/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, it remains to prove termination of the 28-rule system { 0 0 0 1 1 1 2 3 3 1 3 3 2 -> 0 2 2 1 0 1 2 3 0 0 3 2 2 3 1 2 2 , 0 0 0 3 3 1 1 1 3 3 1 3 2 -> 3 0 2 1 0 3 3 3 1 2 2 2 1 2 1 2 2 , 0 0 2 0 3 1 3 2 1 0 0 2 3 -> 0 2 2 2 1 3 3 3 2 2 0 3 1 3 2 1 2 , 0 1 0 0 3 3 2 1 2 0 1 2 3 -> 3 2 2 1 2 2 0 3 0 2 2 2 1 2 2 3 1 , 0 1 2 0 1 1 0 2 2 1 2 0 2 -> 2 0 3 3 2 2 1 0 3 3 3 3 2 2 2 3 3 , 0 1 2 1 1 1 2 2 0 1 3 2 0 -> 2 3 2 0 1 2 3 0 3 3 2 1 3 3 1 3 3 , 0 2 2 0 0 3 1 0 3 2 1 3 0 -> 3 1 2 2 1 3 3 2 2 3 0 2 2 1 1 1 0 , 0 2 3 3 1 0 3 3 0 2 3 1 1 -> 2 1 3 2 2 2 0 2 2 2 3 3 2 2 2 0 3 , 0 3 0 3 0 2 3 0 0 3 1 2 1 -> 3 1 1 2 2 3 0 1 2 2 2 2 3 2 2 2 0 , 0 3 0 3 1 0 1 2 2 0 3 1 3 -> 2 3 2 2 3 0 3 0 3 3 2 2 1 2 2 0 3 , 1 0 0 1 2 2 2 3 2 3 2 0 1 -> 1 2 1 0 2 2 1 2 1 0 3 3 2 2 2 3 3 , 1 0 2 3 0 3 2 3 2 2 3 2 3 -> 1 3 2 2 1 2 2 2 3 3 2 2 3 1 2 1 2 , 1 3 1 0 1 1 3 2 2 1 1 2 1 -> 1 2 3 2 3 2 1 2 2 2 2 2 2 0 1 2 2 , 2 0 0 1 3 0 3 1 3 0 1 2 1 -> 2 2 3 3 0 1 0 0 3 3 3 1 0 2 2 1 2 , 2 0 0 2 3 0 3 1 0 0 2 1 3 -> 2 0 2 1 2 2 2 2 3 2 3 1 3 3 1 3 1 , 2 1 0 2 2 0 0 1 3 2 0 3 3 -> 2 0 2 2 1 3 2 1 1 1 2 2 1 3 3 3 3 , 2 1 0 3 0 3 0 3 3 0 2 1 1 -> 2 2 0 1 2 1 1 0 2 2 2 3 2 3 0 2 2 , 2 1 1 2 0 1 1 3 0 2 3 0 1 -> 2 2 3 3 3 3 3 2 1 0 1 2 2 3 3 2 2 , 2 1 1 3 3 0 3 2 3 2 1 1 3 -> 2 3 2 3 2 2 3 3 2 1 2 2 3 3 0 1 3 , 2 1 1 3 3 3 0 3 0 3 0 0 2 -> 2 0 2 2 0 2 1 3 3 3 2 3 3 2 3 3 2 , 2 2 0 0 1 0 2 3 0 3 0 1 0 -> 2 2 2 1 0 2 0 1 3 1 3 0 3 3 3 3 2 , 2 2 0 0 3 0 2 2 3 0 1 3 3 -> 2 2 1 1 0 1 2 1 2 0 2 2 2 0 2 2 2 , 2 2 0 3 0 1 0 2 3 2 3 1 2 -> 2 2 0 2 2 2 1 0 0 3 1 3 1 3 3 2 2 , 2 2 1 0 2 1 2 1 1 0 1 2 0 -> 2 2 0 2 0 3 1 2 2 0 1 2 2 2 2 2 2 , 2 3 1 1 0 2 3 1 2 3 3 1 1 -> 2 2 2 1 2 1 1 2 0 2 0 0 3 0 1 3 3 , 2 3 2 0 3 0 1 3 2 2 2 0 2 -> 2 1 2 2 3 0 0 1 3 2 2 3 2 2 3 3 2 , 2 3 2 1 1 1 3 2 3 2 3 2 1 -> 2 2 2 0 3 2 2 0 2 3 2 3 0 2 2 0 2 , 3 0 2 3 0 1 0 3 3 0 0 1 0 -> 3 0 0 1 2 2 3 3 3 2 0 1 2 0 3 3 2 } The system was reversed. After renaming modulo { 2->0, 3->1, 1->2, 0->3 }, it remains to prove termination of the 28-rule system { 0 1 1 2 1 1 0 2 2 2 3 3 3 -> 0 0 2 1 0 0 1 3 3 1 0 2 3 2 0 0 3 , 0 1 2 1 1 2 2 2 1 1 3 3 3 -> 0 0 2 0 2 0 0 0 2 1 1 1 3 2 0 3 1 , 1 0 3 3 2 0 1 2 1 3 0 3 3 -> 0 2 0 1 2 1 3 0 0 1 1 1 2 0 0 0 3 , 1 0 2 3 0 2 0 1 1 3 3 2 3 -> 2 1 0 0 2 0 0 0 3 1 3 0 0 2 0 0 1 , 0 3 0 2 0 0 3 2 2 3 0 2 3 -> 1 1 0 0 0 1 1 1 1 3 2 0 0 1 1 3 0 , 3 0 1 2 3 0 0 2 2 2 0 2 3 -> 1 1 2 1 1 2 0 1 1 3 1 0 2 3 0 1 0 , 3 1 2 0 1 3 2 1 3 3 0 0 3 -> 3 2 2 2 0 0 3 1 0 0 1 1 2 0 0 2 1 , 2 2 1 0 3 1 1 3 2 1 1 0 3 -> 1 3 0 0 0 1 1 0 0 0 3 0 0 0 1 2 0 , 2 0 2 1 3 3 1 0 3 1 3 1 3 -> 3 0 0 0 1 0 0 0 0 2 3 1 0 0 2 2 1 , 1 2 1 3 0 0 2 3 2 1 3 1 3 -> 1 3 0 0 2 0 0 1 1 3 1 3 1 0 0 1 0 , 2 3 0 1 0 1 0 0 0 2 3 3 2 -> 1 1 0 0 0 1 1 3 2 0 2 0 0 3 2 0 2 , 1 0 1 0 0 1 0 1 3 1 0 3 2 -> 0 2 0 2 1 0 0 1 1 0 0 0 2 0 0 1 2 , 2 0 2 2 0 0 1 2 2 3 2 1 2 -> 0 0 2 3 0 0 0 0 0 0 2 0 1 0 1 0 2 , 2 0 2 3 1 2 1 3 1 2 3 3 0 -> 0 2 0 0 3 2 1 1 1 3 3 2 3 1 1 0 0 , 1 2 0 3 3 2 1 3 1 0 3 3 0 -> 2 1 2 1 1 2 1 0 1 0 0 0 0 2 0 3 0 , 1 1 3 0 1 2 3 3 0 0 3 2 0 -> 1 1 1 1 2 0 0 2 2 2 0 1 2 0 0 3 0 , 2 2 0 3 1 1 3 1 3 1 3 2 0 -> 0 0 3 1 0 1 0 0 0 3 2 2 0 2 3 0 0 , 2 3 1 0 3 1 2 2 3 0 2 2 0 -> 0 0 1 1 0 0 2 3 2 0 1 1 1 1 1 0 0 , 1 2 2 0 1 0 1 3 1 1 2 2 0 -> 1 2 3 1 1 0 0 2 0 1 1 0 0 1 0 1 0 , 0 3 3 1 3 1 3 1 1 1 2 2 0 -> 0 1 1 0 1 1 0 1 1 1 2 0 3 0 0 3 0 , 3 2 3 1 3 1 0 3 2 3 3 0 0 -> 0 1 1 1 1 3 1 2 1 2 3 0 3 2 0 0 0 , 1 1 2 3 1 0 0 3 1 3 3 0 0 -> 0 0 0 3 0 0 0 3 0 2 0 2 3 2 2 0 0 , 0 2 1 0 1 0 3 2 3 1 3 0 0 -> 0 0 1 1 2 1 2 1 3 3 2 0 0 0 3 0 0 , 3 0 2 3 2 2 0 2 0 3 2 0 0 -> 0 0 0 0 0 0 2 3 0 0 2 1 3 0 3 0 0 , 2 2 1 1 0 2 1 0 3 2 2 1 0 -> 1 1 2 3 1 3 3 0 3 0 2 2 0 2 0 0 0 , 0 3 0 0 0 1 2 3 1 3 0 1 0 -> 0 1 1 0 0 1 0 0 1 2 3 3 1 0 0 2 0 , 2 0 1 0 1 0 1 2 2 2 0 1 0 -> 0 3 0 0 3 1 0 1 0 3 0 0 1 3 0 0 0 , 3 2 3 3 1 1 3 2 3 1 0 3 1 -> 0 1 1 3 0 2 3 0 1 1 1 0 0 2 3 3 1 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,1)->2, (1,2)->3, (2,1)->4, (1,0)->5, (0,2)->6, (2,2)->7, (2,3)->8, (3,3)->9, (3,0)->10, (1,3)->11, (3,1)->12, (3,2)->13, (2,0)->14, (0,3)->15, (3,5)->16, (4,0)->17, (1,5)->18, (4,1)->19, (4,2)->20, (0,5)->21, (4,3)->22, (2,5)->23 }, it remains to prove termination of the 700-rule system { 0 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 0 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 0 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 0 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 0 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 5 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 5 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 5 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 5 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 5 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 14 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 14 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 14 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 14 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 14 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 10 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 10 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 10 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 10 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 10 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 17 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 17 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 17 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 17 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 17 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 0 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 0 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 0 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 0 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 0 1 3 4 2 3 7 7 4 2 11 9 9 16 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 18 , 5 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 5 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 5 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 5 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 5 1 3 4 2 3 7 7 4 2 11 9 9 16 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 18 , 14 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 14 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 14 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 14 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 14 1 3 4 2 3 7 7 4 2 11 9 9 16 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 18 , 10 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 10 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 10 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 10 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 10 1 3 4 2 3 7 7 4 2 11 9 9 16 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 18 , 17 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 17 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 17 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 17 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 17 1 3 4 2 3 7 7 4 2 11 9 9 16 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 18 , 1 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 1 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 1 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 1 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 1 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 2 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 2 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 2 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 2 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 2 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 4 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 4 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 4 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 4 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 4 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 12 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 12 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 12 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 12 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 12 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 19 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 19 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 19 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 19 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 19 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 1 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 1 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 1 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 1 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 1 5 6 8 10 6 14 1 2 11 9 13 8 16 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 18 , 2 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 2 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 2 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 2 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 2 5 6 8 10 6 14 1 2 11 9 13 8 16 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 18 , 4 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 4 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 4 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 4 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 4 5 6 8 10 6 14 1 2 11 9 13 8 16 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 18 , 12 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 12 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 12 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 12 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 12 5 6 8 10 6 14 1 2 11 9 13 8 16 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 18 , 19 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 20 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 19 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 20 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 19 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 20 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 19 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 20 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 19 5 6 8 10 6 14 1 2 11 9 13 8 16 -> 20 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 18 , 0 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 0 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 0 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 0 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 0 15 10 6 14 0 15 13 7 8 10 6 8 16 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 21 , 5 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 5 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 5 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 5 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 5 15 10 6 14 0 15 13 7 8 10 6 8 16 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 21 , 14 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 14 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 14 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 14 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 14 15 10 6 14 0 15 13 7 8 10 6 8 16 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 21 , 10 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 10 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 10 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 10 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 10 15 10 6 14 0 15 13 7 8 10 6 8 16 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 21 , 17 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 19 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 17 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 19 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 17 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 19 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 17 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 19 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 17 15 10 6 14 0 15 13 7 8 10 6 8 16 -> 19 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 21 , 15 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 15 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 15 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 15 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 15 10 1 3 8 10 0 6 7 7 14 6 8 16 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 21 , 11 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 11 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 11 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 11 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 11 10 1 3 8 10 0 6 7 7 14 6 8 16 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 21 , 8 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 8 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 8 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 8 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 8 10 1 3 8 10 0 6 7 7 14 6 8 16 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 21 , 9 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 9 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 9 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 9 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 9 10 1 3 8 10 0 6 7 7 14 6 8 16 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 21 , 22 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 19 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 22 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 19 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 22 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 19 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 22 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 19 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 22 10 1 3 8 10 0 6 7 7 14 6 8 16 -> 19 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 21 , 15 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 15 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 15 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 15 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 15 12 3 14 1 11 13 4 11 9 10 0 15 16 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 18 , 11 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 11 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 11 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 11 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 11 12 3 14 1 11 13 4 11 9 10 0 15 16 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 18 , 8 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 8 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 8 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 8 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 8 12 3 14 1 11 13 4 11 9 10 0 15 16 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 18 , 9 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 9 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 9 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 9 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 9 12 3 14 1 11 13 4 11 9 10 0 15 16 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 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10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 10 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 10 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 10 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 10 6 4 5 1 5 15 13 8 12 11 10 0 21 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 21 , 17 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 17 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 17 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 17 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 17 6 4 5 1 5 15 13 8 12 11 10 0 21 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 21 , 15 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 15 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 15 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 15 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 15 10 6 8 13 7 14 6 14 15 13 14 0 21 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 21 , 11 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 11 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 11 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 11 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 11 10 6 8 13 7 14 6 14 15 13 14 0 21 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 21 , 8 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 8 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 8 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 8 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 8 10 6 8 13 7 14 6 14 15 13 14 0 21 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 21 , 9 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 9 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 9 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 9 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 9 10 6 8 13 7 14 6 14 15 13 14 0 21 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 21 , 22 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 22 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 22 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 22 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 22 10 6 8 13 7 14 6 14 15 13 14 0 21 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 21 , 6 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 6 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 6 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 6 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 6 7 4 2 5 6 4 5 15 13 7 4 5 21 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 21 , 3 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 3 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 3 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 3 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 3 7 4 2 5 6 4 5 15 13 7 4 5 21 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 21 , 7 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 7 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 7 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 7 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 7 7 4 2 5 6 4 5 15 13 7 4 5 21 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 21 , 13 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 13 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 13 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 13 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 13 7 4 2 5 6 4 5 15 13 7 4 5 21 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 21 , 20 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 19 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 20 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 19 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 20 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 19 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 20 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 19 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 20 7 4 2 5 6 4 5 15 13 7 4 5 21 -> 19 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 21 , 0 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 0 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 0 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 0 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 0 15 10 0 0 1 3 8 12 11 10 1 5 21 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 21 , 5 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 5 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 5 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 5 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 5 15 10 0 0 1 3 8 12 11 10 1 5 21 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 21 , 14 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 14 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 14 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 14 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 14 15 10 0 0 1 3 8 12 11 10 1 5 21 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 21 , 10 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 10 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 10 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 10 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 10 15 10 0 0 1 3 8 12 11 10 1 5 21 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 21 , 17 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 17 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 17 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 17 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 17 15 10 0 0 1 3 8 12 11 10 1 5 21 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 21 , 6 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 6 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 6 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 6 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 6 14 1 5 1 5 1 3 7 7 14 1 5 21 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 21 , 3 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 3 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 3 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 3 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 3 14 1 5 1 5 1 3 7 7 14 1 5 21 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 21 , 7 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 7 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 7 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 7 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 7 14 1 5 1 5 1 3 7 7 14 1 5 21 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 21 , 13 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 13 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 13 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 13 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 13 14 1 5 1 5 1 3 7 7 14 1 5 21 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 21 , 20 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 20 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 20 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 20 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 20 14 1 5 1 5 1 3 7 7 14 1 5 21 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 21 , 15 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 15 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 15 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 15 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 15 13 8 9 12 2 11 13 8 12 5 15 12 18 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 18 , 11 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 11 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 11 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 11 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 11 13 8 9 12 2 11 13 8 12 5 15 12 18 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 18 , 8 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 8 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 8 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 8 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 8 13 8 9 12 2 11 13 8 12 5 15 12 18 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 18 , 9 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 9 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 9 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 9 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 9 13 8 9 12 2 11 13 8 12 5 15 12 18 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 18 , 22 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 22 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 22 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 22 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 22 13 8 9 12 2 11 13 8 12 5 15 12 18 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 18 } 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 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 1 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 19->18, 20->19, 22->20, 23->21, 21->22, 18->23 }, it remains to prove termination of the 660-rule system { 0 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 0 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 0 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 0 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 0 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 5 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 5 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 5 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 5 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 5 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 14 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 14 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 14 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 14 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 14 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 10 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 10 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 10 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 10 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 10 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 17 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 17 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 17 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 17 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 17 1 2 3 4 2 5 6 7 7 8 9 9 16 -> 17 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 16 , 0 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 0 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 0 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 0 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 5 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 5 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 5 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 5 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 14 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 14 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 14 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 14 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 10 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 10 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 10 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 10 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 17 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 17 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 17 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 17 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 17 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 1 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 1 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 1 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 1 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 1 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 2 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 2 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 2 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 2 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 2 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 4 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 4 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 4 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 4 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 4 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 12 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 12 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 12 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 12 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 12 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 18 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 18 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 18 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 18 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 18 5 15 9 13 14 1 3 4 11 10 15 9 16 -> 17 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 16 , 1 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 1 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 1 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 1 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 2 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 2 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 2 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 2 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 4 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 4 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 4 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 4 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 12 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 12 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 12 5 6 8 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0 22 , 18 2 3 8 12 5 0 15 12 11 9 10 0 0 -> 17 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 0 , 18 2 3 8 12 5 0 15 12 11 9 10 0 1 -> 17 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 1 , 18 2 3 8 12 5 0 15 12 11 9 10 0 6 -> 17 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 6 , 18 2 3 8 12 5 0 15 12 11 9 10 0 15 -> 17 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 15 , 18 2 3 8 12 5 0 15 12 11 9 10 0 22 -> 17 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 22 , 0 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 0 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 0 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 0 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 0 6 4 5 1 5 15 13 8 12 11 10 0 22 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 22 , 5 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 5 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 5 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 5 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 5 6 4 5 1 5 15 13 8 12 11 10 0 22 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 22 , 14 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 14 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 14 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 14 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 14 6 4 5 1 5 15 13 8 12 11 10 0 22 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 22 , 10 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 10 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 10 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 10 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 10 6 4 5 1 5 15 13 8 12 11 10 0 22 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 22 , 17 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 17 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 17 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 17 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 17 6 4 5 1 5 15 13 8 12 11 10 0 22 -> 17 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 22 , 15 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 15 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 15 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 15 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 15 10 6 8 13 7 14 6 14 15 13 14 0 22 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 22 , 11 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 11 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 11 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 11 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 11 10 6 8 13 7 14 6 14 15 13 14 0 22 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 22 , 8 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 8 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 8 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 8 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 8 10 6 8 13 7 14 6 14 15 13 14 0 22 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 22 , 9 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 9 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 9 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 9 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 9 10 6 8 13 7 14 6 14 15 13 14 0 22 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 22 , 20 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 20 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 20 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 20 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 20 10 6 8 13 7 14 6 14 15 13 14 0 22 -> 17 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 22 , 6 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 6 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 6 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 6 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 6 7 4 2 5 6 4 5 15 13 7 4 5 22 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 22 , 3 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 3 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 3 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 3 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 3 7 4 2 5 6 4 5 15 13 7 4 5 22 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 22 , 7 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 7 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 7 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 7 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 7 7 4 2 5 6 4 5 15 13 7 4 5 22 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 22 , 13 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 13 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 13 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 13 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 13 7 4 2 5 6 4 5 15 13 7 4 5 22 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 22 , 19 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 18 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 19 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 18 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 19 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 18 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 19 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 18 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 19 7 4 2 5 6 4 5 15 13 7 4 5 22 -> 18 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 22 , 0 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 0 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 0 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 0 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 0 15 10 0 0 1 3 8 12 11 10 1 5 22 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 22 , 5 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 5 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 5 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 5 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 5 15 10 0 0 1 3 8 12 11 10 1 5 22 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 22 , 14 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 14 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 14 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 14 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 14 15 10 0 0 1 3 8 12 11 10 1 5 22 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 22 , 10 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 10 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 10 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 10 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 10 15 10 0 0 1 3 8 12 11 10 1 5 22 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 22 , 17 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 17 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 17 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 17 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 17 15 10 0 0 1 3 8 12 11 10 1 5 22 -> 17 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 22 , 6 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 6 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 6 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 6 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 6 14 1 5 1 5 1 3 7 7 14 1 5 22 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 22 , 3 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 3 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 3 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 3 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 3 14 1 5 1 5 1 3 7 7 14 1 5 22 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 22 , 7 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 7 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 7 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 7 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 7 14 1 5 1 5 1 3 7 7 14 1 5 22 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 22 , 13 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 13 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 13 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 13 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 13 14 1 5 1 5 1 3 7 7 14 1 5 22 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 22 , 19 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 19 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 19 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 19 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 19 14 1 5 1 5 1 3 7 7 14 1 5 22 -> 17 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 22 , 15 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 15 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 15 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 15 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 15 13 8 9 12 2 11 13 8 12 5 15 12 23 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 23 , 11 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 11 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 11 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 11 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 11 13 8 9 12 2 11 13 8 12 5 15 12 23 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 23 , 8 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 8 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 8 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 8 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 8 13 8 9 12 2 11 13 8 12 5 15 12 23 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 23 , 9 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 9 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 9 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 9 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 9 13 8 9 12 2 11 13 8 12 5 15 12 23 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 23 , 20 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 20 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 20 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 20 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 20 13 8 9 12 2 11 13 8 12 5 15 12 23 -> 17 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 23 } 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 4 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 5 | | 0 1 | \ / 8 is interpreted by / \ | 1 8 | | 0 1 | \ / 9 is interpreted by / \ | 1 3 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 5 | | 0 1 | \ / 12 is interpreted by / \ | 1 2 | | 0 1 | \ / 13 is interpreted by / \ | 1 4 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 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.