 0 0 2 1 0 0 0 1 1 0 1 1 0 1 1 0 0 , 1 0 0 0 0 1 1 1 0 0 2 1 1 -> 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 , 1 0 0 0 1 1 1 2 0 0 1 0 2 -> 0 1 1 0 1 0 0 1 0 0 0 0 0 2 0 1 2 , 1 0 0 0 1 2 0 1 0 0 0 1 0 -> 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 , 1 0 0 0 2 1 0 0 2 0 1 0 1 -> 2 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 , 1 0 0 1 0 1 2 1 0 2 1 1 0 -> 0 1 1 1 0 0 0 0 0 2 1 1 1 1 1 1 0 , 1 0 0 1 0 2 1 1 0 1 1 0 1 -> 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 , 1 0 0 1 2 0 0 0 2 2 1 1 2 -> 1 0 0 0 1 0 2 2 0 1 1 1 0 1 2 1 2 , 1 0 0 1 2 1 1 1 0 2 0 2 1 -> 1 0 0 1 0 0 1 2 0 1 0 1 2 2 1 0 0 , 1 0 0 2 0 1 0 1 0 2 1 0 2 -> 0 1 0 0 0 2 0 1 1 0 1 0 1 1 0 0 2 , 1 0 1 0 1 2 1 1 2 1 0 0 1 -> 1 1 0 0 1 0 0 2 2 0 0 0 0 1 1 0 0 , 1 0 1 2 0 1 2 1 0 0 1 0 0 -> 0 0 0 0 0 1 1 0 1 1 1 1 0 2 1 0 1 , 1 0 2 2 1 0 1 0 1 0 1 0 2 -> 1 1 1 0 0 0 0 0 0 1 1 0 0 0 2 1 2 , 1 1 0 1 0 2 2 2 1 0 0 0 0 -> 1 1 0 1 1 0 1 0 1 0 1 0 0 2 0 0 1 , 1 1 0 2 2 0 0 1 2 1 2 1 2 -> 1 1 2 0 0 0 1 1 0 2 2 1 1 0 1 0 2 , 1 1 1 1 0 1 0 2 1 1 0 0 2 -> 1 1 1 0 0 1 0 1 1 0 1 0 0 2 1 0 2 , 1 1 1 2 1 1 0 2 0 2 0 1 0 -> 1 1 1 0 0 1 0 2 2 0 0 1 2 1 0 1 0 , 1 1 2 1 1 0 1 1 0 1 1 0 2 -> 1 1 2 0 1 0 1 0 0 0 0 0 1 0 0 1 2 , 1 1 2 2 1 1 1 1 0 1 1 0 0 -> 1 0 1 1 1 2 1 1 0 1 0 1 1 1 0 0 0 , 1 1 2 2 2 1 0 0 1 1 0 0 0 -> 0 1 0 1 1 1 1 1 0 2 1 0 1 1 0 0 0 , 1 2 0 1 0 1 1 1 0 1 1 1 1 -> 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 , 1 2 1 0 0 0 0 1 0 1 1 2 1 -> 0 1 0 0 1 0 0 0 1 1 0 0 2 1 0 0 0 , 1 2 1 0 1 0 0 1 0 2 0 1 1 -> 1 0 0 1 0 0 0 2 2 0 0 1 0 0 1 1 0 , 1 2 2 0 1 1 1 1 1 1 0 1 0 -> 1 0 0 2 2 0 0 1 0 0 1 0 0 0 1 1 0 , 2 1 0 0 1 1 0 1 2 1 0 1 1 -> 1 0 0 0 1 0 0 0 0 2 1 0 0 1 1 0 1 , 2 1 0 1 2 0 0 2 0 1 0 1 2 -> 2 1 0 0 1 0 0 0 0 1 0 2 2 2 0 1 2 , 2 1 0 2 2 2 2 1 0 0 0 0 1 -> 1 1 1 0 0 0 1 1 2 1 0 0 1 2 0 1 0 , 2 1 1 0 1 0 1 1 1 2 1 1 0 -> 1 1 2 1 1 0 0 1 1 0 0 1 1 0 1 0 0 , 2 1 1 0 2 1 0 2 1 0 0 0 1 -> 0 1 0 1 1 1 1 2 0 1 0 0 1 0 0 1 0 , 2 1 1 1 1 1 1 1 0 0 2 0 1 -> 1 1 1 0 1 1 1 0 1 0 0 1 0 2 0 1 0 , 2 2 1 0 0 2 1 1 1 1 1 0 1 -> 2 2 2 0 0 0 1 0 1 0 1 1 0 1 1 1 0 , 2 2 1 0 0 2 1 2 0 0 1 0 2 -> 2 1 0 0 0 2 1 0 0 1 2 0 0 1 1 1 2 , 2 2 2 0 0 0 1 0 0 0 0 1 0 -> 0 2 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 } The system was reversed. After renaming modulo { 1->0, 0->1, 2->2 }, it remains to prove termination of the 44-rule system { 0 1 2 0 1 1 1 1 0 0 1 1 1 -> 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 , 0 0 1 1 0 0 2 2 0 0 1 1 1 -> 1 0 1 1 1 0 0 1 0 1 1 1 2 1 0 0 1 , 1 0 1 1 0 1 1 0 2 1 1 0 1 -> 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 , 2 0 1 2 1 1 1 1 0 0 1 0 1 -> 2 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 , 1 1 1 0 1 0 2 1 0 0 1 0 1 -> 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 , 0 2 1 1 1 2 1 0 1 1 0 0 1 -> 0 0 0 2 0 0 1 1 0 0 1 0 1 0 0 1 1 , 0 0 0 2 1 1 1 1 1 0 2 0 1 -> 0 1 1 1 0 0 1 1 1 0 1 2 0 0 1 0 1 , 0 1 1 1 1 1 1 0 2 1 1 2 1 -> 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 , 0 0 0 1 2 2 0 2 0 1 0 2 1 -> 0 0 0 0 2 0 1 1 0 0 2 1 1 0 0 2 1 , 0 1 1 1 2 0 1 0 2 1 0 2 1 -> 1 0 1 1 1 2 1 0 1 1 0 0 0 0 2 1 1 , 0 0 1 0 2 1 1 1 1 0 0 2 1 -> 1 1 1 1 1 0 0 0 2 1 0 1 0 1 0 1 1 , 0 1 0 1 0 1 0 0 1 1 2 2 1 -> 1 1 0 0 1 0 0 1 0 0 1 1 1 0 2 1 1 , 0 0 2 1 1 0 0 0 1 1 1 1 0 -> 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 , 2 1 0 1 1 2 0 0 0 1 1 1 0 -> 2 0 1 2 1 1 1 1 1 0 1 1 0 1 0 0 1 , 1 0 1 1 1 0 1 2 0 1 1 1 0 -> 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 , 0 1 0 1 2 1 1 0 2 1 1 1 0 -> 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 2 , 1 0 0 2 1 0 2 0 1 0 1 1 0 -> 1 0 0 0 0 0 0 2 1 1 1 1 1 0 0 0 1 , 0 1 0 0 1 0 0 2 1 0 1 1 0 -> 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 , 2 0 0 2 2 1 1 1 2 0 1 1 0 -> 2 0 2 0 1 0 0 0 1 2 2 1 0 1 1 1 0 , 0 2 1 2 1 0 0 0 2 0 1 1 0 -> 1 1 0 2 2 0 1 0 1 2 0 1 1 0 1 1 0 , 2 1 0 2 1 0 1 0 1 2 1 1 0 -> 2 1 1 0 0 1 0 1 0 0 1 2 1 1 1 0 1 , 0 1 1 0 2 0 0 2 0 1 0 1 0 -> 1 1 0 0 1 1 1 1 2 2 1 1 0 1 1 0 0 , 1 1 0 1 1 0 2 0 1 2 0 1 0 -> 0 1 0 2 1 0 0 0 0 1 0 0 1 1 1 1 1 , 2 1 0 1 0 1 0 1 0 2 2 1 0 -> 2 0 2 1 1 1 0 0 1 1 1 1 1 1 0 0 0 , 1 1 1 1 0 2 2 2 1 0 1 0 0 -> 0 1 1 2 1 1 0 1 0 1 0 1 0 0 1 0 0 , 2 0 2 0 2 0 1 1 2 2 1 0 0 -> 2 1 0 1 0 0 2 2 1 0 0 1 1 1 2 0 0 , 2 1 1 0 0 2 1 0 1 0 0 0 0 -> 2 1 0 2 1 1 0 1 0 0 1 0 1 1 0 0 0 , 1 0 1 2 1 2 1 0 0 2 0 0 0 -> 1 0 1 0 2 0 1 1 2 2 1 0 1 1 0 0 0 , 2 1 0 0 1 0 0 1 0 0 2 0 0 -> 2 0 1 1 0 1 1 1 1 1 0 1 0 1 2 0 0 , 1 1 0 0 1 0 0 0 0 2 2 0 0 -> 1 1 1 0 0 0 1 0 1 0 0 2 0 0 0 1 0 , 1 1 1 0 0 1 1 0 2 2 2 0 0 -> 1 1 1 0 0 1 0 2 1 0 0 0 0 0 1 0 1 , 0 0 0 0 1 0 0 0 1 0 1 2 0 -> 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 , 0 2 0 0 1 0 1 1 1 1 0 2 0 -> 1 1 1 0 2 1 1 0 0 1 1 1 0 1 1 0 1 , 0 0 1 2 1 0 1 1 0 1 0 2 0 -> 1 0 0 1 1 0 1 1 2 2 1 1 1 0 1 1 0 , 1 0 1 0 0 0 0 0 0 1 2 2 0 -> 1 0 0 1 1 1 0 1 1 0 1 1 2 2 1 1 0 , 0 0 1 0 2 0 1 0 0 1 1 0 2 -> 0 1 0 0 1 1 0 2 1 1 1 1 0 1 1 1 0 , 2 0 1 0 1 2 1 1 2 0 1 0 2 -> 2 0 1 2 2 2 1 0 1 1 1 1 0 1 1 0 2 , 0 1 1 1 1 0 2 2 2 2 1 0 2 -> 1 0 1 2 0 1 1 0 2 0 0 1 1 1 0 0 0 , 1 0 0 2 0 0 0 1 0 1 0 0 2 -> 1 1 0 1 0 0 1 1 0 0 1 1 0 0 2 0 0 , 0 1 1 1 0 2 1 0 2 1 0 0 2 -> 1 0 1 1 0 1 1 0 1 2 0 0 0 0 1 0 1 , 0 1 2 1 1 0 0 0 0 0 0 0 2 -> 1 0 1 2 1 0 1 1 0 1 0 0 0 1 0 0 0 , 0 1 0 0 0 0 0 2 1 1 0 2 2 -> 1 0 0 0 1 0 0 1 0 1 0 1 1 1 2 2 2 , 2 1 0 1 1 2 0 2 1 1 0 2 2 -> 2 0 0 0 1 1 2 0 1 1 0 2 1 1 1 0 2 , 1 0 1 1 1 1 0 1 1 1 2 2 2 -> 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 2 1 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,0)->3, (1,1)->4, (1,0)->5, (0,2)->6, (1,4)->7, (0,4)->8, (2,1)->9, (3,0)->10, (3,1)->11, (2,2)->12, (3,2)->13, (2,4)->14 }, it remains to prove termination of the 704-rule system { 0 1 2 3 1 4 4 4 5 0 1 4 4 5 -> 1 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 0 , 0 1 2 3 1 4 4 4 5 0 1 4 4 4 -> 1 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 1 , 0 1 2 3 1 4 4 4 5 0 1 4 4 2 -> 1 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 6 , 0 1 2 3 1 4 4 4 5 0 1 4 4 7 -> 1 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 8 , 5 1 2 3 1 4 4 4 5 0 1 4 4 5 -> 4 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 0 , 5 1 2 3 1 4 4 4 5 0 1 4 4 4 -> 4 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 1 , 5 1 2 3 1 4 4 4 5 0 1 4 4 2 -> 4 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 6 , 5 1 2 3 1 4 4 4 5 0 1 4 4 7 -> 4 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 8 , 3 1 2 3 1 4 4 4 5 0 1 4 4 5 -> 9 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 0 , 3 1 2 3 1 4 4 4 5 0 1 4 4 4 -> 9 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 1 , 3 1 2 3 1 4 4 4 5 0 1 4 4 2 -> 9 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 6 , 3 1 2 3 1 4 4 4 5 0 1 4 4 7 -> 9 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 8 , 10 1 2 3 1 4 4 4 5 0 1 4 4 5 -> 11 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 0 , 10 1 2 3 1 4 4 4 5 0 1 4 4 4 -> 11 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 1 , 10 1 2 3 1 4 4 4 5 0 1 4 4 2 -> 11 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 6 , 10 1 2 3 1 4 4 4 5 0 1 4 4 7 -> 11 4 5 0 1 5 0 1 4 5 1 4 4 5 0 0 0 8 , 0 0 1 4 5 0 6 12 3 0 1 4 4 5 -> 1 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 5 , 0 0 1 4 5 0 6 12 3 0 1 4 4 4 -> 1 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 4 , 0 0 1 4 5 0 6 12 3 0 1 4 4 2 -> 1 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 2 , 0 0 1 4 5 0 6 12 3 0 1 4 4 7 -> 1 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 7 , 5 0 1 4 5 0 6 12 3 0 1 4 4 5 -> 4 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 5 , 5 0 1 4 5 0 6 12 3 0 1 4 4 4 -> 4 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 4 , 5 0 1 4 5 0 6 12 3 0 1 4 4 2 -> 4 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 2 , 5 0 1 4 5 0 6 12 3 0 1 4 4 7 -> 4 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 7 , 3 0 1 4 5 0 6 12 3 0 1 4 4 5 -> 9 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 5 , 3 0 1 4 5 0 6 12 3 0 1 4 4 4 -> 9 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 4 , 3 0 1 4 5 0 6 12 3 0 1 4 4 2 -> 9 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 2 , 3 0 1 4 5 0 6 12 3 0 1 4 4 7 -> 9 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 7 , 10 0 1 4 5 0 6 12 3 0 1 4 4 5 -> 11 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 5 , 10 0 1 4 5 0 6 12 3 0 1 4 4 4 -> 11 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 4 , 10 0 1 4 5 0 6 12 3 0 1 4 4 2 -> 11 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 2 , 10 0 1 4 5 0 6 12 3 0 1 4 4 7 -> 11 5 1 4 4 5 0 1 5 1 4 4 2 9 5 0 1 7 , 1 5 1 4 5 1 4 5 6 9 4 5 1 5 -> 1 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 5 , 1 5 1 4 5 1 4 5 6 9 4 5 1 4 -> 1 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 4 , 1 5 1 4 5 1 4 5 6 9 4 5 1 2 -> 1 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 2 , 1 5 1 4 5 1 4 5 6 9 4 5 1 7 -> 1 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 7 , 4 5 1 4 5 1 4 5 6 9 4 5 1 5 -> 4 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 5 , 4 5 1 4 5 1 4 5 6 9 4 5 1 4 -> 4 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 4 , 4 5 1 4 5 1 4 5 6 9 4 5 1 2 -> 4 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 2 , 4 5 1 4 5 1 4 5 6 9 4 5 1 7 -> 4 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 7 , 9 5 1 4 5 1 4 5 6 9 4 5 1 5 -> 9 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 5 , 9 5 1 4 5 1 4 5 6 9 4 5 1 4 -> 9 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 4 , 9 5 1 4 5 1 4 5 6 9 4 5 1 2 -> 9 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 2 , 9 5 1 4 5 1 4 5 6 9 4 5 1 7 -> 9 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 7 , 11 5 1 4 5 1 4 5 6 9 4 5 1 5 -> 11 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 5 , 11 5 1 4 5 1 4 5 6 9 4 5 1 4 -> 11 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 4 , 11 5 1 4 5 1 4 5 6 9 4 5 1 2 -> 11 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 2 , 11 5 1 4 5 1 4 5 6 9 4 5 1 7 -> 11 4 5 0 0 1 4 5 1 5 0 1 4 4 5 0 1 7 , 6 3 1 2 9 4 4 4 5 0 1 5 1 5 -> 6 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 0 , 6 3 1 2 9 4 4 4 5 0 1 5 1 4 -> 6 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 1 , 6 3 1 2 9 4 4 4 5 0 1 5 1 2 -> 6 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 6 , 6 3 1 2 9 4 4 4 5 0 1 5 1 7 -> 6 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 8 , 2 3 1 2 9 4 4 4 5 0 1 5 1 5 -> 2 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 0 , 2 3 1 2 9 4 4 4 5 0 1 5 1 4 -> 2 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 1 , 2 3 1 2 9 4 4 4 5 0 1 5 1 2 -> 2 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 6 , 2 3 1 2 9 4 4 4 5 0 1 5 1 7 -> 2 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 8 , 12 3 1 2 9 4 4 4 5 0 1 5 1 5 -> 12 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 0 , 12 3 1 2 9 4 4 4 5 0 1 5 1 4 -> 12 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 1 , 12 3 1 2 9 4 4 4 5 0 1 5 1 2 -> 12 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 6 , 12 3 1 2 9 4 4 4 5 0 1 5 1 7 -> 12 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 8 , 13 3 1 2 9 4 4 4 5 0 1 5 1 5 -> 13 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 0 , 13 3 1 2 9 4 4 4 5 0 1 5 1 4 -> 13 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 1 , 13 3 1 2 9 4 4 4 5 0 1 5 1 2 -> 13 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 6 , 13 3 1 2 9 4 4 4 5 0 1 5 1 7 -> 13 9 4 5 0 0 1 5 0 1 5 1 4 4 5 0 0 8 , 1 4 4 5 1 5 6 9 5 0 1 5 1 5 -> 1 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 5 , 1 4 4 5 1 5 6 9 5 0 1 5 1 4 -> 1 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 4 , 1 4 4 5 1 5 6 9 5 0 1 5 1 2 -> 1 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 2 , 1 4 4 5 1 5 6 9 5 0 1 5 1 7 -> 1 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 7 , 4 4 4 5 1 5 6 9 5 0 1 5 1 5 -> 4 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 5 , 4 4 4 5 1 5 6 9 5 0 1 5 1 4 -> 4 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 4 , 4 4 4 5 1 5 6 9 5 0 1 5 1 2 -> 4 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 2 , 4 4 4 5 1 5 6 9 5 0 1 5 1 7 -> 4 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 7 , 9 4 4 5 1 5 6 9 5 0 1 5 1 5 -> 9 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 5 , 9 4 4 5 1 5 6 9 5 0 1 5 1 4 -> 9 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 4 , 9 4 4 5 1 5 6 9 5 0 1 5 1 2 -> 9 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 2 , 9 4 4 5 1 5 6 9 5 0 1 5 1 7 -> 9 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 7 , 11 4 4 5 1 5 6 9 5 0 1 5 1 5 -> 11 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 5 , 11 4 4 5 1 5 6 9 5 0 1 5 1 4 -> 11 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 4 , 11 4 4 5 1 5 6 9 5 0 1 5 1 2 -> 11 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 2 , 11 4 4 5 1 5 6 9 5 0 1 5 1 7 -> 11 5 0 0 1 5 1 4 5 1 4 5 0 1 5 0 1 7 , 0 6 9 4 4 2 9 5 1 4 5 0 1 5 -> 0 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 5 , 0 6 9 4 4 2 9 5 1 4 5 0 1 4 -> 0 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 4 , 0 6 9 4 4 2 9 5 1 4 5 0 1 2 -> 0 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 2 , 0 6 9 4 4 2 9 5 1 4 5 0 1 7 -> 0 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 7 , 5 6 9 4 4 2 9 5 1 4 5 0 1 5 -> 5 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 5 , 5 6 9 4 4 2 9 5 1 4 5 0 1 4 -> 5 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 4 , 5 6 9 4 4 2 9 5 1 4 5 0 1 2 -> 5 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 2 , 5 6 9 4 4 2 9 5 1 4 5 0 1 7 -> 5 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 7 , 3 6 9 4 4 2 9 5 1 4 5 0 1 5 -> 3 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 5 , 3 6 9 4 4 2 9 5 1 4 5 0 1 4 -> 3 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 4 , 3 6 9 4 4 2 9 5 1 4 5 0 1 2 -> 3 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 2 , 3 6 9 4 4 2 9 5 1 4 5 0 1 7 -> 3 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 7 , 10 6 9 4 4 2 9 5 1 4 5 0 1 5 -> 10 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 5 , 10 6 9 4 4 2 9 5 1 4 5 0 1 4 -> 10 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 4 , 10 6 9 4 4 2 9 5 1 4 5 0 1 2 -> 10 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 2 , 10 6 9 4 4 2 9 5 1 4 5 0 1 7 -> 10 0 0 6 3 0 1 4 5 0 1 5 1 5 0 1 4 7 , 0 0 0 6 9 4 4 4 4 5 6 3 1 5 -> 0 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 5 , 0 0 0 6 9 4 4 4 4 5 6 3 1 4 -> 0 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 4 , 0 0 0 6 9 4 4 4 4 5 6 3 1 2 -> 0 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 2 , 0 0 0 6 9 4 4 4 4 5 6 3 1 7 -> 0 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 7 , 5 0 0 6 9 4 4 4 4 5 6 3 1 5 -> 5 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 5 , 5 0 0 6 9 4 4 4 4 5 6 3 1 4 -> 5 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 4 , 5 0 0 6 9 4 4 4 4 5 6 3 1 2 -> 5 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 2 , 5 0 0 6 9 4 4 4 4 5 6 3 1 7 -> 5 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 7 , 3 0 0 6 9 4 4 4 4 5 6 3 1 5 -> 3 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 5 , 3 0 0 6 9 4 4 4 4 5 6 3 1 4 -> 3 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 4 , 3 0 0 6 9 4 4 4 4 5 6 3 1 2 -> 3 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 2 , 3 0 0 6 9 4 4 4 4 5 6 3 1 7 -> 3 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 7 , 10 0 0 6 9 4 4 4 4 5 6 3 1 5 -> 10 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 5 , 10 0 0 6 9 4 4 4 4 5 6 3 1 4 -> 10 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 4 , 10 0 0 6 9 4 4 4 4 5 6 3 1 2 -> 10 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 2 , 10 0 0 6 9 4 4 4 4 5 6 3 1 7 -> 10 1 4 4 5 0 1 4 4 5 1 2 3 0 1 5 1 7 , 0 1 4 4 4 4 4 5 6 9 4 2 9 5 -> 0 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 0 , 0 1 4 4 4 4 4 5 6 9 4 2 9 4 -> 0 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 1 , 0 1 4 4 4 4 4 5 6 9 4 2 9 2 -> 0 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 6 , 0 1 4 4 4 4 4 5 6 9 4 2 9 7 -> 0 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 8 , 5 1 4 4 4 4 4 5 6 9 4 2 9 5 -> 5 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 0 , 5 1 4 4 4 4 4 5 6 9 4 2 9 4 -> 5 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 1 , 5 1 4 4 4 4 4 5 6 9 4 2 9 2 -> 5 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 6 , 5 1 4 4 4 4 4 5 6 9 4 2 9 7 -> 5 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 8 , 3 1 4 4 4 4 4 5 6 9 4 2 9 5 -> 3 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 0 , 3 1 4 4 4 4 4 5 6 9 4 2 9 4 -> 3 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 1 , 3 1 4 4 4 4 4 5 6 9 4 2 9 2 -> 3 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 6 , 3 1 4 4 4 4 4 5 6 9 4 2 9 7 -> 3 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 8 , 10 1 4 4 4 4 4 5 6 9 4 2 9 5 -> 10 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 0 , 10 1 4 4 4 4 4 5 6 9 4 2 9 4 -> 10 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 1 , 10 1 4 4 4 4 4 5 6 9 4 2 9 2 -> 10 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 6 , 10 1 4 4 4 4 4 5 6 9 4 2 9 7 -> 10 1 4 4 4 5 1 4 4 5 0 0 1 5 1 4 5 8 , 0 0 0 1 2 12 3 6 3 1 5 6 9 5 -> 0 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 5 , 0 0 0 1 2 12 3 6 3 1 5 6 9 4 -> 0 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 4 , 0 0 0 1 2 12 3 6 3 1 5 6 9 2 -> 0 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 2 , 0 0 0 1 2 12 3 6 3 1 5 6 9 7 -> 0 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 7 , 5 0 0 1 2 12 3 6 3 1 5 6 9 5 -> 5 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 5 , 5 0 0 1 2 12 3 6 3 1 5 6 9 4 -> 5 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 4 , 5 0 0 1 2 12 3 6 3 1 5 6 9 2 -> 5 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 2 , 5 0 0 1 2 12 3 6 3 1 5 6 9 7 -> 5 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 7 , 3 0 0 1 2 12 3 6 3 1 5 6 9 5 -> 3 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 5 , 3 0 0 1 2 12 3 6 3 1 5 6 9 4 -> 3 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 4 , 3 0 0 1 2 12 3 6 3 1 5 6 9 2 -> 3 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 2 , 3 0 0 1 2 12 3 6 3 1 5 6 9 7 -> 3 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 7 , 10 0 0 1 2 12 3 6 3 1 5 6 9 5 -> 10 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 5 , 10 0 0 1 2 12 3 6 3 1 5 6 9 4 -> 10 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 4 , 10 0 0 1 2 12 3 6 3 1 5 6 9 2 -> 10 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 2 , 10 0 0 1 2 12 3 6 3 1 5 6 9 7 -> 10 0 0 0 6 3 1 4 5 0 6 9 4 5 0 6 9 7 , 0 1 4 4 2 3 1 5 6 9 5 6 9 5 -> 1 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 5 , 0 1 4 4 2 3 1 5 6 9 5 6 9 4 -> 1 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 4 , 0 1 4 4 2 3 1 5 6 9 5 6 9 2 -> 1 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 2 , 0 1 4 4 2 3 1 5 6 9 5 6 9 7 -> 1 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 7 , 5 1 4 4 2 3 1 5 6 9 5 6 9 5 -> 4 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 5 , 5 1 4 4 2 3 1 5 6 9 5 6 9 4 -> 4 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 4 , 5 1 4 4 2 3 1 5 6 9 5 6 9 2 -> 4 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 2 , 5 1 4 4 2 3 1 5 6 9 5 6 9 7 -> 4 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 7 , 3 1 4 4 2 3 1 5 6 9 5 6 9 5 -> 9 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 5 , 3 1 4 4 2 3 1 5 6 9 5 6 9 4 -> 9 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 4 , 3 1 4 4 2 3 1 5 6 9 5 6 9 2 -> 9 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 2 , 3 1 4 4 2 3 1 5 6 9 5 6 9 7 -> 9 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 7 , 10 1 4 4 2 3 1 5 6 9 5 6 9 5 -> 11 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 5 , 10 1 4 4 2 3 1 5 6 9 5 6 9 4 -> 11 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 4 , 10 1 4 4 2 3 1 5 6 9 5 6 9 2 -> 11 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 2 , 10 1 4 4 2 3 1 5 6 9 5 6 9 7 -> 11 5 1 4 4 2 9 5 1 4 5 0 0 0 6 9 4 7 , 0 0 1 5 6 9 4 4 4 5 0 6 9 5 -> 1 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 5 , 0 0 1 5 6 9 4 4 4 5 0 6 9 4 -> 1 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 4 , 0 0 1 5 6 9 4 4 4 5 0 6 9 2 -> 1 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 2 , 0 0 1 5 6 9 4 4 4 5 0 6 9 7 -> 1 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 7 , 5 0 1 5 6 9 4 4 4 5 0 6 9 5 -> 4 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 5 , 5 0 1 5 6 9 4 4 4 5 0 6 9 4 -> 4 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 4 , 5 0 1 5 6 9 4 4 4 5 0 6 9 2 -> 4 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 2 , 5 0 1 5 6 9 4 4 4 5 0 6 9 7 -> 4 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 7 , 3 0 1 5 6 9 4 4 4 5 0 6 9 5 -> 9 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 5 , 3 0 1 5 6 9 4 4 4 5 0 6 9 4 -> 9 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 4 , 3 0 1 5 6 9 4 4 4 5 0 6 9 2 -> 9 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 2 , 3 0 1 5 6 9 4 4 4 5 0 6 9 7 -> 9 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 7 , 10 0 1 5 6 9 4 4 4 5 0 6 9 5 -> 11 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 5 , 10 0 1 5 6 9 4 4 4 5 0 6 9 4 -> 11 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 4 , 10 0 1 5 6 9 4 4 4 5 0 6 9 2 -> 11 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 2 , 10 0 1 5 6 9 4 4 4 5 0 6 9 7 -> 11 4 4 4 4 5 0 0 6 9 5 1 5 1 5 1 4 7 , 0 1 5 1 5 1 5 0 1 4 2 12 9 5 -> 1 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 5 , 0 1 5 1 5 1 5 0 1 4 2 12 9 4 -> 1 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 4 , 0 1 5 1 5 1 5 0 1 4 2 12 9 2 -> 1 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 2 , 0 1 5 1 5 1 5 0 1 4 2 12 9 7 -> 1 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 7 , 5 1 5 1 5 1 5 0 1 4 2 12 9 5 -> 4 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 5 , 5 1 5 1 5 1 5 0 1 4 2 12 9 4 -> 4 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 4 , 5 1 5 1 5 1 5 0 1 4 2 12 9 2 -> 4 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 2 , 5 1 5 1 5 1 5 0 1 4 2 12 9 7 -> 4 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 7 , 3 1 5 1 5 1 5 0 1 4 2 12 9 5 -> 9 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 5 , 3 1 5 1 5 1 5 0 1 4 2 12 9 4 -> 9 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 4 , 3 1 5 1 5 1 5 0 1 4 2 12 9 2 -> 9 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 2 , 3 1 5 1 5 1 5 0 1 4 2 12 9 7 -> 9 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 7 , 10 1 5 1 5 1 5 0 1 4 2 12 9 5 -> 11 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 5 , 10 1 5 1 5 1 5 0 1 4 2 12 9 4 -> 11 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 4 , 10 1 5 1 5 1 5 0 1 4 2 12 9 2 -> 11 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 2 , 10 1 5 1 5 1 5 0 1 4 2 12 9 7 -> 11 4 5 0 1 5 0 1 5 0 1 4 4 5 6 9 4 7 , 0 0 6 9 4 5 0 0 1 4 4 4 5 0 -> 1 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 0 , 0 0 6 9 4 5 0 0 1 4 4 4 5 1 -> 1 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 1 , 0 0 6 9 4 5 0 0 1 4 4 4 5 6 -> 1 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 6 , 0 0 6 9 4 5 0 0 1 4 4 4 5 8 -> 1 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 8 , 5 0 6 9 4 5 0 0 1 4 4 4 5 0 -> 4 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 0 , 5 0 6 9 4 5 0 0 1 4 4 4 5 1 -> 4 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 1 , 5 0 6 9 4 5 0 0 1 4 4 4 5 6 -> 4 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 6 , 5 0 6 9 4 5 0 0 1 4 4 4 5 8 -> 4 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 8 , 3 0 6 9 4 5 0 0 1 4 4 4 5 0 -> 9 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 0 , 3 0 6 9 4 5 0 0 1 4 4 4 5 1 -> 9 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 1 , 3 0 6 9 4 5 0 0 1 4 4 4 5 6 -> 9 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 6 , 3 0 6 9 4 5 0 0 1 4 4 4 5 8 -> 9 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 8 , 10 0 6 9 4 5 0 0 1 4 4 4 5 0 -> 11 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 0 , 10 0 6 9 4 5 0 0 1 4 4 4 5 1 -> 11 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 1 , 10 0 6 9 4 5 0 0 1 4 4 4 5 6 -> 11 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 6 , 10 0 6 9 4 5 0 0 1 4 4 4 5 8 -> 11 4 5 1 5 0 1 5 0 0 0 0 0 0 0 0 0 8 , 6 9 5 1 4 2 3 0 0 1 4 4 5 0 -> 6 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 5 , 6 9 5 1 4 2 3 0 0 1 4 4 5 1 -> 6 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 4 , 6 9 5 1 4 2 3 0 0 1 4 4 5 6 -> 6 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 2 , 6 9 5 1 4 2 3 0 0 1 4 4 5 8 -> 6 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 7 , 2 9 5 1 4 2 3 0 0 1 4 4 5 0 -> 2 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 5 , 2 9 5 1 4 2 3 0 0 1 4 4 5 1 -> 2 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 4 , 2 9 5 1 4 2 3 0 0 1 4 4 5 6 -> 2 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 2 , 2 9 5 1 4 2 3 0 0 1 4 4 5 8 -> 2 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 7 , 12 9 5 1 4 2 3 0 0 1 4 4 5 0 -> 12 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 5 , 12 9 5 1 4 2 3 0 0 1 4 4 5 1 -> 12 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 4 , 12 9 5 1 4 2 3 0 0 1 4 4 5 6 -> 12 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 2 , 12 9 5 1 4 2 3 0 0 1 4 4 5 8 -> 12 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 7 , 13 9 5 1 4 2 3 0 0 1 4 4 5 0 -> 13 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 5 , 13 9 5 1 4 2 3 0 0 1 4 4 5 1 -> 13 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 4 , 13 9 5 1 4 2 3 0 0 1 4 4 5 6 -> 13 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 2 , 13 9 5 1 4 2 3 0 0 1 4 4 5 8 -> 13 3 1 2 9 4 4 4 4 5 1 4 5 1 5 0 1 7 , 1 5 1 4 4 5 1 2 3 1 4 4 5 0 -> 0 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 0 , 1 5 1 4 4 5 1 2 3 1 4 4 5 1 -> 0 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 1 , 1 5 1 4 4 5 1 2 3 1 4 4 5 6 -> 0 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 6 , 1 5 1 4 4 5 1 2 3 1 4 4 5 8 -> 0 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 8 , 4 5 1 4 4 5 1 2 3 1 4 4 5 0 -> 5 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 0 , 4 5 1 4 4 5 1 2 3 1 4 4 5 1 -> 5 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 1 , 4 5 1 4 4 5 1 2 3 1 4 4 5 6 -> 5 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 6 , 4 5 1 4 4 5 1 2 3 1 4 4 5 8 -> 5 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 8 , 9 5 1 4 4 5 1 2 3 1 4 4 5 0 -> 3 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 0 , 9 5 1 4 4 5 1 2 3 1 4 4 5 1 -> 3 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 1 , 9 5 1 4 4 5 1 2 3 1 4 4 5 6 -> 3 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 6 , 9 5 1 4 4 5 1 2 3 1 4 4 5 8 -> 3 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 8 , 11 5 1 4 4 5 1 2 3 1 4 4 5 0 -> 10 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 0 , 11 5 1 4 4 5 1 2 3 1 4 4 5 1 -> 10 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 1 , 11 5 1 4 4 5 1 2 3 1 4 4 5 6 -> 10 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 6 , 11 5 1 4 4 5 1 2 3 1 4 4 5 8 -> 10 1 5 0 0 1 5 0 1 5 0 1 4 4 5 0 0 8 , 0 1 5 1 2 9 4 5 6 9 4 4 5 0 -> 1 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 3 , 0 1 5 1 2 9 4 5 6 9 4 4 5 1 -> 1 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 9 , 0 1 5 1 2 9 4 5 6 9 4 4 5 6 -> 1 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 12 , 0 1 5 1 2 9 4 5 6 9 4 4 5 8 -> 1 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 14 , 5 1 5 1 2 9 4 5 6 9 4 4 5 0 -> 4 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 3 , 5 1 5 1 2 9 4 5 6 9 4 4 5 1 -> 4 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 9 , 5 1 5 1 2 9 4 5 6 9 4 4 5 6 -> 4 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 12 , 5 1 5 1 2 9 4 5 6 9 4 4 5 8 -> 4 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 14 , 3 1 5 1 2 9 4 5 6 9 4 4 5 0 -> 9 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 3 , 3 1 5 1 2 9 4 5 6 9 4 4 5 1 -> 9 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 9 , 3 1 5 1 2 9 4 5 6 9 4 4 5 6 -> 9 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 12 , 3 1 5 1 2 9 4 5 6 9 4 4 5 8 -> 9 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 14 , 10 1 5 1 2 9 4 5 6 9 4 4 5 0 -> 11 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 3 , 10 1 5 1 2 9 4 5 6 9 4 4 5 1 -> 11 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 9 , 10 1 5 1 2 9 4 5 6 9 4 4 5 6 -> 11 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 12 , 10 1 5 1 2 9 4 5 6 9 4 4 5 8 -> 11 4 4 5 1 4 4 4 4 5 1 5 0 1 4 5 6 14 , 1 5 0 6 9 5 6 3 1 5 1 4 5 0 -> 1 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 5 , 1 5 0 6 9 5 6 3 1 5 1 4 5 1 -> 1 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 4 , 1 5 0 6 9 5 6 3 1 5 1 4 5 6 -> 1 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 2 , 1 5 0 6 9 5 6 3 1 5 1 4 5 8 -> 1 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 7 , 4 5 0 6 9 5 6 3 1 5 1 4 5 0 -> 4 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 5 , 4 5 0 6 9 5 6 3 1 5 1 4 5 1 -> 4 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 4 , 4 5 0 6 9 5 6 3 1 5 1 4 5 6 -> 4 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 2 , 4 5 0 6 9 5 6 3 1 5 1 4 5 8 -> 4 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 7 , 9 5 0 6 9 5 6 3 1 5 1 4 5 0 -> 9 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 5 , 9 5 0 6 9 5 6 3 1 5 1 4 5 1 -> 9 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 4 , 9 5 0 6 9 5 6 3 1 5 1 4 5 6 -> 9 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 2 , 9 5 0 6 9 5 6 3 1 5 1 4 5 8 -> 9 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 7 , 11 5 0 6 9 5 6 3 1 5 1 4 5 0 -> 11 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 5 , 11 5 0 6 9 5 6 3 1 5 1 4 5 1 -> 11 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 4 , 11 5 0 6 9 5 6 3 1 5 1 4 5 6 -> 11 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 2 , 11 5 0 6 9 5 6 3 1 5 1 4 5 8 -> 11 5 0 0 0 0 0 6 9 4 4 4 4 5 0 0 1 7 , 0 1 5 0 1 5 0 6 9 5 1 4 5 0 -> 0 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 0 , 0 1 5 0 1 5 0 6 9 5 1 4 5 1 -> 0 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 1 , 0 1 5 0 1 5 0 6 9 5 1 4 5 6 -> 0 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 6 , 0 1 5 0 1 5 0 6 9 5 1 4 5 8 -> 0 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 8 , 5 1 5 0 1 5 0 6 9 5 1 4 5 0 -> 5 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 0 , 5 1 5 0 1 5 0 6 9 5 1 4 5 1 -> 5 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 1 , 5 1 5 0 1 5 0 6 9 5 1 4 5 6 -> 5 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 6 , 5 1 5 0 1 5 0 6 9 5 1 4 5 8 -> 5 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 8 , 3 1 5 0 1 5 0 6 9 5 1 4 5 0 -> 3 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 0 , 3 1 5 0 1 5 0 6 9 5 1 4 5 1 -> 3 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 1 , 3 1 5 0 1 5 0 6 9 5 1 4 5 6 -> 3 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 6 , 3 1 5 0 1 5 0 6 9 5 1 4 5 8 -> 3 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 8 , 10 1 5 0 1 5 0 6 9 5 1 4 5 0 -> 10 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 0 , 10 1 5 0 1 5 0 6 9 5 1 4 5 1 -> 10 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 1 , 10 1 5 0 1 5 0 6 9 5 1 4 5 6 -> 10 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 6 , 10 1 5 0 1 5 0 6 9 5 1 4 5 8 -> 10 0 1 4 5 0 0 1 5 1 5 1 4 5 0 0 0 8 , 6 3 0 6 12 9 4 4 2 3 1 4 5 0 -> 6 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 0 , 6 3 0 6 12 9 4 4 2 3 1 4 5 1 -> 6 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 1 , 6 3 0 6 12 9 4 4 2 3 1 4 5 6 -> 6 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 6 , 6 3 0 6 12 9 4 4 2 3 1 4 5 8 -> 6 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 8 , 2 3 0 6 12 9 4 4 2 3 1 4 5 0 -> 2 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 0 , 2 3 0 6 12 9 4 4 2 3 1 4 5 1 -> 2 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 1 , 2 3 0 6 12 9 4 4 2 3 1 4 5 6 -> 2 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 6 , 2 3 0 6 12 9 4 4 2 3 1 4 5 8 -> 2 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 8 , 12 3 0 6 12 9 4 4 2 3 1 4 5 0 -> 12 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 0 , 12 3 0 6 12 9 4 4 2 3 1 4 5 1 -> 12 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 1 , 12 3 0 6 12 9 4 4 2 3 1 4 5 6 -> 12 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 6 , 12 3 0 6 12 9 4 4 2 3 1 4 5 8 -> 12 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 8 , 13 3 0 6 12 9 4 4 2 3 1 4 5 0 -> 13 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 0 , 13 3 0 6 12 9 4 4 2 3 1 4 5 1 -> 13 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 1 , 13 3 0 6 12 9 4 4 2 3 1 4 5 6 -> 13 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 6 , 13 3 0 6 12 9 4 4 2 3 1 4 5 8 -> 13 3 6 3 1 5 0 0 1 2 12 9 5 1 4 4 5 8 , 0 6 9 2 9 5 0 0 6 3 1 4 5 0 -> 1 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 0 , 0 6 9 2 9 5 0 0 6 3 1 4 5 1 -> 1 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 1 , 0 6 9 2 9 5 0 0 6 3 1 4 5 6 -> 1 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 6 , 0 6 9 2 9 5 0 0 6 3 1 4 5 8 -> 1 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 8 , 5 6 9 2 9 5 0 0 6 3 1 4 5 0 -> 4 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 0 , 5 6 9 2 9 5 0 0 6 3 1 4 5 1 -> 4 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 1 , 5 6 9 2 9 5 0 0 6 3 1 4 5 6 -> 4 4 5 6 12 3 1 5 1 2 3 1 4 5 1 4 5 6 , 5 6 9 2 9 5 0 0 6 3 1 4 5 8 -> 4 4 5 6 12 3 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1 5 0 0 1 5 1 2 3 6 -> 10 1 5 0 1 5 0 1 4 5 1 5 0 0 1 4 5 6 , 10 0 0 0 1 5 0 0 1 5 1 2 3 8 -> 10 1 5 0 1 5 0 1 4 5 1 5 0 0 1 4 5 8 , 0 6 3 0 1 5 1 4 4 4 5 6 3 0 -> 1 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 5 , 0 6 3 0 1 5 1 4 4 4 5 6 3 1 -> 1 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 4 , 0 6 3 0 1 5 1 4 4 4 5 6 3 6 -> 1 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 2 , 0 6 3 0 1 5 1 4 4 4 5 6 3 8 -> 1 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 7 , 5 6 3 0 1 5 1 4 4 4 5 6 3 0 -> 4 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 5 , 5 6 3 0 1 5 1 4 4 4 5 6 3 1 -> 4 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 4 , 5 6 3 0 1 5 1 4 4 4 5 6 3 6 -> 4 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 2 , 5 6 3 0 1 5 1 4 4 4 5 6 3 8 -> 4 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 7 , 3 6 3 0 1 5 1 4 4 4 5 6 3 0 -> 9 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 5 , 3 6 3 0 1 5 1 4 4 4 5 6 3 1 -> 9 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 4 , 3 6 3 0 1 5 1 4 4 4 5 6 3 6 -> 9 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 2 , 3 6 3 0 1 5 1 4 4 4 5 6 3 8 -> 9 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 7 , 10 6 3 0 1 5 1 4 4 4 5 6 3 0 -> 11 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 5 , 10 6 3 0 1 5 1 4 4 4 5 6 3 1 -> 11 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 4 , 10 6 3 0 1 5 1 4 4 4 5 6 3 6 -> 11 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 2 , 10 6 3 0 1 5 1 4 4 4 5 6 3 8 -> 11 4 4 5 6 9 4 5 0 1 4 4 5 1 4 5 1 7 , 0 0 1 2 9 5 1 4 5 1 5 6 3 0 -> 1 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 0 , 0 0 1 2 9 5 1 4 5 1 5 6 3 1 -> 1 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 1 , 0 0 1 2 9 5 1 4 5 1 5 6 3 6 -> 1 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 6 , 0 0 1 2 9 5 1 4 5 1 5 6 3 8 -> 1 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 8 , 5 0 1 2 9 5 1 4 5 1 5 6 3 0 -> 4 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 0 , 5 0 1 2 9 5 1 4 5 1 5 6 3 1 -> 4 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 1 , 5 0 1 2 9 5 1 4 5 1 5 6 3 6 -> 4 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 6 , 5 0 1 2 9 5 1 4 5 1 5 6 3 8 -> 4 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 8 , 3 0 1 2 9 5 1 4 5 1 5 6 3 0 -> 9 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 0 , 3 0 1 2 9 5 1 4 5 1 5 6 3 1 -> 9 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 1 , 3 0 1 2 9 5 1 4 5 1 5 6 3 6 -> 9 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 6 , 3 0 1 2 9 5 1 4 5 1 5 6 3 8 -> 9 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 8 , 10 0 1 2 9 5 1 4 5 1 5 6 3 0 -> 11 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 0 , 10 0 1 2 9 5 1 4 5 1 5 6 3 1 -> 11 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 1 , 10 0 1 2 9 5 1 4 5 1 5 6 3 6 -> 11 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 6 , 10 0 1 2 9 5 1 4 5 1 5 6 3 8 -> 11 5 0 1 4 5 1 4 2 12 9 4 4 5 1 4 5 8 , 1 5 1 5 0 0 0 0 0 1 2 12 3 0 -> 1 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 0 , 1 5 1 5 0 0 0 0 0 1 2 12 3 1 -> 1 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 1 , 1 5 1 5 0 0 0 0 0 1 2 12 3 6 -> 1 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 6 , 1 5 1 5 0 0 0 0 0 1 2 12 3 8 -> 1 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 8 , 4 5 1 5 0 0 0 0 0 1 2 12 3 0 -> 4 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 0 , 4 5 1 5 0 0 0 0 0 1 2 12 3 1 -> 4 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 1 , 4 5 1 5 0 0 0 0 0 1 2 12 3 6 -> 4 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 6 , 4 5 1 5 0 0 0 0 0 1 2 12 3 8 -> 4 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 8 , 9 5 1 5 0 0 0 0 0 1 2 12 3 0 -> 9 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 0 , 9 5 1 5 0 0 0 0 0 1 2 12 3 1 -> 9 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 1 , 9 5 1 5 0 0 0 0 0 1 2 12 3 6 -> 9 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 6 , 9 5 1 5 0 0 0 0 0 1 2 12 3 8 -> 9 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 8 , 11 5 1 5 0 0 0 0 0 1 2 12 3 0 -> 11 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 0 , 11 5 1 5 0 0 0 0 0 1 2 12 3 1 -> 11 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 1 , 11 5 1 5 0 0 0 0 0 1 2 12 3 6 -> 11 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 6 , 11 5 1 5 0 0 0 0 0 1 2 12 3 8 -> 11 5 0 1 4 4 5 1 4 5 1 4 2 12 9 4 5 8 , 0 0 1 5 6 3 1 5 0 1 4 5 6 3 -> 0 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 0 , 0 0 1 5 6 3 1 5 0 1 4 5 6 9 -> 0 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 1 , 0 0 1 5 6 3 1 5 0 1 4 5 6 12 -> 0 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 6 , 0 0 1 5 6 3 1 5 0 1 4 5 6 14 -> 0 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 8 , 5 0 1 5 6 3 1 5 0 1 4 5 6 3 -> 5 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 0 , 5 0 1 5 6 3 1 5 0 1 4 5 6 9 -> 5 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 1 , 5 0 1 5 6 3 1 5 0 1 4 5 6 12 -> 5 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 6 , 5 0 1 5 6 3 1 5 0 1 4 5 6 14 -> 5 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 8 , 3 0 1 5 6 3 1 5 0 1 4 5 6 3 -> 3 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 0 , 3 0 1 5 6 3 1 5 0 1 4 5 6 9 -> 3 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 1 , 3 0 1 5 6 3 1 5 0 1 4 5 6 12 -> 3 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 6 , 3 0 1 5 6 3 1 5 0 1 4 5 6 14 -> 3 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 8 , 10 0 1 5 6 3 1 5 0 1 4 5 6 3 -> 10 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 0 , 10 0 1 5 6 3 1 5 0 1 4 5 6 9 -> 10 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 1 , 10 0 1 5 6 3 1 5 0 1 4 5 6 12 -> 10 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 6 , 10 0 1 5 6 3 1 5 0 1 4 5 6 14 -> 10 1 5 0 1 4 5 6 9 4 4 4 5 1 4 4 5 8 , 6 3 1 5 1 2 9 4 2 3 1 5 6 3 -> 6 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 3 , 6 3 1 5 1 2 9 4 2 3 1 5 6 9 -> 6 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 9 , 6 3 1 5 1 2 9 4 2 3 1 5 6 12 -> 6 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 12 , 6 3 1 5 1 2 9 4 2 3 1 5 6 14 -> 6 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 14 , 2 3 1 5 1 2 9 4 2 3 1 5 6 3 -> 2 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 3 , 2 3 1 5 1 2 9 4 2 3 1 5 6 9 -> 2 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 9 , 2 3 1 5 1 2 9 4 2 3 1 5 6 12 -> 2 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 12 , 2 3 1 5 1 2 9 4 2 3 1 5 6 14 -> 2 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 14 , 12 3 1 5 1 2 9 4 2 3 1 5 6 3 -> 12 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 3 , 12 3 1 5 1 2 9 4 2 3 1 5 6 9 -> 12 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 9 , 12 3 1 5 1 2 9 4 2 3 1 5 6 12 -> 12 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 12 , 12 3 1 5 1 2 9 4 2 3 1 5 6 14 -> 12 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 14 , 13 3 1 5 1 2 9 4 2 3 1 5 6 3 -> 13 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 3 , 13 3 1 5 1 2 9 4 2 3 1 5 6 9 -> 13 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 9 , 13 3 1 5 1 2 9 4 2 3 1 5 6 12 -> 13 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 12 , 13 3 1 5 1 2 9 4 2 3 1 5 6 14 -> 13 3 1 2 12 12 9 5 1 4 4 4 5 1 4 5 6 14 , 0 1 4 4 4 5 6 12 12 12 9 5 6 3 -> 1 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 0 , 0 1 4 4 4 5 6 12 12 12 9 5 6 9 -> 1 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 1 , 0 1 4 4 4 5 6 12 12 12 9 5 6 12 -> 1 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 6 , 0 1 4 4 4 5 6 12 12 12 9 5 6 14 -> 1 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 8 , 5 1 4 4 4 5 6 12 12 12 9 5 6 3 -> 4 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 0 , 5 1 4 4 4 5 6 12 12 12 9 5 6 9 -> 4 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 1 , 5 1 4 4 4 5 6 12 12 12 9 5 6 12 -> 4 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 6 , 5 1 4 4 4 5 6 12 12 12 9 5 6 14 -> 4 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 8 , 3 1 4 4 4 5 6 12 12 12 9 5 6 3 -> 9 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 0 , 3 1 4 4 4 5 6 12 12 12 9 5 6 9 -> 9 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 1 , 3 1 4 4 4 5 6 12 12 12 9 5 6 12 -> 9 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 6 , 3 1 4 4 4 5 6 12 12 12 9 5 6 14 -> 9 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 8 , 10 1 4 4 4 5 6 12 12 12 9 5 6 3 -> 11 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 0 , 10 1 4 4 4 5 6 12 12 12 9 5 6 9 -> 11 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 1 , 10 1 4 4 4 5 6 12 12 12 9 5 6 12 -> 11 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 6 , 10 1 4 4 4 5 6 12 12 12 9 5 6 14 -> 11 5 1 2 3 1 4 5 6 3 0 1 4 4 5 0 0 8 , 1 5 0 6 3 0 0 1 5 1 5 0 6 3 -> 1 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 0 , 1 5 0 6 3 0 0 1 5 1 5 0 6 9 -> 1 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 1 , 1 5 0 6 3 0 0 1 5 1 5 0 6 12 -> 1 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 6 , 1 5 0 6 3 0 0 1 5 1 5 0 6 14 -> 1 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 8 , 4 5 0 6 3 0 0 1 5 1 5 0 6 3 -> 4 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 0 , 4 5 0 6 3 0 0 1 5 1 5 0 6 9 -> 4 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 1 , 4 5 0 6 3 0 0 1 5 1 5 0 6 12 -> 4 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 6 , 4 5 0 6 3 0 0 1 5 1 5 0 6 14 -> 4 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 8 , 9 5 0 6 3 0 0 1 5 1 5 0 6 3 -> 9 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 0 , 9 5 0 6 3 0 0 1 5 1 5 0 6 9 -> 9 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 1 , 9 5 0 6 3 0 0 1 5 1 5 0 6 12 -> 9 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 6 , 9 5 0 6 3 0 0 1 5 1 5 0 6 14 -> 9 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 8 , 11 5 0 6 3 0 0 1 5 1 5 0 6 3 -> 11 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 0 , 11 5 0 6 3 0 0 1 5 1 5 0 6 9 -> 11 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 1 , 11 5 0 6 3 0 0 1 5 1 5 0 6 12 -> 11 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 6 , 11 5 0 6 3 0 0 1 5 1 5 0 6 14 -> 11 4 5 1 5 0 1 4 5 0 1 4 5 0 6 3 0 8 , 0 1 4 4 5 6 9 5 6 9 5 0 6 3 -> 1 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 5 , 0 1 4 4 5 6 9 5 6 9 5 0 6 9 -> 1 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 4 , 0 1 4 4 5 6 9 5 6 9 5 0 6 12 -> 1 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 2 , 0 1 4 4 5 6 9 5 6 9 5 0 6 14 -> 1 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 7 , 5 1 4 4 5 6 9 5 6 9 5 0 6 3 -> 4 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 5 , 5 1 4 4 5 6 9 5 6 9 5 0 6 9 -> 4 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 4 , 5 1 4 4 5 6 9 5 6 9 5 0 6 12 -> 4 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 2 , 5 1 4 4 5 6 9 5 6 9 5 0 6 14 -> 4 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 7 , 3 1 4 4 5 6 9 5 6 9 5 0 6 3 -> 9 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 5 , 3 1 4 4 5 6 9 5 6 9 5 0 6 9 -> 9 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 4 , 3 1 4 4 5 6 9 5 6 9 5 0 6 12 -> 9 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 2 , 3 1 4 4 5 6 9 5 6 9 5 0 6 14 -> 9 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 7 , 10 1 4 4 5 6 9 5 6 9 5 0 6 3 -> 11 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 5 , 10 1 4 4 5 6 9 5 6 9 5 0 6 9 -> 11 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 4 , 10 1 4 4 5 6 9 5 6 9 5 0 6 12 -> 11 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 2 , 10 1 4 4 5 6 9 5 6 9 5 0 6 14 -> 11 5 1 4 5 1 4 5 1 2 3 0 0 0 1 5 1 7 , 0 1 2 9 4 5 0 0 0 0 0 0 6 3 -> 1 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 0 , 0 1 2 9 4 5 0 0 0 0 0 0 6 9 -> 1 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 1 , 0 1 2 9 4 5 0 0 0 0 0 0 6 12 -> 1 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 6 , 0 1 2 9 4 5 0 0 0 0 0 0 6 14 -> 1 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 8 , 5 1 2 9 4 5 0 0 0 0 0 0 6 3 -> 4 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 0 , 5 1 2 9 4 5 0 0 0 0 0 0 6 9 -> 4 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 1 , 5 1 2 9 4 5 0 0 0 0 0 0 6 12 -> 4 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 6 , 5 1 2 9 4 5 0 0 0 0 0 0 6 14 -> 4 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 8 , 3 1 2 9 4 5 0 0 0 0 0 0 6 3 -> 9 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 0 , 3 1 2 9 4 5 0 0 0 0 0 0 6 9 -> 9 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 1 , 3 1 2 9 4 5 0 0 0 0 0 0 6 12 -> 9 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 6 , 3 1 2 9 4 5 0 0 0 0 0 0 6 14 -> 9 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 8 , 10 1 2 9 4 5 0 0 0 0 0 0 6 3 -> 11 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 0 , 10 1 2 9 4 5 0 0 0 0 0 0 6 9 -> 11 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 1 , 10 1 2 9 4 5 0 0 0 0 0 0 6 12 -> 11 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 6 , 10 1 2 9 4 5 0 0 0 0 0 0 6 14 -> 11 5 1 2 9 5 1 4 5 1 5 0 0 1 5 0 0 8 , 0 1 5 0 0 0 0 6 9 4 5 6 12 3 -> 1 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 3 , 0 1 5 0 0 0 0 6 9 4 5 6 12 9 -> 1 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 9 , 0 1 5 0 0 0 0 6 9 4 5 6 12 12 -> 1 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 12 , 0 1 5 0 0 0 0 6 9 4 5 6 12 14 -> 1 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 14 , 5 1 5 0 0 0 0 6 9 4 5 6 12 3 -> 4 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 3 , 5 1 5 0 0 0 0 6 9 4 5 6 12 9 -> 4 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 9 , 5 1 5 0 0 0 0 6 9 4 5 6 12 12 -> 4 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 12 , 5 1 5 0 0 0 0 6 9 4 5 6 12 14 -> 4 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 14 , 3 1 5 0 0 0 0 6 9 4 5 6 12 3 -> 9 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 3 , 3 1 5 0 0 0 0 6 9 4 5 6 12 9 -> 9 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 9 , 3 1 5 0 0 0 0 6 9 4 5 6 12 12 -> 9 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 12 , 3 1 5 0 0 0 0 6 9 4 5 6 12 14 -> 9 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 14 , 10 1 5 0 0 0 0 6 9 4 5 6 12 3 -> 11 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 3 , 10 1 5 0 0 0 0 6 9 4 5 6 12 9 -> 11 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 9 , 10 1 5 0 0 0 0 6 9 4 5 6 12 12 -> 11 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 12 , 10 1 5 0 0 0 0 6 9 4 5 6 12 14 -> 11 5 0 0 1 5 0 1 5 1 5 1 4 4 2 12 12 14 , 6 9 5 1 4 2 3 6 9 4 5 6 12 3 -> 6 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 3 , 6 9 5 1 4 2 3 6 9 4 5 6 12 9 -> 6 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 9 , 6 9 5 1 4 2 3 6 9 4 5 6 12 12 -> 6 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 12 , 6 9 5 1 4 2 3 6 9 4 5 6 12 14 -> 6 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 14 , 2 9 5 1 4 2 3 6 9 4 5 6 12 3 -> 2 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 3 , 2 9 5 1 4 2 3 6 9 4 5 6 12 9 -> 2 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 9 , 2 9 5 1 4 2 3 6 9 4 5 6 12 12 -> 2 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 12 , 2 9 5 1 4 2 3 6 9 4 5 6 12 14 -> 2 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 14 , 12 9 5 1 4 2 3 6 9 4 5 6 12 3 -> 12 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 3 , 12 9 5 1 4 2 3 6 9 4 5 6 12 9 -> 12 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 9 , 12 9 5 1 4 2 3 6 9 4 5 6 12 12 -> 12 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 12 , 12 9 5 1 4 2 3 6 9 4 5 6 12 14 -> 12 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 14 , 13 9 5 1 4 2 3 6 9 4 5 6 12 3 -> 13 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 3 , 13 9 5 1 4 2 3 6 9 4 5 6 12 9 -> 13 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 9 , 13 9 5 1 4 2 3 6 9 4 5 6 12 12 -> 13 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 12 , 13 9 5 1 4 2 3 6 9 4 5 6 12 14 -> 13 3 0 0 1 4 2 3 1 4 5 6 9 4 4 5 6 14 , 1 5 1 4 4 4 5 1 4 4 2 12 12 3 -> 1 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 5 , 1 5 1 4 4 4 5 1 4 4 2 12 12 9 -> 1 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 4 , 1 5 1 4 4 4 5 1 4 4 2 12 12 12 -> 1 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 2 , 1 5 1 4 4 4 5 1 4 4 2 12 12 14 -> 1 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 7 , 4 5 1 4 4 4 5 1 4 4 2 12 12 3 -> 4 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 5 , 4 5 1 4 4 4 5 1 4 4 2 12 12 9 -> 4 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 4 , 4 5 1 4 4 4 5 1 4 4 2 12 12 12 -> 4 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 2 , 4 5 1 4 4 4 5 1 4 4 2 12 12 14 -> 4 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 7 , 9 5 1 4 4 4 5 1 4 4 2 12 12 3 -> 9 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 5 , 9 5 1 4 4 4 5 1 4 4 2 12 12 9 -> 9 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 4 , 9 5 1 4 4 4 5 1 4 4 2 12 12 12 -> 9 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 2 , 9 5 1 4 4 4 5 1 4 4 2 12 12 14 -> 9 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 7 , 11 5 1 4 4 4 5 1 4 4 2 12 12 3 -> 11 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 5 , 11 5 1 4 4 4 5 1 4 4 2 12 12 9 -> 11 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 4 , 11 5 1 4 4 4 5 1 4 4 2 12 12 12 -> 11 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 2 , 11 5 1 4 4 4 5 1 4 4 2 12 12 14 -> 11 5 1 5 1 4 4 5 0 1 5 0 0 1 4 2 9 7 } 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 7 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 2 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 6 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 3 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 6->0, 9->1, 5->2, 1->3, 4->4, 2->5, 3->6, 0->7, 12->8, 13->9, 8->10 }, it remains to prove termination of the 40-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 5 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 5 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 5 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 5 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 8 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 9 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 9 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 9 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 9 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 0 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 0 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 0 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 0 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 5 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 5 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 5 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 5 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 8 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 8 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 8 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 8 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 9 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 9 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 9 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 9 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 0 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 0 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 5 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 8 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 8 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 9 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 9 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 39-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 5 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 5 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 5 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 5 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 8 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 9 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 9 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 9 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 9 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 0 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 0 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 0 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 0 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 0 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 5 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 5 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 5 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 5 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 5 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 8 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 8 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 8 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 8 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 8 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 9 6 7 0 8 1 4 4 5 6 3 4 2 7 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 7 , 9 6 7 0 8 1 4 4 5 6 3 4 2 3 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 3 , 9 6 7 0 8 1 4 4 5 6 3 4 2 0 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 0 , 9 6 7 0 8 1 4 4 5 6 3 4 2 10 -> 9 6 0 6 3 2 7 7 3 5 8 1 2 3 4 4 2 10 , 0 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 0 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 0 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 5 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 5 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 8 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 8 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 8 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 9 1 4 2 7 0 1 2 3 2 7 7 7 7 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 0 1 2 3 2 7 7 7 3 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 0 1 2 3 2 7 7 7 0 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 0 , 9 1 4 2 7 0 1 2 3 2 7 7 7 10 -> 9 1 2 0 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / 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 | \ / 9 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 | \ / 10 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 { 5->0, 1->1, 2->2, 3->3, 4->4, 6->5, 7->6, 8->7, 9->8, 0->9, 10->10 }, it remains to prove termination of the 38-rule system { 0 1 2 3 4 0 5 6 6 3 4 4 2 6 -> 0 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 2 , 0 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 0 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 7 1 2 3 4 0 5 6 6 3 4 4 2 6 -> 7 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 2 , 7 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 7 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 8 1 2 3 4 0 5 6 6 3 4 4 2 6 -> 8 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 2 , 8 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 8 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 9 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 9 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 9 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 9 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 0 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 0 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 0 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 0 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 7 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 7 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 7 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 7 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 8 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 8 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 8 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 8 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 9 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 9 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 9 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 9 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 0 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 0 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 0 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 0 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 7 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 7 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 7 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 7 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 8 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 8 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 8 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 8 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 } 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 37-rule system { 0 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 0 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 7 1 2 3 4 0 5 6 6 3 4 4 2 6 -> 7 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 2 , 7 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 7 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 8 1 2 3 4 0 5 6 6 3 4 4 2 6 -> 8 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 2 , 8 1 2 3 4 0 5 6 6 3 4 4 2 3 -> 8 5 3 0 1 4 4 4 4 2 3 4 2 3 2 6 3 4 , 9 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 9 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 9 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 9 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 9 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 0 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 0 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 0 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 0 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 0 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 7 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 7 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 7 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 7 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 7 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 8 5 6 9 7 1 4 4 0 5 3 4 2 6 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 6 , 8 5 6 9 7 1 4 4 0 5 3 4 2 3 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 3 , 8 5 6 9 7 1 4 4 0 5 3 4 2 9 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 9 , 8 5 6 9 7 1 4 4 0 5 3 4 2 10 -> 8 5 9 5 3 2 6 6 3 0 7 1 2 3 4 4 2 10 , 9 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 9 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 9 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 9 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 9 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 0 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 0 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 0 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 0 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 0 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 7 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 7 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 7 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 7 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 7 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 , 8 1 4 2 6 9 1 2 3 2 6 6 6 6 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 6 , 8 1 4 2 6 9 1 2 3 2 6 6 6 3 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 3 , 8 1 4 2 6 9 1 2 3 2 6 6 6 9 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 9 , 8 1 4 2 6 9 1 2 3 2 6 6 6 10 -> 8 1 2 9 1 4 2 3 2 6 3 2 3 4 2 6 6 10 } 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / 9 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 | \ / 10 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, 0->5, 5->6, 6->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 36-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 8 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 9 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 9 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 9 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 9 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 5 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 5 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 5 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 5 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 0 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 0 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 0 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 0 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 8 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 8 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 8 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 8 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 9 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 9 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 5 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 0 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 0 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 8 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 8 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 35-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 8 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 8 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 9 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 9 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 9 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 9 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 9 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 5 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 5 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 5 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 5 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 5 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 0 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 0 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 0 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 0 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 0 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 8 6 7 9 0 1 4 4 5 6 3 4 2 7 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 7 , 8 6 7 9 0 1 4 4 5 6 3 4 2 3 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 3 , 8 6 7 9 0 1 4 4 5 6 3 4 2 9 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 9 , 8 6 7 9 0 1 4 4 5 6 3 4 2 10 -> 8 6 9 6 3 2 7 7 3 5 0 1 2 3 4 4 2 10 , 9 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 9 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 9 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 5 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 5 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 0 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 0 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 0 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 8 1 4 2 7 9 1 2 3 2 7 7 7 7 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 9 1 2 3 2 7 7 7 3 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 9 1 2 3 2 7 7 7 9 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 9 , 8 1 4 2 7 9 1 2 3 2 7 7 7 10 -> 8 1 2 9 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / 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 | \ / 9 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 | \ / 10 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, 9->8, 0->9, 10->10 }, it remains to prove termination of the 34-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 7 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 2 , 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 8 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 8 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 8 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 5 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 5 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 5 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 5 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 9 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 9 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 9 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 9 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 0 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 0 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 0 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 0 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 8 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 8 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 5 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 9 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 9 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 0 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 0 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 33-rule system { 0 1 2 3 4 5 6 7 7 3 4 4 2 3 -> 0 6 3 5 1 4 4 4 4 2 3 4 2 3 2 7 3 4 , 8 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 8 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 8 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 8 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 8 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 5 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 5 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 5 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 5 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 5 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 9 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 9 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 9 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 9 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 9 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 0 6 7 8 9 1 4 4 5 6 3 4 2 7 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 7 , 0 6 7 8 9 1 4 4 5 6 3 4 2 3 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 3 , 0 6 7 8 9 1 4 4 5 6 3 4 2 8 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 8 , 0 6 7 8 9 1 4 4 5 6 3 4 2 10 -> 0 6 8 6 3 2 7 7 3 5 9 1 2 3 4 4 2 10 , 8 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 8 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 8 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 8 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 8 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 5 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 5 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 5 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 5 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 5 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 9 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 9 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 9 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 9 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 9 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 , 0 1 4 2 7 8 1 2 3 2 7 7 7 7 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 7 , 0 1 4 2 7 8 1 2 3 2 7 7 7 3 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 3 , 0 1 4 2 7 8 1 2 3 2 7 7 7 8 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 8 , 0 1 4 2 7 8 1 2 3 2 7 7 7 10 -> 0 1 2 8 1 4 2 3 2 7 3 2 3 4 2 7 7 10 } 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 | \ / 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 | \ / 9 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 | \ / 10 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, 6->1, 7->2, 9->3, 1->4, 4->5, 5->6, 3->7, 2->8, 10->9, 0->10 }, it remains to prove termination of the 32-rule system { 0 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 0 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 0 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 0 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 6 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 6 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 6 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 6 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 3 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 3 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 3 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 3 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 10 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 10 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 10 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 10 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 0 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 0 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 6 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 3 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 3 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 10 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 31-rule system { 0 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 0 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 0 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 6 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 6 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 6 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 6 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 3 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 3 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 3 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 3 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 10 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 10 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 10 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 10 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 0 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 0 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 6 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 3 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 3 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 10 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 30-rule system { 0 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 0 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 6 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 6 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 6 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 6 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 3 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 3 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 3 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 3 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 10 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 10 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 10 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 10 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 0 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 0 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 6 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 3 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 3 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 10 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 29-rule system { 0 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 0 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 6 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 6 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 6 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 6 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 6 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 3 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 3 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 3 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 3 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 3 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 10 1 2 0 3 4 5 5 6 1 7 5 8 2 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 2 , 10 1 2 0 3 4 5 5 6 1 7 5 8 7 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 7 , 10 1 2 0 3 4 5 5 6 1 7 5 8 0 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 0 , 10 1 2 0 3 4 5 5 6 1 7 5 8 9 -> 10 1 0 1 7 8 2 2 7 6 3 4 8 7 5 5 8 9 , 0 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 0 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 0 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 6 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 6 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 3 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 3 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 3 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 0 4 8 7 8 2 2 2 2 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 0 4 8 7 8 2 2 2 7 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 0 4 8 7 8 2 2 2 0 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 0 , 10 4 5 8 2 0 4 8 7 8 2 2 2 9 -> 10 4 8 0 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 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 { 6->0, 1->1, 2->2, 0->3, 3->4, 4->5, 5->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 28-rule system { 0 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 0 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 0 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 0 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 4 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 4 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 4 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 4 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 10 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 10 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 10 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 10 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 3 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 3 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 3 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 3 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 0 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 0 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 0 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 0 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 4 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 4 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 4 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 4 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 10 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 10 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 10 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 10 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 27-rule system { 0 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 0 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 0 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 4 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 4 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 4 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 4 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 10 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 10 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 10 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 10 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 3 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 3 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 3 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 3 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 0 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 0 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 0 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 0 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 4 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 4 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 4 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 4 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 10 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 10 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 10 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 10 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 26-rule system { 0 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 0 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 4 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 4 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 4 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 4 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 10 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 10 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 10 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 10 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 3 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 3 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 3 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 3 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 0 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 0 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 0 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 0 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 4 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 4 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 4 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 4 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 10 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 10 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 10 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 10 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 25-rule system { 0 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 0 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 4 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 4 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 4 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 4 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 4 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 10 1 2 3 4 5 6 6 0 1 7 6 8 2 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 2 , 10 1 2 3 4 5 6 6 0 1 7 6 8 7 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 7 , 10 1 2 3 4 5 6 6 0 1 7 6 8 3 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 3 , 10 1 2 3 4 5 6 6 0 1 7 6 8 9 -> 10 1 3 1 7 8 2 2 7 0 4 5 8 7 6 6 8 9 , 3 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 3 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 3 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 3 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 3 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 0 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 0 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 0 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 0 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 0 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 4 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 4 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 4 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 4 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 4 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 , 10 5 6 8 2 3 5 8 7 8 2 2 2 2 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 2 , 10 5 6 8 2 3 5 8 7 8 2 2 2 7 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 7 , 10 5 6 8 2 3 5 8 7 8 2 2 2 3 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 3 , 10 5 6 8 2 3 5 8 7 8 2 2 2 9 -> 10 5 8 3 5 6 8 7 8 2 7 8 7 6 8 2 2 9 } 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 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 { 4->0, 1->1, 2->2, 3->3, 5->4, 6->5, 0->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 24-rule system { 0 1 2 3 0 4 5 5 6 1 7 5 8 2 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 2 , 0 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 0 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 0 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 10 1 2 3 0 4 5 5 6 1 7 5 8 2 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 2 , 10 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 10 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 10 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 3 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 3 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 6 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 0 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 0 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 10 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 23-rule system { 0 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 0 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 0 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 10 1 2 3 0 4 5 5 6 1 7 5 8 2 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 2 , 10 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 10 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 10 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 3 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 3 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 6 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 0 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 0 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 10 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 22-rule system { 0 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 0 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 10 1 2 3 0 4 5 5 6 1 7 5 8 2 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 2 , 10 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 10 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 10 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 3 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 3 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 6 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 0 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 0 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 10 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 21-rule system { 0 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 0 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 10 1 2 3 0 4 5 5 6 1 7 5 8 2 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 2 , 10 1 2 3 0 4 5 5 6 1 7 5 8 7 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 7 , 10 1 2 3 0 4 5 5 6 1 7 5 8 3 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 3 , 10 1 2 3 0 4 5 5 6 1 7 5 8 9 -> 10 1 3 1 7 8 2 2 7 6 0 4 8 7 5 5 8 9 , 3 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 3 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 3 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 3 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 3 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 6 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 6 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 6 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 6 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 6 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 0 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 0 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 0 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 0 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 0 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 , 10 4 5 8 2 3 4 8 7 8 2 2 2 2 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 2 , 10 4 5 8 2 3 4 8 7 8 2 2 2 7 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 7 , 10 4 5 8 2 3 4 8 7 8 2 2 2 3 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 3 , 10 4 5 8 2 3 4 8 7 8 2 2 2 9 -> 10 4 8 3 4 5 8 7 8 2 7 8 7 5 8 2 2 9 } 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 9 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 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 { 10->0, 1->1, 2->2, 3->3, 0->4, 4->5, 5->6, 6->7, 7->8, 8->9, 9->10 }, it remains to prove termination of the 20-rule system { 0 1 2 3 4 5 6 6 7 1 8 6 9 2 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 2 , 0 1 2 3 4 5 6 6 7 1 8 6 9 8 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 8 , 0 1 2 3 4 5 6 6 7 1 8 6 9 3 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 3 , 0 1 2 3 4 5 6 6 7 1 8 6 9 10 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 10 , 3 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 3 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 3 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 3 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 7 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 7 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 7 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 7 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 4 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 4 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 4 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 4 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 0 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 0 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 0 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 0 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 } 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 19-rule system { 0 1 2 3 4 5 6 6 7 1 8 6 9 8 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 8 , 0 1 2 3 4 5 6 6 7 1 8 6 9 3 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 3 , 0 1 2 3 4 5 6 6 7 1 8 6 9 10 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 10 , 3 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 3 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 3 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 3 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 7 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 7 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 7 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 7 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 4 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 4 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 4 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 4 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 0 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 0 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 0 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 0 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 } 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 18-rule system { 0 1 2 3 4 5 6 6 7 1 8 6 9 3 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 3 , 0 1 2 3 4 5 6 6 7 1 8 6 9 10 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 10 , 3 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 3 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 3 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 3 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 7 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 7 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 7 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 7 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 4 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 4 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 4 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 4 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 0 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 0 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 0 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 0 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 } 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 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 | \ / 10 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10 }, it remains to prove termination of the 17-rule system { 0 1 2 3 4 5 6 6 7 1 8 6 9 10 -> 0 1 3 1 8 9 2 2 8 7 4 5 9 8 6 6 9 10 , 3 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 3 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 3 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 3 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 3 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 7 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 7 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 7 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 7 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 7 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 4 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 4 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 4 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 4 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 4 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 , 0 5 6 9 2 3 5 9 8 9 2 2 2 2 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 2 , 0 5 6 9 2 3 5 9 8 9 2 2 2 8 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 8 , 0 5 6 9 2 3 5 9 8 9 2 2 2 3 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 3 , 0 5 6 9 2 3 5 9 8 9 2 2 2 10 -> 0 5 9 3 5 6 9 8 9 2 8 9 8 6 9 2 2 10 } 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 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 1 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 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 | \ / 10 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 3->0, 5->1, 6->2, 9->3, 2->4, 8->5, 10->6, 7->7, 4->8, 0->9 }, it remains to prove termination of the 16-rule system { 0 1 2 3 4 0 1 3 5 3 4 4 4 4 -> 0 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 4 , 0 1 2 3 4 0 1 3 5 3 4 4 4 5 -> 0 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 5 , 0 1 2 3 4 0 1 3 5 3 4 4 4 0 -> 0 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 0 , 0 1 2 3 4 0 1 3 5 3 4 4 4 6 -> 0 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 6 , 7 1 2 3 4 0 1 3 5 3 4 4 4 4 -> 7 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 4 , 7 1 2 3 4 0 1 3 5 3 4 4 4 5 -> 7 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 5 , 7 1 2 3 4 0 1 3 5 3 4 4 4 0 -> 7 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 0 , 7 1 2 3 4 0 1 3 5 3 4 4 4 6 -> 7 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 6 , 8 1 2 3 4 0 1 3 5 3 4 4 4 4 -> 8 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 4 , 8 1 2 3 4 0 1 3 5 3 4 4 4 5 -> 8 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 5 , 8 1 2 3 4 0 1 3 5 3 4 4 4 0 -> 8 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 0 , 8 1 2 3 4 0 1 3 5 3 4 4 4 6 -> 8 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 6 , 9 1 2 3 4 0 1 3 5 3 4 4 4 4 -> 9 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 4 , 9 1 2 3 4 0 1 3 5 3 4 4 4 5 -> 9 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 5 , 9 1 2 3 4 0 1 3 5 3 4 4 4 0 -> 9 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 0 , 9 1 2 3 4 0 1 3 5 3 4 4 4 6 -> 9 1 3 0 1 2 3 5 3 4 5 3 5 2 3 4 4 6 } 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 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.