/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 }, it remains to prove termination of the 79-rule system { 0 0 1 2 ⟶ 0 3 1 0 2 , 0 1 2 2 ⟶ 1 2 0 3 2 2 , 0 1 2 4 ⟶ 0 3 2 3 1 4 , 0 5 0 5 ⟶ 0 3 0 5 5 , 0 5 1 2 ⟶ 1 0 1 5 2 , 0 5 1 2 ⟶ 0 1 0 1 5 2 , 0 5 1 2 ⟶ 0 3 2 3 1 5 , 0 5 4 2 ⟶ 0 4 5 3 2 , 0 5 5 2 ⟶ 5 0 1 5 2 , 1 0 0 5 ⟶ 1 1 0 0 1 5 4 , 1 0 1 2 ⟶ 1 1 3 0 2 , 1 0 1 2 ⟶ 1 1 0 3 2 2 , 1 0 1 2 ⟶ 1 1 0 3 2 3 , 1 0 5 4 ⟶ 0 1 1 5 4 , 1 2 0 5 ⟶ 0 3 2 3 1 5 , 1 2 0 5 ⟶ 5 0 3 3 2 1 , 1 5 0 2 ⟶ 1 1 0 1 1 5 2 , 1 5 1 2 ⟶ 0 1 1 5 2 , 1 5 1 2 ⟶ 1 0 1 5 3 2 , 5 0 0 2 ⟶ 5 0 3 0 2 , 5 0 1 2 ⟶ 5 1 0 3 2 , 5 0 1 2 ⟶ 5 1 0 3 2 3 , 0 0 0 1 2 ⟶ 0 2 0 1 0 3 3 4 , 0 0 2 5 2 ⟶ 0 3 2 0 5 2 , 0 1 2 5 0 ⟶ 3 3 2 2 0 0 1 5 , 0 1 2 5 2 ⟶ 0 3 2 1 5 3 2 , 0 3 5 2 2 ⟶ 0 4 5 3 2 2 , 0 4 2 0 5 ⟶ 0 4 0 3 2 1 5 , 0 4 2 5 2 ⟶ 0 5 4 3 3 2 2 , 0 5 0 2 2 ⟶ 0 2 5 0 3 2 , 0 5 0 5 1 ⟶ 0 1 0 3 5 5 , 0 5 1 3 0 ⟶ 0 0 1 1 5 3 , 0 5 2 2 4 ⟶ 0 5 3 2 2 4 , 0 5 2 3 1 ⟶ 0 1 5 3 2 2 2 , 0 5 2 4 1 ⟶ 0 4 3 2 5 1 , 0 5 3 5 2 ⟶ 0 0 3 5 5 2 , 0 5 5 3 1 ⟶ 5 0 1 5 3 3 2 , 1 0 5 5 1 ⟶ 0 4 5 1 5 1 , 1 1 2 2 0 ⟶ 1 1 3 2 2 0 , 1 1 2 3 4 ⟶ 1 1 3 2 2 4 , 1 1 3 5 2 ⟶ 1 1 5 3 3 2 , 1 5 0 5 0 ⟶ 0 1 5 3 5 1 0 , 1 5 5 1 2 ⟶ 1 5 1 1 5 3 2 2 , 5 0 2 0 5 ⟶ 5 0 3 3 2 0 5 , 5 0 2 3 4 ⟶ 5 0 3 2 3 4 , 5 5 0 1 2 ⟶ 5 5 3 0 2 1 , 0 0 0 5 1 2 ⟶ 0 0 1 5 0 2 4 , 0 0 1 2 4 1 ⟶ 1 3 0 2 3 0 4 1 , 0 0 2 1 2 0 ⟶ 0 1 0 3 2 2 2 0 , 0 0 2 3 0 5 ⟶ 0 0 3 0 3 2 5 , 0 0 5 2 3 4 ⟶ 0 4 0 3 1 2 5 , 0 0 5 5 3 4 ⟶ 1 4 1 0 0 3 5 5 , 0 1 2 0 1 2 ⟶ 1 0 3 2 2 1 1 0 , 0 1 2 2 0 5 ⟶ 0 4 1 5 0 3 2 2 , 0 1 2 5 5 5 ⟶ 0 2 5 1 5 3 5 , 0 1 3 1 5 2 ⟶ 1 0 1 5 3 3 2 , 0 1 4 4 0 5 ⟶ 4 3 0 0 1 5 4 , 0 2 5 3 5 1 ⟶ 0 3 3 2 2 1 5 5 , 0 5 0 0 5 4 ⟶ 0 1 0 1 0 4 5 5 , 0 5 1 2 1 4 ⟶ 1 1 5 3 2 2 0 4 , 0 5 5 1 2 5 ⟶ 0 2 1 5 5 4 5 , 1 0 0 2 3 4 ⟶ 1 4 0 0 3 3 2 , 1 0 1 3 5 1 ⟶ 0 1 1 1 5 3 2 2 , 1 0 5 4 2 1 ⟶ 0 1 1 5 3 4 2 , 1 1 0 1 2 2 ⟶ 1 0 1 1 3 1 2 2 , 1 2 1 2 0 0 ⟶ 0 3 2 2 1 0 1 , 1 4 1 0 0 5 ⟶ 0 0 1 5 4 2 1 , 1 4 3 5 0 2 ⟶ 0 3 3 2 1 5 4 , 0 0 1 2 3 5 5 ⟶ 5 1 5 0 3 0 2 1 , 0 0 2 3 4 2 1 ⟶ 0 0 4 1 3 2 3 2 , 0 1 0 0 5 3 4 ⟶ 0 3 0 5 0 4 3 1 , 0 1 2 4 4 0 5 ⟶ 5 4 0 1 0 3 2 4 , 0 5 2 5 1 3 4 ⟶ 1 4 5 2 0 3 1 5 , 0 5 5 0 2 5 1 ⟶ 5 3 0 0 1 5 2 5 , 0 5 5 2 5 3 4 ⟶ 0 3 2 1 4 5 5 5 , 1 0 1 2 3 4 5 ⟶ 3 0 2 1 5 1 3 4 , 1 1 0 2 0 2 2 ⟶ 1 1 0 2 0 3 2 2 , 1 2 4 3 5 3 5 ⟶ 5 1 3 2 2 4 3 5 , 1 4 3 5 2 5 2 ⟶ 5 1 3 2 2 1 5 4 } The system was reversed. After renaming modulo the bijection { 2 ↦ 0, 1 ↦ 1, 0 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 }, it remains to prove termination of the 79-rule system { 0 1 2 2 ⟶ 0 2 1 3 2 , 0 0 1 2 ⟶ 0 0 3 2 0 1 , 4 0 1 2 ⟶ 4 1 3 0 3 2 , 5 2 5 2 ⟶ 5 5 2 3 2 , 0 1 5 2 ⟶ 0 5 1 2 1 , 0 1 5 2 ⟶ 0 5 1 2 1 2 , 0 1 5 2 ⟶ 5 1 3 0 3 2 , 0 4 5 2 ⟶ 0 3 5 4 2 , 0 5 5 2 ⟶ 0 5 1 2 5 , 5 2 2 1 ⟶ 4 5 1 2 2 1 1 , 0 1 2 1 ⟶ 0 2 3 1 1 , 0 1 2 1 ⟶ 0 0 3 2 1 1 , 0 1 2 1 ⟶ 3 0 3 2 1 1 , 4 5 2 1 ⟶ 4 5 1 1 2 , 5 2 0 1 ⟶ 5 1 3 0 3 2 , 5 2 0 1 ⟶ 1 0 3 3 2 5 , 0 2 5 1 ⟶ 0 5 1 1 2 1 1 , 0 1 5 1 ⟶ 0 5 1 1 2 , 0 1 5 1 ⟶ 0 3 5 1 2 1 , 0 2 2 5 ⟶ 0 2 3 2 5 , 0 1 2 5 ⟶ 0 3 2 1 5 , 0 1 2 5 ⟶ 3 0 3 2 1 5 , 0 1 2 2 2 ⟶ 4 3 3 2 1 2 0 2 , 0 5 0 2 2 ⟶ 0 5 2 0 3 2 , 2 5 0 1 2 ⟶ 5 1 2 2 0 0 3 3 , 0 5 0 1 2 ⟶ 0 3 5 1 0 3 2 , 0 0 5 3 2 ⟶ 0 0 3 5 4 2 , 5 2 0 4 2 ⟶ 5 1 0 3 2 4 2 , 0 5 0 4 2 ⟶ 0 0 3 3 4 5 2 , 0 0 2 5 2 ⟶ 0 3 2 5 0 2 , 1 5 2 5 2 ⟶ 5 5 3 2 1 2 , 2 3 1 5 2 ⟶ 3 5 1 1 2 2 , 4 0 0 5 2 ⟶ 4 0 0 3 5 2 , 1 3 0 5 2 ⟶ 0 0 0 3 5 1 2 , 1 4 0 5 2 ⟶ 1 5 0 3 4 2 , 0 5 3 5 2 ⟶ 0 5 5 3 2 2 , 1 3 5 5 2 ⟶ 0 3 3 5 1 2 5 , 1 5 5 2 1 ⟶ 1 5 1 5 4 2 , 2 0 0 1 1 ⟶ 2 0 0 3 1 1 , 4 3 0 1 1 ⟶ 4 0 0 3 1 1 , 0 5 3 1 1 ⟶ 0 3 3 5 1 1 , 2 5 2 5 1 ⟶ 2 1 5 3 5 1 2 , 0 1 5 5 1 ⟶ 0 0 3 5 1 1 5 1 , 5 2 0 2 5 ⟶ 5 2 0 3 3 2 5 , 4 3 0 2 5 ⟶ 4 3 0 3 2 5 , 0 1 2 5 5 ⟶ 1 0 2 3 5 5 , 0 1 5 2 2 2 ⟶ 4 0 2 5 1 2 2 , 1 4 0 1 2 2 ⟶ 1 4 2 3 0 2 3 1 , 2 0 1 0 2 2 ⟶ 2 0 0 0 3 2 1 2 , 5 2 3 0 2 2 ⟶ 5 0 3 2 3 2 2 , 4 3 0 5 2 2 ⟶ 5 0 1 3 2 4 2 , 4 3 5 5 2 2 ⟶ 5 5 3 2 2 1 4 1 , 0 1 2 0 1 2 ⟶ 2 1 1 0 0 3 2 1 , 5 2 0 0 1 2 ⟶ 0 0 3 2 5 1 4 2 , 5 5 5 0 1 2 ⟶ 5 3 5 1 5 0 2 , 0 5 1 3 1 2 ⟶ 0 3 3 5 1 2 1 , 5 2 4 4 1 2 ⟶ 4 5 1 2 2 3 4 , 1 5 3 5 0 2 ⟶ 5 5 1 0 0 3 3 2 , 4 5 2 2 5 2 ⟶ 5 5 4 2 1 2 1 2 , 4 1 0 1 5 2 ⟶ 4 2 0 0 3 5 1 1 , 5 0 1 5 5 2 ⟶ 5 4 5 5 1 0 2 , 4 3 0 2 2 1 ⟶ 0 3 3 2 2 4 1 , 1 5 3 1 2 1 ⟶ 0 0 3 5 1 1 1 2 , 1 0 4 5 2 1 ⟶ 0 4 3 5 1 1 2 , 0 0 1 2 1 1 ⟶ 0 0 1 3 1 1 2 1 , 2 2 0 1 0 1 ⟶ 1 2 1 0 0 3 2 , 5 2 2 1 4 1 ⟶ 1 0 4 5 1 2 2 , 0 2 5 3 4 1 ⟶ 4 5 1 0 3 3 2 , 5 5 3 0 1 2 2 ⟶ 1 0 2 3 2 5 1 5 , 1 0 4 3 0 2 2 ⟶ 0 3 0 3 1 4 2 2 , 4 3 5 2 2 1 2 ⟶ 1 3 4 2 5 2 3 2 , 5 2 4 4 0 1 2 ⟶ 4 0 3 2 1 2 4 5 , 4 3 1 5 0 5 2 ⟶ 5 1 3 2 0 5 4 1 , 1 5 0 2 5 5 2 ⟶ 5 0 5 1 2 2 3 5 , 4 3 5 0 5 5 2 ⟶ 5 5 5 4 1 0 3 2 , 5 4 3 0 1 2 1 ⟶ 4 3 1 5 1 0 2 3 , 0 0 2 0 2 1 1 ⟶ 0 0 3 2 0 2 1 1 , 5 3 5 3 4 0 1 ⟶ 5 3 4 0 0 3 1 5 , 0 5 0 5 3 4 1 ⟶ 4 5 1 0 0 3 1 5 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,2) ↦ 3, (2,0) ↦ 4, (0,2) ↦ 5, (2,1) ↦ 6, (1,3) ↦ 7, (3,2) ↦ 8, (2,3) ↦ 9, (2,4) ↦ 10, (2,5) ↦ 11, (2,7) ↦ 12, (1,0) ↦ 13, (3,0) ↦ 14, (4,0) ↦ 15, (5,0) ↦ 16, (6,0) ↦ 17, (0,3) ↦ 18, (1,1) ↦ 19, (1,4) ↦ 20, (1,5) ↦ 21, (1,7) ↦ 22, (0,4) ↦ 23, (4,1) ↦ 24, (3,4) ↦ 25, (4,4) ↦ 26, (5,4) ↦ 27, (6,4) ↦ 28, (0,5) ↦ 29, (5,2) ↦ 30, (5,5) ↦ 31, (3,5) ↦ 32, (4,5) ↦ 33, (6,5) ↦ 34, (5,1) ↦ 35, (4,2) ↦ 36, (5,3) ↦ 37, (5,7) ↦ 38, (3,1) ↦ 39, (3,3) ↦ 40, (4,3) ↦ 41, (6,3) ↦ 42, (6,1) ↦ 43, (3,7) ↦ 44, (6,2) ↦ 45, (4,7) ↦ 46 }, it remains to prove termination of the 3871-rule system { 0 1 2 3 4 ⟶ 0 5 6 7 8 4 , 0 1 2 3 6 ⟶ 0 5 6 7 8 6 , 0 1 2 3 3 ⟶ 0 5 6 7 8 3 , 0 1 2 3 9 ⟶ 0 5 6 7 8 9 , 0 1 2 3 10 ⟶ 0 5 6 7 8 10 , 0 1 2 3 11 ⟶ 0 5 6 7 8 11 , 0 1 2 3 12 ⟶ 0 5 6 7 8 12 , 13 1 2 3 4 ⟶ 13 5 6 7 8 4 , 13 1 2 3 6 ⟶ 13 5 6 7 8 6 , 13 1 2 3 3 ⟶ 13 5 6 7 8 3 , 13 1 2 3 9 ⟶ 13 5 6 7 8 9 , 13 1 2 3 10 ⟶ 13 5 6 7 8 10 , 13 1 2 3 11 ⟶ 13 5 6 7 8 11 , 13 1 2 3 12 ⟶ 13 5 6 7 8 12 , 4 1 2 3 4 ⟶ 4 5 6 7 8 4 , 4 1 2 3 6 ⟶ 4 5 6 7 8 6 , 4 1 2 3 3 ⟶ 4 5 6 7 8 3 , 4 1 2 3 9 ⟶ 4 5 6 7 8 9 , 4 1 2 3 10 ⟶ 4 5 6 7 8 10 , 4 1 2 3 11 ⟶ 4 5 6 7 8 11 , 4 1 2 3 12 ⟶ 4 5 6 7 8 12 , 14 1 2 3 4 ⟶ 14 5 6 7 8 4 , 14 1 2 3 6 ⟶ 14 5 6 7 8 6 , 14 1 2 3 3 ⟶ 14 5 6 7 8 3 , 14 1 2 3 9 ⟶ 14 5 6 7 8 9 , 14 1 2 3 10 ⟶ 14 5 6 7 8 10 , 14 1 2 3 11 ⟶ 14 5 6 7 8 11 , 14 1 2 3 12 ⟶ 14 5 6 7 8 12 , 15 1 2 3 4 ⟶ 15 5 6 7 8 4 , 15 1 2 3 6 ⟶ 15 5 6 7 8 6 , 15 1 2 3 3 ⟶ 15 5 6 7 8 3 , 15 1 2 3 9 ⟶ 15 5 6 7 8 9 , 15 1 2 3 10 ⟶ 15 5 6 7 8 10 , 15 1 2 3 11 ⟶ 15 5 6 7 8 11 , 15 1 2 3 12 ⟶ 15 5 6 7 8 12 , 16 1 2 3 4 ⟶ 16 5 6 7 8 4 , 16 1 2 3 6 ⟶ 16 5 6 7 8 6 , 16 1 2 3 3 ⟶ 16 5 6 7 8 3 , 16 1 2 3 9 ⟶ 16 5 6 7 8 9 , 16 1 2 3 10 ⟶ 16 5 6 7 8 10 , 16 1 2 3 11 ⟶ 16 5 6 7 8 11 , 16 1 2 3 12 ⟶ 16 5 6 7 8 12 , 17 1 2 3 4 ⟶ 17 5 6 7 8 4 , 17 1 2 3 6 ⟶ 17 5 6 7 8 6 , 17 1 2 3 3 ⟶ 17 5 6 7 8 3 , 17 1 2 3 9 ⟶ 17 5 6 7 8 9 , 17 1 2 3 10 ⟶ 17 5 6 7 8 10 , 17 1 2 3 11 ⟶ 17 5 6 7 8 11 , 17 1 2 3 12 ⟶ 17 5 6 7 8 12 , 0 0 1 2 4 ⟶ 0 0 18 8 4 1 13 , 0 0 1 2 6 ⟶ 0 0 18 8 4 1 19 , 0 0 1 2 3 ⟶ 0 0 18 8 4 1 2 , 0 0 1 2 9 ⟶ 0 0 18 8 4 1 7 , 0 0 1 2 10 ⟶ 0 0 18 8 4 1 20 , 0 0 1 2 11 ⟶ 0 0 18 8 4 1 21 , 0 0 1 2 12 ⟶ 0 0 18 8 4 1 22 , 13 0 1 2 4 ⟶ 13 0 18 8 4 1 13 , 13 0 1 2 6 ⟶ 13 0 18 8 4 1 19 , 13 0 1 2 3 ⟶ 13 0 18 8 4 1 2 , 13 0 1 2 9 ⟶ 13 0 18 8 4 1 7 , 13 0 1 2 10 ⟶ 13 0 18 8 4 1 20 , 13 0 1 2 11 ⟶ 13 0 18 8 4 1 21 , 13 0 1 2 12 ⟶ 13 0 18 8 4 1 22 , 4 0 1 2 4 ⟶ 4 0 18 8 4 1 13 , 4 0 1 2 6 ⟶ 4 0 18 8 4 1 19 , 4 0 1 2 3 ⟶ 4 0 18 8 4 1 2 , 4 0 1 2 9 ⟶ 4 0 18 8 4 1 7 , 4 0 1 2 10 ⟶ 4 0 18 8 4 1 20 , 4 0 1 2 11 ⟶ 4 0 18 8 4 1 21 , 4 0 1 2 12 ⟶ 4 0 18 8 4 1 22 , 14 0 1 2 4 ⟶ 14 0 18 8 4 1 13 , 14 0 1 2 6 ⟶ 14 0 18 8 4 1 19 , 14 0 1 2 3 ⟶ 14 0 18 8 4 1 2 , 14 0 1 2 9 ⟶ 14 0 18 8 4 1 7 , 14 0 1 2 10 ⟶ 14 0 18 8 4 1 20 , 14 0 1 2 11 ⟶ 14 0 18 8 4 1 21 , 14 0 1 2 12 ⟶ 14 0 18 8 4 1 22 , 15 0 1 2 4 ⟶ 15 0 18 8 4 1 13 , 15 0 1 2 6 ⟶ 15 0 18 8 4 1 19 , 15 0 1 2 3 ⟶ 15 0 18 8 4 1 2 , 15 0 1 2 9 ⟶ 15 0 18 8 4 1 7 , 15 0 1 2 10 ⟶ 15 0 18 8 4 1 20 , 15 0 1 2 11 ⟶ 15 0 18 8 4 1 21 , 15 0 1 2 12 ⟶ 15 0 18 8 4 1 22 , 16 0 1 2 4 ⟶ 16 0 18 8 4 1 13 , 16 0 1 2 6 ⟶ 16 0 18 8 4 1 19 , 16 0 1 2 3 ⟶ 16 0 18 8 4 1 2 , 16 0 1 2 9 ⟶ 16 0 18 8 4 1 7 , 16 0 1 2 10 ⟶ 16 0 18 8 4 1 20 , 16 0 1 2 11 ⟶ 16 0 18 8 4 1 21 , 16 0 1 2 12 ⟶ 16 0 18 8 4 1 22 , 17 0 1 2 4 ⟶ 17 0 18 8 4 1 13 , 17 0 1 2 6 ⟶ 17 0 18 8 4 1 19 , 17 0 1 2 3 ⟶ 17 0 18 8 4 1 2 , 17 0 1 2 9 ⟶ 17 0 18 8 4 1 7 , 17 0 1 2 10 ⟶ 17 0 18 8 4 1 20 , 17 0 1 2 11 ⟶ 17 0 18 8 4 1 21 , 17 0 1 2 12 ⟶ 17 0 18 8 4 1 22 , 23 15 1 2 4 ⟶ 23 24 7 14 18 8 4 , 23 15 1 2 6 ⟶ 23 24 7 14 18 8 6 , 23 15 1 2 3 ⟶ 23 24 7 14 18 8 3 , 23 15 1 2 9 ⟶ 23 24 7 14 18 8 9 , 23 15 1 2 10 ⟶ 23 24 7 14 18 8 10 , 23 15 1 2 11 ⟶ 23 24 7 14 18 8 11 , 23 15 1 2 12 ⟶ 23 24 7 14 18 8 12 , 20 15 1 2 4 ⟶ 20 24 7 14 18 8 4 , 20 15 1 2 6 ⟶ 20 24 7 14 18 8 6 , 20 15 1 2 3 ⟶ 20 24 7 14 18 8 3 , 20 15 1 2 9 ⟶ 20 24 7 14 18 8 9 , 20 15 1 2 10 ⟶ 20 24 7 14 18 8 10 , 20 15 1 2 11 ⟶ 20 24 7 14 18 8 11 , 20 15 1 2 12 ⟶ 20 24 7 14 18 8 12 , 10 15 1 2 4 ⟶ 10 24 7 14 18 8 4 , 10 15 1 2 6 ⟶ 10 24 7 14 18 8 6 , 10 15 1 2 3 ⟶ 10 24 7 14 18 8 3 , 10 15 1 2 9 ⟶ 10 24 7 14 18 8 9 , 10 15 1 2 10 ⟶ 10 24 7 14 18 8 10 , 10 15 1 2 11 ⟶ 10 24 7 14 18 8 11 , 10 15 1 2 12 ⟶ 10 24 7 14 18 8 12 , 25 15 1 2 4 ⟶ 25 24 7 14 18 8 4 , 25 15 1 2 6 ⟶ 25 24 7 14 18 8 6 , 25 15 1 2 3 ⟶ 25 24 7 14 18 8 3 , 25 15 1 2 9 ⟶ 25 24 7 14 18 8 9 , 25 15 1 2 10 ⟶ 25 24 7 14 18 8 10 , 25 15 1 2 11 ⟶ 25 24 7 14 18 8 11 , 25 15 1 2 12 ⟶ 25 24 7 14 18 8 12 , 26 15 1 2 4 ⟶ 26 24 7 14 18 8 4 , 26 15 1 2 6 ⟶ 26 24 7 14 18 8 6 , 26 15 1 2 3 ⟶ 26 24 7 14 18 8 3 , 26 15 1 2 9 ⟶ 26 24 7 14 18 8 9 , 26 15 1 2 10 ⟶ 26 24 7 14 18 8 10 , 26 15 1 2 11 ⟶ 26 24 7 14 18 8 11 , 26 15 1 2 12 ⟶ 26 24 7 14 18 8 12 , 27 15 1 2 4 ⟶ 27 24 7 14 18 8 4 , 27 15 1 2 6 ⟶ 27 24 7 14 18 8 6 , 27 15 1 2 3 ⟶ 27 24 7 14 18 8 3 , 27 15 1 2 9 ⟶ 27 24 7 14 18 8 9 , 27 15 1 2 10 ⟶ 27 24 7 14 18 8 10 , 27 15 1 2 11 ⟶ 27 24 7 14 18 8 11 , 27 15 1 2 12 ⟶ 27 24 7 14 18 8 12 , 28 15 1 2 4 ⟶ 28 24 7 14 18 8 4 , 28 15 1 2 6 ⟶ 28 24 7 14 18 8 6 , 28 15 1 2 3 ⟶ 28 24 7 14 18 8 3 , 28 15 1 2 9 ⟶ 28 24 7 14 18 8 9 , 28 15 1 2 10 ⟶ 28 24 7 14 18 8 10 , 28 15 1 2 11 ⟶ 28 24 7 14 18 8 11 , 28 15 1 2 12 ⟶ 28 24 7 14 18 8 12 , 29 30 11 30 4 ⟶ 29 31 30 9 8 4 , 29 30 11 30 6 ⟶ 29 31 30 9 8 6 , 29 30 11 30 3 ⟶ 29 31 30 9 8 3 , 29 30 11 30 9 ⟶ 29 31 30 9 8 9 , 29 30 11 30 10 ⟶ 29 31 30 9 8 10 , 29 30 11 30 11 ⟶ 29 31 30 9 8 11 , 29 30 11 30 12 ⟶ 29 31 30 9 8 12 , 21 30 11 30 4 ⟶ 21 31 30 9 8 4 , 21 30 11 30 6 ⟶ 21 31 30 9 8 6 , 21 30 11 30 3 ⟶ 21 31 30 9 8 3 , 21 30 11 30 9 ⟶ 21 31 30 9 8 9 , 21 30 11 30 10 ⟶ 21 31 30 9 8 10 , 21 30 11 30 11 ⟶ 21 31 30 9 8 11 , 21 30 11 30 12 ⟶ 21 31 30 9 8 12 , 11 30 11 30 4 ⟶ 11 31 30 9 8 4 , 11 30 11 30 6 ⟶ 11 31 30 9 8 6 , 11 30 11 30 3 ⟶ 11 31 30 9 8 3 , 11 30 11 30 9 ⟶ 11 31 30 9 8 9 , 11 30 11 30 10 ⟶ 11 31 30 9 8 10 , 11 30 11 30 11 ⟶ 11 31 30 9 8 11 , 11 30 11 30 12 ⟶ 11 31 30 9 8 12 , 32 30 11 30 4 ⟶ 32 31 30 9 8 4 , 32 30 11 30 6 ⟶ 32 31 30 9 8 6 , 32 30 11 30 3 ⟶ 32 31 30 9 8 3 , 32 30 11 30 9 ⟶ 32 31 30 9 8 9 , 32 30 11 30 10 ⟶ 32 31 30 9 8 10 , 32 30 11 30 11 ⟶ 32 31 30 9 8 11 , 32 30 11 30 12 ⟶ 32 31 30 9 8 12 , 33 30 11 30 4 ⟶ 33 31 30 9 8 4 , 33 30 11 30 6 ⟶ 33 31 30 9 8 6 , 33 30 11 30 3 ⟶ 33 31 30 9 8 3 , 33 30 11 30 9 ⟶ 33 31 30 9 8 9 , 33 30 11 30 10 ⟶ 33 31 30 9 8 10 , 33 30 11 30 11 ⟶ 33 31 30 9 8 11 , 33 30 11 30 12 ⟶ 33 31 30 9 8 12 , 31 30 11 30 4 ⟶ 31 31 30 9 8 4 , 31 30 11 30 6 ⟶ 31 31 30 9 8 6 , 31 30 11 30 3 ⟶ 31 31 30 9 8 3 , 31 30 11 30 9 ⟶ 31 31 30 9 8 9 , 31 30 11 30 10 ⟶ 31 31 30 9 8 10 , 31 30 11 30 11 ⟶ 31 31 30 9 8 11 , 31 30 11 30 12 ⟶ 31 31 30 9 8 12 , 34 30 11 30 4 ⟶ 34 31 30 9 8 4 , 34 30 11 30 6 ⟶ 34 31 30 9 8 6 , 34 30 11 30 3 ⟶ 34 31 30 9 8 3 , 34 30 11 30 9 ⟶ 34 31 30 9 8 9 , 34 30 11 30 10 ⟶ 34 31 30 9 8 10 , 34 30 11 30 11 ⟶ 34 31 30 9 8 11 , 34 30 11 30 12 ⟶ 34 31 30 9 8 12 , 0 1 21 30 4 ⟶ 0 29 35 2 6 13 , 0 1 21 30 6 ⟶ 0 29 35 2 6 19 , 0 1 21 30 3 ⟶ 0 29 35 2 6 2 , 0 1 21 30 9 ⟶ 0 29 35 2 6 7 , 0 1 21 30 10 ⟶ 0 29 35 2 6 20 , 0 1 21 30 11 ⟶ 0 29 35 2 6 21 , 0 1 21 30 12 ⟶ 0 29 35 2 6 22 , 13 1 21 30 4 ⟶ 13 29 35 2 6 13 , 13 1 21 30 6 ⟶ 13 29 35 2 6 19 , 13 1 21 30 3 ⟶ 13 29 35 2 6 2 , 13 1 21 30 9 ⟶ 13 29 35 2 6 7 , 13 1 21 30 10 ⟶ 13 29 35 2 6 20 , 13 1 21 30 11 ⟶ 13 29 35 2 6 21 , 13 1 21 30 12 ⟶ 13 29 35 2 6 22 , 4 1 21 30 4 ⟶ 4 29 35 2 6 13 , 4 1 21 30 6 ⟶ 4 29 35 2 6 19 , 4 1 21 30 3 ⟶ 4 29 35 2 6 2 , 4 1 21 30 9 ⟶ 4 29 35 2 6 7 , 4 1 21 30 10 ⟶ 4 29 35 2 6 20 , 4 1 21 30 11 ⟶ 4 29 35 2 6 21 , 4 1 21 30 12 ⟶ 4 29 35 2 6 22 , 14 1 21 30 4 ⟶ 14 29 35 2 6 13 , 14 1 21 30 6 ⟶ 14 29 35 2 6 19 , 14 1 21 30 3 ⟶ 14 29 35 2 6 2 , 14 1 21 30 9 ⟶ 14 29 35 2 6 7 , 14 1 21 30 10 ⟶ 14 29 35 2 6 20 , 14 1 21 30 11 ⟶ 14 29 35 2 6 21 , 14 1 21 30 12 ⟶ 14 29 35 2 6 22 , 15 1 21 30 4 ⟶ 15 29 35 2 6 13 , 15 1 21 30 6 ⟶ 15 29 35 2 6 19 , 15 1 21 30 3 ⟶ 15 29 35 2 6 2 , 15 1 21 30 9 ⟶ 15 29 35 2 6 7 , 15 1 21 30 10 ⟶ 15 29 35 2 6 20 , 15 1 21 30 11 ⟶ 15 29 35 2 6 21 , 15 1 21 30 12 ⟶ 15 29 35 2 6 22 , 16 1 21 30 4 ⟶ 16 29 35 2 6 13 , 16 1 21 30 6 ⟶ 16 29 35 2 6 19 , 16 1 21 30 3 ⟶ 16 29 35 2 6 2 , 16 1 21 30 9 ⟶ 16 29 35 2 6 7 , 16 1 21 30 10 ⟶ 16 29 35 2 6 20 , 16 1 21 30 11 ⟶ 16 29 35 2 6 21 , 16 1 21 30 12 ⟶ 16 29 35 2 6 22 , 17 1 21 30 4 ⟶ 17 29 35 2 6 13 , 17 1 21 30 6 ⟶ 17 29 35 2 6 19 , 17 1 21 30 3 ⟶ 17 29 35 2 6 2 , 17 1 21 30 9 ⟶ 17 29 35 2 6 7 , 17 1 21 30 10 ⟶ 17 29 35 2 6 20 , 17 1 21 30 11 ⟶ 17 29 35 2 6 21 , 17 1 21 30 12 ⟶ 17 29 35 2 6 22 , 0 1 21 30 4 ⟶ 0 29 35 2 6 2 4 , 0 1 21 30 6 ⟶ 0 29 35 2 6 2 6 , 0 1 21 30 3 ⟶ 0 29 35 2 6 2 3 , 0 1 21 30 9 ⟶ 0 29 35 2 6 2 9 , 0 1 21 30 10 ⟶ 0 29 35 2 6 2 10 , 0 1 21 30 11 ⟶ 0 29 35 2 6 2 11 , 0 1 21 30 12 ⟶ 0 29 35 2 6 2 12 , 13 1 21 30 4 ⟶ 13 29 35 2 6 2 4 , 13 1 21 30 6 ⟶ 13 29 35 2 6 2 6 , 13 1 21 30 3 ⟶ 13 29 35 2 6 2 3 , 13 1 21 30 9 ⟶ 13 29 35 2 6 2 9 , 13 1 21 30 10 ⟶ 13 29 35 2 6 2 10 , 13 1 21 30 11 ⟶ 13 29 35 2 6 2 11 , 13 1 21 30 12 ⟶ 13 29 35 2 6 2 12 , 4 1 21 30 4 ⟶ 4 29 35 2 6 2 4 , 4 1 21 30 6 ⟶ 4 29 35 2 6 2 6 , 4 1 21 30 3 ⟶ 4 29 35 2 6 2 3 , 4 1 21 30 9 ⟶ 4 29 35 2 6 2 9 , 4 1 21 30 10 ⟶ 4 29 35 2 6 2 10 , 4 1 21 30 11 ⟶ 4 29 35 2 6 2 11 , 4 1 21 30 12 ⟶ 4 29 35 2 6 2 12 , 14 1 21 30 4 ⟶ 14 29 35 2 6 2 4 , 14 1 21 30 6 ⟶ 14 29 35 2 6 2 6 , 14 1 21 30 3 ⟶ 14 29 35 2 6 2 3 , 14 1 21 30 9 ⟶ 14 29 35 2 6 2 9 , 14 1 21 30 10 ⟶ 14 29 35 2 6 2 10 , 14 1 21 30 11 ⟶ 14 29 35 2 6 2 11 , 14 1 21 30 12 ⟶ 14 29 35 2 6 2 12 , 15 1 21 30 4 ⟶ 15 29 35 2 6 2 4 , 15 1 21 30 6 ⟶ 15 29 35 2 6 2 6 , 15 1 21 30 3 ⟶ 15 29 35 2 6 2 3 , 15 1 21 30 9 ⟶ 15 29 35 2 6 2 9 , 15 1 21 30 10 ⟶ 15 29 35 2 6 2 10 , 15 1 21 30 11 ⟶ 15 29 35 2 6 2 11 , 15 1 21 30 12 ⟶ 15 29 35 2 6 2 12 , 16 1 21 30 4 ⟶ 16 29 35 2 6 2 4 , 16 1 21 30 6 ⟶ 16 29 35 2 6 2 6 , 16 1 21 30 3 ⟶ 16 29 35 2 6 2 3 , 16 1 21 30 9 ⟶ 16 29 35 2 6 2 9 , 16 1 21 30 10 ⟶ 16 29 35 2 6 2 10 , 16 1 21 30 11 ⟶ 16 29 35 2 6 2 11 , 16 1 21 30 12 ⟶ 16 29 35 2 6 2 12 , 17 1 21 30 4 ⟶ 17 29 35 2 6 2 4 , 17 1 21 30 6 ⟶ 17 29 35 2 6 2 6 , 17 1 21 30 3 ⟶ 17 29 35 2 6 2 3 , 17 1 21 30 9 ⟶ 17 29 35 2 6 2 9 , 17 1 21 30 10 ⟶ 17 29 35 2 6 2 10 , 17 1 21 30 11 ⟶ 17 29 35 2 6 2 11 , 17 1 21 30 12 ⟶ 17 29 35 2 6 2 12 , 0 1 21 30 4 ⟶ 29 35 7 14 18 8 4 , 0 1 21 30 6 ⟶ 29 35 7 14 18 8 6 , 0 1 21 30 3 ⟶ 29 35 7 14 18 8 3 , 0 1 21 30 9 ⟶ 29 35 7 14 18 8 9 , 0 1 21 30 10 ⟶ 29 35 7 14 18 8 10 , 0 1 21 30 11 ⟶ 29 35 7 14 18 8 11 , 0 1 21 30 12 ⟶ 29 35 7 14 18 8 12 , 13 1 21 30 4 ⟶ 21 35 7 14 18 8 4 , 13 1 21 30 6 ⟶ 21 35 7 14 18 8 6 , 13 1 21 30 3 ⟶ 21 35 7 14 18 8 3 , 13 1 21 30 9 ⟶ 21 35 7 14 18 8 9 , 13 1 21 30 10 ⟶ 21 35 7 14 18 8 10 , 13 1 21 30 11 ⟶ 21 35 7 14 18 8 11 , 13 1 21 30 12 ⟶ 21 35 7 14 18 8 12 , 4 1 21 30 4 ⟶ 11 35 7 14 18 8 4 , 4 1 21 30 6 ⟶ 11 35 7 14 18 8 6 , 4 1 21 30 3 ⟶ 11 35 7 14 18 8 3 , 4 1 21 30 9 ⟶ 11 35 7 14 18 8 9 , 4 1 21 30 10 ⟶ 11 35 7 14 18 8 10 , 4 1 21 30 11 ⟶ 11 35 7 14 18 8 11 , 4 1 21 30 12 ⟶ 11 35 7 14 18 8 12 , 14 1 21 30 4 ⟶ 32 35 7 14 18 8 4 , 14 1 21 30 6 ⟶ 32 35 7 14 18 8 6 , 14 1 21 30 3 ⟶ 32 35 7 14 18 8 3 , 14 1 21 30 9 ⟶ 32 35 7 14 18 8 9 , 14 1 21 30 10 ⟶ 32 35 7 14 18 8 10 , 14 1 21 30 11 ⟶ 32 35 7 14 18 8 11 , 14 1 21 30 12 ⟶ 32 35 7 14 18 8 12 , 15 1 21 30 4 ⟶ 33 35 7 14 18 8 4 , 15 1 21 30 6 ⟶ 33 35 7 14 18 8 6 , 15 1 21 30 3 ⟶ 33 35 7 14 18 8 3 , 15 1 21 30 9 ⟶ 33 35 7 14 18 8 9 , 15 1 21 30 10 ⟶ 33 35 7 14 18 8 10 , 15 1 21 30 11 ⟶ 33 35 7 14 18 8 11 , 15 1 21 30 12 ⟶ 33 35 7 14 18 8 12 , 16 1 21 30 4 ⟶ 31 35 7 14 18 8 4 , 16 1 21 30 6 ⟶ 31 35 7 14 18 8 6 , 16 1 21 30 3 ⟶ 31 35 7 14 18 8 3 , 16 1 21 30 9 ⟶ 31 35 7 14 18 8 9 , 16 1 21 30 10 ⟶ 31 35 7 14 18 8 10 , 16 1 21 30 11 ⟶ 31 35 7 14 18 8 11 , 16 1 21 30 12 ⟶ 31 35 7 14 18 8 12 , 17 1 21 30 4 ⟶ 34 35 7 14 18 8 4 , 17 1 21 30 6 ⟶ 34 35 7 14 18 8 6 , 17 1 21 30 3 ⟶ 34 35 7 14 18 8 3 , 17 1 21 30 9 ⟶ 34 35 7 14 18 8 9 , 17 1 21 30 10 ⟶ 34 35 7 14 18 8 10 , 17 1 21 30 11 ⟶ 34 35 7 14 18 8 11 , 17 1 21 30 12 ⟶ 34 35 7 14 18 8 12 , 0 23 33 30 4 ⟶ 0 18 32 27 36 4 , 0 23 33 30 6 ⟶ 0 18 32 27 36 6 , 0 23 33 30 3 ⟶ 0 18 32 27 36 3 , 0 23 33 30 9 ⟶ 0 18 32 27 36 9 , 0 23 33 30 10 ⟶ 0 18 32 27 36 10 , 0 23 33 30 11 ⟶ 0 18 32 27 36 11 , 0 23 33 30 12 ⟶ 0 18 32 27 36 12 , 13 23 33 30 4 ⟶ 13 18 32 27 36 4 , 13 23 33 30 6 ⟶ 13 18 32 27 36 6 , 13 23 33 30 3 ⟶ 13 18 32 27 36 3 , 13 23 33 30 9 ⟶ 13 18 32 27 36 9 , 13 23 33 30 10 ⟶ 13 18 32 27 36 10 , 13 23 33 30 11 ⟶ 13 18 32 27 36 11 , 13 23 33 30 12 ⟶ 13 18 32 27 36 12 , 4 23 33 30 4 ⟶ 4 18 32 27 36 4 , 4 23 33 30 6 ⟶ 4 18 32 27 36 6 , 4 23 33 30 3 ⟶ 4 18 32 27 36 3 , 4 23 33 30 9 ⟶ 4 18 32 27 36 9 , 4 23 33 30 10 ⟶ 4 18 32 27 36 10 , 4 23 33 30 11 ⟶ 4 18 32 27 36 11 , 4 23 33 30 12 ⟶ 4 18 32 27 36 12 , 14 23 33 30 4 ⟶ 14 18 32 27 36 4 , 14 23 33 30 6 ⟶ 14 18 32 27 36 6 , 14 23 33 30 3 ⟶ 14 18 32 27 36 3 , 14 23 33 30 9 ⟶ 14 18 32 27 36 9 , 14 23 33 30 10 ⟶ 14 18 32 27 36 10 , 14 23 33 30 11 ⟶ 14 18 32 27 36 11 , 14 23 33 30 12 ⟶ 14 18 32 27 36 12 , 15 23 33 30 4 ⟶ 15 18 32 27 36 4 , 15 23 33 30 6 ⟶ 15 18 32 27 36 6 , 15 23 33 30 3 ⟶ 15 18 32 27 36 3 , 15 23 33 30 9 ⟶ 15 18 32 27 36 9 , 15 23 33 30 10 ⟶ 15 18 32 27 36 10 , 15 23 33 30 11 ⟶ 15 18 32 27 36 11 , 15 23 33 30 12 ⟶ 15 18 32 27 36 12 , 16 23 33 30 4 ⟶ 16 18 32 27 36 4 , 16 23 33 30 6 ⟶ 16 18 32 27 36 6 , 16 23 33 30 3 ⟶ 16 18 32 27 36 3 , 16 23 33 30 9 ⟶ 16 18 32 27 36 9 , 16 23 33 30 10 ⟶ 16 18 32 27 36 10 , 16 23 33 30 11 ⟶ 16 18 32 27 36 11 , 16 23 33 30 12 ⟶ 16 18 32 27 36 12 , 17 23 33 30 4 ⟶ 17 18 32 27 36 4 , 17 23 33 30 6 ⟶ 17 18 32 27 36 6 , 17 23 33 30 3 ⟶ 17 18 32 27 36 3 , 17 23 33 30 9 ⟶ 17 18 32 27 36 9 , 17 23 33 30 10 ⟶ 17 18 32 27 36 10 , 17 23 33 30 11 ⟶ 17 18 32 27 36 11 , 17 23 33 30 12 ⟶ 17 18 32 27 36 12 , 0 29 31 30 4 ⟶ 0 29 35 2 11 16 , 0 29 31 30 6 ⟶ 0 29 35 2 11 35 , 0 29 31 30 3 ⟶ 0 29 35 2 11 30 , 0 29 31 30 9 ⟶ 0 29 35 2 11 37 , 0 29 31 30 10 ⟶ 0 29 35 2 11 27 , 0 29 31 30 11 ⟶ 0 29 35 2 11 31 , 0 29 31 30 12 ⟶ 0 29 35 2 11 38 , 13 29 31 30 4 ⟶ 13 29 35 2 11 16 , 13 29 31 30 6 ⟶ 13 29 35 2 11 35 , 13 29 31 30 3 ⟶ 13 29 35 2 11 30 , 13 29 31 30 9 ⟶ 13 29 35 2 11 37 , 13 29 31 30 10 ⟶ 13 29 35 2 11 27 , 13 29 31 30 11 ⟶ 13 29 35 2 11 31 , 13 29 31 30 12 ⟶ 13 29 35 2 11 38 , 4 29 31 30 4 ⟶ 4 29 35 2 11 16 , 4 29 31 30 6 ⟶ 4 29 35 2 11 35 , 4 29 31 30 3 ⟶ 4 29 35 2 11 30 , 4 29 31 30 9 ⟶ 4 29 35 2 11 37 , 4 29 31 30 10 ⟶ 4 29 35 2 11 27 , 4 29 31 30 11 ⟶ 4 29 35 2 11 31 , 4 29 31 30 12 ⟶ 4 29 35 2 11 38 , 14 29 31 30 4 ⟶ 14 29 35 2 11 16 , 14 29 31 30 6 ⟶ 14 29 35 2 11 35 , 14 29 31 30 3 ⟶ 14 29 35 2 11 30 , 14 29 31 30 9 ⟶ 14 29 35 2 11 37 , 14 29 31 30 10 ⟶ 14 29 35 2 11 27 , 14 29 31 30 11 ⟶ 14 29 35 2 11 31 , 14 29 31 30 12 ⟶ 14 29 35 2 11 38 , 15 29 31 30 4 ⟶ 15 29 35 2 11 16 , 15 29 31 30 6 ⟶ 15 29 35 2 11 35 , 15 29 31 30 3 ⟶ 15 29 35 2 11 30 , 15 29 31 30 9 ⟶ 15 29 35 2 11 37 , 15 29 31 30 10 ⟶ 15 29 35 2 11 27 , 15 29 31 30 11 ⟶ 15 29 35 2 11 31 , 15 29 31 30 12 ⟶ 15 29 35 2 11 38 , 16 29 31 30 4 ⟶ 16 29 35 2 11 16 , 16 29 31 30 6 ⟶ 16 29 35 2 11 35 , 16 29 31 30 3 ⟶ 16 29 35 2 11 30 , 16 29 31 30 9 ⟶ 16 29 35 2 11 37 , 16 29 31 30 10 ⟶ 16 29 35 2 11 27 , 16 29 31 30 11 ⟶ 16 29 35 2 11 31 , 16 29 31 30 12 ⟶ 16 29 35 2 11 38 , 17 29 31 30 4 ⟶ 17 29 35 2 11 16 , 17 29 31 30 6 ⟶ 17 29 35 2 11 35 , 17 29 31 30 3 ⟶ 17 29 35 2 11 30 , 17 29 31 30 9 ⟶ 17 29 35 2 11 37 , 17 29 31 30 10 ⟶ 17 29 35 2 11 27 , 17 29 31 30 11 ⟶ 17 29 35 2 11 31 , 17 29 31 30 12 ⟶ 17 29 35 2 11 38 , 29 30 3 6 13 ⟶ 23 33 35 2 3 6 19 13 , 29 30 3 6 19 ⟶ 23 33 35 2 3 6 19 19 , 29 30 3 6 2 ⟶ 23 33 35 2 3 6 19 2 , 29 30 3 6 7 ⟶ 23 33 35 2 3 6 19 7 , 29 30 3 6 20 ⟶ 23 33 35 2 3 6 19 20 , 29 30 3 6 21 ⟶ 23 33 35 2 3 6 19 21 , 29 30 3 6 22 ⟶ 23 33 35 2 3 6 19 22 , 21 30 3 6 13 ⟶ 20 33 35 2 3 6 19 13 , 21 30 3 6 19 ⟶ 20 33 35 2 3 6 19 19 , 21 30 3 6 2 ⟶ 20 33 35 2 3 6 19 2 , 21 30 3 6 7 ⟶ 20 33 35 2 3 6 19 7 , 21 30 3 6 20 ⟶ 20 33 35 2 3 6 19 20 , 21 30 3 6 21 ⟶ 20 33 35 2 3 6 19 21 , 21 30 3 6 22 ⟶ 20 33 35 2 3 6 19 22 , 11 30 3 6 13 ⟶ 10 33 35 2 3 6 19 13 , 11 30 3 6 19 ⟶ 10 33 35 2 3 6 19 19 , 11 30 3 6 2 ⟶ 10 33 35 2 3 6 19 2 , 11 30 3 6 7 ⟶ 10 33 35 2 3 6 19 7 , 11 30 3 6 20 ⟶ 10 33 35 2 3 6 19 20 , 11 30 3 6 21 ⟶ 10 33 35 2 3 6 19 21 , 11 30 3 6 22 ⟶ 10 33 35 2 3 6 19 22 , 32 30 3 6 13 ⟶ 25 33 35 2 3 6 19 13 , 32 30 3 6 19 ⟶ 25 33 35 2 3 6 19 19 , 32 30 3 6 2 ⟶ 25 33 35 2 3 6 19 2 , 32 30 3 6 7 ⟶ 25 33 35 2 3 6 19 7 , 32 30 3 6 20 ⟶ 25 33 35 2 3 6 19 20 , 32 30 3 6 21 ⟶ 25 33 35 2 3 6 19 21 , 32 30 3 6 22 ⟶ 25 33 35 2 3 6 19 22 , 33 30 3 6 13 ⟶ 26 33 35 2 3 6 19 13 , 33 30 3 6 19 ⟶ 26 33 35 2 3 6 19 19 , 33 30 3 6 2 ⟶ 26 33 35 2 3 6 19 2 , 33 30 3 6 7 ⟶ 26 33 35 2 3 6 19 7 , 33 30 3 6 20 ⟶ 26 33 35 2 3 6 19 20 , 33 30 3 6 21 ⟶ 26 33 35 2 3 6 19 21 , 33 30 3 6 22 ⟶ 26 33 35 2 3 6 19 22 , 31 30 3 6 13 ⟶ 27 33 35 2 3 6 19 13 , 31 30 3 6 19 ⟶ 27 33 35 2 3 6 19 19 , 31 30 3 6 2 ⟶ 27 33 35 2 3 6 19 2 , 31 30 3 6 7 ⟶ 27 33 35 2 3 6 19 7 , 31 30 3 6 20 ⟶ 27 33 35 2 3 6 19 20 , 31 30 3 6 21 ⟶ 27 33 35 2 3 6 19 21 , 31 30 3 6 22 ⟶ 27 33 35 2 3 6 19 22 , 34 30 3 6 13 ⟶ 28 33 35 2 3 6 19 13 , 34 30 3 6 19 ⟶ 28 33 35 2 3 6 19 19 , 34 30 3 6 2 ⟶ 28 33 35 2 3 6 19 2 , 34 30 3 6 7 ⟶ 28 33 35 2 3 6 19 7 , 34 30 3 6 20 ⟶ 28 33 35 2 3 6 19 20 , 34 30 3 6 21 ⟶ 28 33 35 2 3 6 19 21 , 34 30 3 6 22 ⟶ 28 33 35 2 3 6 19 22 , 0 1 2 6 13 ⟶ 0 5 9 39 19 13 , 0 1 2 6 19 ⟶ 0 5 9 39 19 19 , 0 1 2 6 2 ⟶ 0 5 9 39 19 2 , 0 1 2 6 7 ⟶ 0 5 9 39 19 7 , 0 1 2 6 20 ⟶ 0 5 9 39 19 20 , 0 1 2 6 21 ⟶ 0 5 9 39 19 21 , 0 1 2 6 22 ⟶ 0 5 9 39 19 22 , 13 1 2 6 13 ⟶ 13 5 9 39 19 13 , 13 1 2 6 19 ⟶ 13 5 9 39 19 19 , 13 1 2 6 2 ⟶ 13 5 9 39 19 2 , 13 1 2 6 7 ⟶ 13 5 9 39 19 7 , 13 1 2 6 20 ⟶ 13 5 9 39 19 20 , 13 1 2 6 21 ⟶ 13 5 9 39 19 21 , 13 1 2 6 22 ⟶ 13 5 9 39 19 22 , 4 1 2 6 13 ⟶ 4 5 9 39 19 13 , 4 1 2 6 19 ⟶ 4 5 9 39 19 19 , 4 1 2 6 2 ⟶ 4 5 9 39 19 2 , 4 1 2 6 7 ⟶ 4 5 9 39 19 7 , 4 1 2 6 20 ⟶ 4 5 9 39 19 20 , 4 1 2 6 21 ⟶ 4 5 9 39 19 21 , 4 1 2 6 22 ⟶ 4 5 9 39 19 22 , 14 1 2 6 13 ⟶ 14 5 9 39 19 13 , 14 1 2 6 19 ⟶ 14 5 9 39 19 19 , 14 1 2 6 2 ⟶ 14 5 9 39 19 2 , 14 1 2 6 7 ⟶ 14 5 9 39 19 7 , 14 1 2 6 20 ⟶ 14 5 9 39 19 20 , 14 1 2 6 21 ⟶ 14 5 9 39 19 21 , 14 1 2 6 22 ⟶ 14 5 9 39 19 22 , 15 1 2 6 13 ⟶ 15 5 9 39 19 13 , 15 1 2 6 19 ⟶ 15 5 9 39 19 19 , 15 1 2 6 2 ⟶ 15 5 9 39 19 2 , 15 1 2 6 7 ⟶ 15 5 9 39 19 7 , 15 1 2 6 20 ⟶ 15 5 9 39 19 20 , 15 1 2 6 21 ⟶ 15 5 9 39 19 21 , 15 1 2 6 22 ⟶ 15 5 9 39 19 22 , 16 1 2 6 13 ⟶ 16 5 9 39 19 13 , 16 1 2 6 19 ⟶ 16 5 9 39 19 19 , 16 1 2 6 2 ⟶ 16 5 9 39 19 2 , 16 1 2 6 7 ⟶ 16 5 9 39 19 7 , 16 1 2 6 20 ⟶ 16 5 9 39 19 20 , 16 1 2 6 21 ⟶ 16 5 9 39 19 21 , 16 1 2 6 22 ⟶ 16 5 9 39 19 22 , 17 1 2 6 13 ⟶ 17 5 9 39 19 13 , 17 1 2 6 19 ⟶ 17 5 9 39 19 19 , 17 1 2 6 2 ⟶ 17 5 9 39 19 2 , 17 1 2 6 7 ⟶ 17 5 9 39 19 7 , 17 1 2 6 20 ⟶ 17 5 9 39 19 20 , 17 1 2 6 21 ⟶ 17 5 9 39 19 21 , 17 1 2 6 22 ⟶ 17 5 9 39 19 22 , 0 1 2 6 13 ⟶ 0 0 18 8 6 19 13 , 0 1 2 6 19 ⟶ 0 0 18 8 6 19 19 , 0 1 2 6 2 ⟶ 0 0 18 8 6 19 2 , 0 1 2 6 7 ⟶ 0 0 18 8 6 19 7 , 0 1 2 6 20 ⟶ 0 0 18 8 6 19 20 , 0 1 2 6 21 ⟶ 0 0 18 8 6 19 21 , 0 1 2 6 22 ⟶ 0 0 18 8 6 19 22 , 13 1 2 6 13 ⟶ 13 0 18 8 6 19 13 , 13 1 2 6 19 ⟶ 13 0 18 8 6 19 19 , 13 1 2 6 2 ⟶ 13 0 18 8 6 19 2 , 13 1 2 6 7 ⟶ 13 0 18 8 6 19 7 , 13 1 2 6 20 ⟶ 13 0 18 8 6 19 20 , 13 1 2 6 21 ⟶ 13 0 18 8 6 19 21 , 13 1 2 6 22 ⟶ 13 0 18 8 6 19 22 , 4 1 2 6 13 ⟶ 4 0 18 8 6 19 13 , 4 1 2 6 19 ⟶ 4 0 18 8 6 19 19 , 4 1 2 6 2 ⟶ 4 0 18 8 6 19 2 , 4 1 2 6 7 ⟶ 4 0 18 8 6 19 7 , 4 1 2 6 20 ⟶ 4 0 18 8 6 19 20 , 4 1 2 6 21 ⟶ 4 0 18 8 6 19 21 , 4 1 2 6 22 ⟶ 4 0 18 8 6 19 22 , 14 1 2 6 13 ⟶ 14 0 18 8 6 19 13 , 14 1 2 6 19 ⟶ 14 0 18 8 6 19 19 , 14 1 2 6 2 ⟶ 14 0 18 8 6 19 2 , 14 1 2 6 7 ⟶ 14 0 18 8 6 19 7 , 14 1 2 6 20 ⟶ 14 0 18 8 6 19 20 , 14 1 2 6 21 ⟶ 14 0 18 8 6 19 21 , 14 1 2 6 22 ⟶ 14 0 18 8 6 19 22 , 15 1 2 6 13 ⟶ 15 0 18 8 6 19 13 , 15 1 2 6 19 ⟶ 15 0 18 8 6 19 19 , 15 1 2 6 2 ⟶ 15 0 18 8 6 19 2 , 15 1 2 6 7 ⟶ 15 0 18 8 6 19 7 , 15 1 2 6 20 ⟶ 15 0 18 8 6 19 20 , 15 1 2 6 21 ⟶ 15 0 18 8 6 19 21 , 15 1 2 6 22 ⟶ 15 0 18 8 6 19 22 , 16 1 2 6 13 ⟶ 16 0 18 8 6 19 13 , 16 1 2 6 19 ⟶ 16 0 18 8 6 19 19 , 16 1 2 6 2 ⟶ 16 0 18 8 6 19 2 , 16 1 2 6 7 ⟶ 16 0 18 8 6 19 7 , 16 1 2 6 20 ⟶ 16 0 18 8 6 19 20 , 16 1 2 6 21 ⟶ 16 0 18 8 6 19 21 , 16 1 2 6 22 ⟶ 16 0 18 8 6 19 22 , 17 1 2 6 13 ⟶ 17 0 18 8 6 19 13 , 17 1 2 6 19 ⟶ 17 0 18 8 6 19 19 , 17 1 2 6 2 ⟶ 17 0 18 8 6 19 2 , 17 1 2 6 7 ⟶ 17 0 18 8 6 19 7 , 17 1 2 6 20 ⟶ 17 0 18 8 6 19 20 , 17 1 2 6 21 ⟶ 17 0 18 8 6 19 21 , 17 1 2 6 22 ⟶ 17 0 18 8 6 19 22 , 0 1 2 6 13 ⟶ 18 14 18 8 6 19 13 , 0 1 2 6 19 ⟶ 18 14 18 8 6 19 19 , 0 1 2 6 2 ⟶ 18 14 18 8 6 19 2 , 0 1 2 6 7 ⟶ 18 14 18 8 6 19 7 , 0 1 2 6 20 ⟶ 18 14 18 8 6 19 20 , 0 1 2 6 21 ⟶ 18 14 18 8 6 19 21 , 0 1 2 6 22 ⟶ 18 14 18 8 6 19 22 , 13 1 2 6 13 ⟶ 7 14 18 8 6 19 13 , 13 1 2 6 19 ⟶ 7 14 18 8 6 19 19 , 13 1 2 6 2 ⟶ 7 14 18 8 6 19 2 , 13 1 2 6 7 ⟶ 7 14 18 8 6 19 7 , 13 1 2 6 20 ⟶ 7 14 18 8 6 19 20 , 13 1 2 6 21 ⟶ 7 14 18 8 6 19 21 , 13 1 2 6 22 ⟶ 7 14 18 8 6 19 22 , 4 1 2 6 13 ⟶ 9 14 18 8 6 19 13 , 4 1 2 6 19 ⟶ 9 14 18 8 6 19 19 , 4 1 2 6 2 ⟶ 9 14 18 8 6 19 2 , 4 1 2 6 7 ⟶ 9 14 18 8 6 19 7 , 4 1 2 6 20 ⟶ 9 14 18 8 6 19 20 , 4 1 2 6 21 ⟶ 9 14 18 8 6 19 21 , 4 1 2 6 22 ⟶ 9 14 18 8 6 19 22 , 14 1 2 6 13 ⟶ 40 14 18 8 6 19 13 , 14 1 2 6 19 ⟶ 40 14 18 8 6 19 19 , 14 1 2 6 2 ⟶ 40 14 18 8 6 19 2 , 14 1 2 6 7 ⟶ 40 14 18 8 6 19 7 , 14 1 2 6 20 ⟶ 40 14 18 8 6 19 20 , 14 1 2 6 21 ⟶ 40 14 18 8 6 19 21 , 14 1 2 6 22 ⟶ 40 14 18 8 6 19 22 , 15 1 2 6 13 ⟶ 41 14 18 8 6 19 13 , 15 1 2 6 19 ⟶ 41 14 18 8 6 19 19 , 15 1 2 6 2 ⟶ 41 14 18 8 6 19 2 , 15 1 2 6 7 ⟶ 41 14 18 8 6 19 7 , 15 1 2 6 20 ⟶ 41 14 18 8 6 19 20 , 15 1 2 6 21 ⟶ 41 14 18 8 6 19 21 , 15 1 2 6 22 ⟶ 41 14 18 8 6 19 22 , 16 1 2 6 13 ⟶ 37 14 18 8 6 19 13 , 16 1 2 6 19 ⟶ 37 14 18 8 6 19 19 , 16 1 2 6 2 ⟶ 37 14 18 8 6 19 2 , 16 1 2 6 7 ⟶ 37 14 18 8 6 19 7 , 16 1 2 6 20 ⟶ 37 14 18 8 6 19 20 , 16 1 2 6 21 ⟶ 37 14 18 8 6 19 21 , 16 1 2 6 22 ⟶ 37 14 18 8 6 19 22 , 17 1 2 6 13 ⟶ 42 14 18 8 6 19 13 , 17 1 2 6 19 ⟶ 42 14 18 8 6 19 19 , 17 1 2 6 2 ⟶ 42 14 18 8 6 19 2 , 17 1 2 6 7 ⟶ 42 14 18 8 6 19 7 , 17 1 2 6 20 ⟶ 42 14 18 8 6 19 20 , 17 1 2 6 21 ⟶ 42 14 18 8 6 19 21 , 17 1 2 6 22 ⟶ 42 14 18 8 6 19 22 , 23 33 30 6 13 ⟶ 23 33 35 19 2 4 , 23 33 30 6 19 ⟶ 23 33 35 19 2 6 , 23 33 30 6 2 ⟶ 23 33 35 19 2 3 , 23 33 30 6 7 ⟶ 23 33 35 19 2 9 , 23 33 30 6 20 ⟶ 23 33 35 19 2 10 , 23 33 30 6 21 ⟶ 23 33 35 19 2 11 , 23 33 30 6 22 ⟶ 23 33 35 19 2 12 , 20 33 30 6 13 ⟶ 20 33 35 19 2 4 , 20 33 30 6 19 ⟶ 20 33 35 19 2 6 , 20 33 30 6 2 ⟶ 20 33 35 19 2 3 , 20 33 30 6 7 ⟶ 20 33 35 19 2 9 , 20 33 30 6 20 ⟶ 20 33 35 19 2 10 , 20 33 30 6 21 ⟶ 20 33 35 19 2 11 , 20 33 30 6 22 ⟶ 20 33 35 19 2 12 , 10 33 30 6 13 ⟶ 10 33 35 19 2 4 , 10 33 30 6 19 ⟶ 10 33 35 19 2 6 , 10 33 30 6 2 ⟶ 10 33 35 19 2 3 , 10 33 30 6 7 ⟶ 10 33 35 19 2 9 , 10 33 30 6 20 ⟶ 10 33 35 19 2 10 , 10 33 30 6 21 ⟶ 10 33 35 19 2 11 , 10 33 30 6 22 ⟶ 10 33 35 19 2 12 , 25 33 30 6 13 ⟶ 25 33 35 19 2 4 , 25 33 30 6 19 ⟶ 25 33 35 19 2 6 , 25 33 30 6 2 ⟶ 25 33 35 19 2 3 , 25 33 30 6 7 ⟶ 25 33 35 19 2 9 , 25 33 30 6 20 ⟶ 25 33 35 19 2 10 , 25 33 30 6 21 ⟶ 25 33 35 19 2 11 , 25 33 30 6 22 ⟶ 25 33 35 19 2 12 , 26 33 30 6 13 ⟶ 26 33 35 19 2 4 , 26 33 30 6 19 ⟶ 26 33 35 19 2 6 , 26 33 30 6 2 ⟶ 26 33 35 19 2 3 , 26 33 30 6 7 ⟶ 26 33 35 19 2 9 , 26 33 30 6 20 ⟶ 26 33 35 19 2 10 , 26 33 30 6 21 ⟶ 26 33 35 19 2 11 , 26 33 30 6 22 ⟶ 26 33 35 19 2 12 , 27 33 30 6 13 ⟶ 27 33 35 19 2 4 , 27 33 30 6 19 ⟶ 27 33 35 19 2 6 , 27 33 30 6 2 ⟶ 27 33 35 19 2 3 , 27 33 30 6 7 ⟶ 27 33 35 19 2 9 , 27 33 30 6 20 ⟶ 27 33 35 19 2 10 , 27 33 30 6 21 ⟶ 27 33 35 19 2 11 , 27 33 30 6 22 ⟶ 27 33 35 19 2 12 , 28 33 30 6 13 ⟶ 28 33 35 19 2 4 , 28 33 30 6 19 ⟶ 28 33 35 19 2 6 , 28 33 30 6 2 ⟶ 28 33 35 19 2 3 , 28 33 30 6 7 ⟶ 28 33 35 19 2 9 , 28 33 30 6 20 ⟶ 28 33 35 19 2 10 , 28 33 30 6 21 ⟶ 28 33 35 19 2 11 , 28 33 30 6 22 ⟶ 28 33 35 19 2 12 , 29 30 4 1 13 ⟶ 29 35 7 14 18 8 4 , 29 30 4 1 19 ⟶ 29 35 7 14 18 8 6 , 29 30 4 1 2 ⟶ 29 35 7 14 18 8 3 , 29 30 4 1 7 ⟶ 29 35 7 14 18 8 9 , 29 30 4 1 20 ⟶ 29 35 7 14 18 8 10 , 29 30 4 1 21 ⟶ 29 35 7 14 18 8 11 , 29 30 4 1 22 ⟶ 29 35 7 14 18 8 12 , 21 30 4 1 13 ⟶ 21 35 7 14 18 8 4 , 21 30 4 1 19 ⟶ 21 35 7 14 18 8 6 , 21 30 4 1 2 ⟶ 21 35 7 14 18 8 3 , 21 30 4 1 7 ⟶ 21 35 7 14 18 8 9 , 21 30 4 1 20 ⟶ 21 35 7 14 18 8 10 , 21 30 4 1 21 ⟶ 21 35 7 14 18 8 11 , 21 30 4 1 22 ⟶ 21 35 7 14 18 8 12 , 11 30 4 1 13 ⟶ 11 35 7 14 18 8 4 , 11 30 4 1 19 ⟶ 11 35 7 14 18 8 6 , 11 30 4 1 2 ⟶ 11 35 7 14 18 8 3 , 11 30 4 1 7 ⟶ 11 35 7 14 18 8 9 , 11 30 4 1 20 ⟶ 11 35 7 14 18 8 10 , 11 30 4 1 21 ⟶ 11 35 7 14 18 8 11 , 11 30 4 1 22 ⟶ 11 35 7 14 18 8 12 , 32 30 4 1 13 ⟶ 32 35 7 14 18 8 4 , 32 30 4 1 19 ⟶ 32 35 7 14 18 8 6 , 32 30 4 1 2 ⟶ 32 35 7 14 18 8 3 , 32 30 4 1 7 ⟶ 32 35 7 14 18 8 9 , 32 30 4 1 20 ⟶ 32 35 7 14 18 8 10 , 32 30 4 1 21 ⟶ 32 35 7 14 18 8 11 , 32 30 4 1 22 ⟶ 32 35 7 14 18 8 12 , 33 30 4 1 13 ⟶ 33 35 7 14 18 8 4 , 33 30 4 1 19 ⟶ 33 35 7 14 18 8 6 , 33 30 4 1 2 ⟶ 33 35 7 14 18 8 3 , 33 30 4 1 7 ⟶ 33 35 7 14 18 8 9 , 33 30 4 1 20 ⟶ 33 35 7 14 18 8 10 , 33 30 4 1 21 ⟶ 33 35 7 14 18 8 11 , 33 30 4 1 22 ⟶ 33 35 7 14 18 8 12 , 31 30 4 1 13 ⟶ 31 35 7 14 18 8 4 , 31 30 4 1 19 ⟶ 31 35 7 14 18 8 6 , 31 30 4 1 2 ⟶ 31 35 7 14 18 8 3 , 31 30 4 1 7 ⟶ 31 35 7 14 18 8 9 , 31 30 4 1 20 ⟶ 31 35 7 14 18 8 10 , 31 30 4 1 21 ⟶ 31 35 7 14 18 8 11 , 31 30 4 1 22 ⟶ 31 35 7 14 18 8 12 , 34 30 4 1 13 ⟶ 34 35 7 14 18 8 4 , 34 30 4 1 19 ⟶ 34 35 7 14 18 8 6 , 34 30 4 1 2 ⟶ 34 35 7 14 18 8 3 , 34 30 4 1 7 ⟶ 34 35 7 14 18 8 9 , 34 30 4 1 20 ⟶ 34 35 7 14 18 8 10 , 34 30 4 1 21 ⟶ 34 35 7 14 18 8 11 , 34 30 4 1 22 ⟶ 34 35 7 14 18 8 12 , 29 30 4 1 13 ⟶ 1 13 18 40 8 11 16 , 29 30 4 1 19 ⟶ 1 13 18 40 8 11 35 , 29 30 4 1 2 ⟶ 1 13 18 40 8 11 30 , 29 30 4 1 7 ⟶ 1 13 18 40 8 11 37 , 29 30 4 1 20 ⟶ 1 13 18 40 8 11 27 , 29 30 4 1 21 ⟶ 1 13 18 40 8 11 31 , 29 30 4 1 22 ⟶ 1 13 18 40 8 11 38 , 21 30 4 1 13 ⟶ 19 13 18 40 8 11 16 , 21 30 4 1 19 ⟶ 19 13 18 40 8 11 35 , 21 30 4 1 2 ⟶ 19 13 18 40 8 11 30 , 21 30 4 1 7 ⟶ 19 13 18 40 8 11 37 , 21 30 4 1 20 ⟶ 19 13 18 40 8 11 27 , 21 30 4 1 21 ⟶ 19 13 18 40 8 11 31 , 21 30 4 1 22 ⟶ 19 13 18 40 8 11 38 , 11 30 4 1 13 ⟶ 6 13 18 40 8 11 16 , 11 30 4 1 19 ⟶ 6 13 18 40 8 11 35 , 11 30 4 1 2 ⟶ 6 13 18 40 8 11 30 , 11 30 4 1 7 ⟶ 6 13 18 40 8 11 37 , 11 30 4 1 20 ⟶ 6 13 18 40 8 11 27 , 11 30 4 1 21 ⟶ 6 13 18 40 8 11 31 , 11 30 4 1 22 ⟶ 6 13 18 40 8 11 38 , 32 30 4 1 13 ⟶ 39 13 18 40 8 11 16 , 32 30 4 1 19 ⟶ 39 13 18 40 8 11 35 , 32 30 4 1 2 ⟶ 39 13 18 40 8 11 30 , 32 30 4 1 7 ⟶ 39 13 18 40 8 11 37 , 32 30 4 1 20 ⟶ 39 13 18 40 8 11 27 , 32 30 4 1 21 ⟶ 39 13 18 40 8 11 31 , 32 30 4 1 22 ⟶ 39 13 18 40 8 11 38 , 33 30 4 1 13 ⟶ 24 13 18 40 8 11 16 , 33 30 4 1 19 ⟶ 24 13 18 40 8 11 35 , 33 30 4 1 2 ⟶ 24 13 18 40 8 11 30 , 33 30 4 1 7 ⟶ 24 13 18 40 8 11 37 , 33 30 4 1 20 ⟶ 24 13 18 40 8 11 27 , 33 30 4 1 21 ⟶ 24 13 18 40 8 11 31 , 33 30 4 1 22 ⟶ 24 13 18 40 8 11 38 , 31 30 4 1 13 ⟶ 35 13 18 40 8 11 16 , 31 30 4 1 19 ⟶ 35 13 18 40 8 11 35 , 31 30 4 1 2 ⟶ 35 13 18 40 8 11 30 , 31 30 4 1 7 ⟶ 35 13 18 40 8 11 37 , 31 30 4 1 20 ⟶ 35 13 18 40 8 11 27 , 31 30 4 1 21 ⟶ 35 13 18 40 8 11 31 , 31 30 4 1 22 ⟶ 35 13 18 40 8 11 38 , 34 30 4 1 13 ⟶ 43 13 18 40 8 11 16 , 34 30 4 1 19 ⟶ 43 13 18 40 8 11 35 , 34 30 4 1 2 ⟶ 43 13 18 40 8 11 30 , 34 30 4 1 7 ⟶ 43 13 18 40 8 11 37 , 34 30 4 1 20 ⟶ 43 13 18 40 8 11 27 , 34 30 4 1 21 ⟶ 43 13 18 40 8 11 31 , 34 30 4 1 22 ⟶ 43 13 18 40 8 11 38 , 0 5 11 35 13 ⟶ 0 29 35 19 2 6 19 13 , 0 5 11 35 19 ⟶ 0 29 35 19 2 6 19 19 , 0 5 11 35 2 ⟶ 0 29 35 19 2 6 19 2 , 0 5 11 35 7 ⟶ 0 29 35 19 2 6 19 7 , 0 5 11 35 20 ⟶ 0 29 35 19 2 6 19 20 , 0 5 11 35 21 ⟶ 0 29 35 19 2 6 19 21 , 0 5 11 35 22 ⟶ 0 29 35 19 2 6 19 22 , 13 5 11 35 13 ⟶ 13 29 35 19 2 6 19 13 , 13 5 11 35 19 ⟶ 13 29 35 19 2 6 19 19 , 13 5 11 35 2 ⟶ 13 29 35 19 2 6 19 2 , 13 5 11 35 7 ⟶ 13 29 35 19 2 6 19 7 , 13 5 11 35 20 ⟶ 13 29 35 19 2 6 19 20 , 13 5 11 35 21 ⟶ 13 29 35 19 2 6 19 21 , 13 5 11 35 22 ⟶ 13 29 35 19 2 6 19 22 , 4 5 11 35 13 ⟶ 4 29 35 19 2 6 19 13 , 4 5 11 35 19 ⟶ 4 29 35 19 2 6 19 19 , 4 5 11 35 2 ⟶ 4 29 35 19 2 6 19 2 , 4 5 11 35 7 ⟶ 4 29 35 19 2 6 19 7 , 4 5 11 35 20 ⟶ 4 29 35 19 2 6 19 20 , 4 5 11 35 21 ⟶ 4 29 35 19 2 6 19 21 , 4 5 11 35 22 ⟶ 4 29 35 19 2 6 19 22 , 14 5 11 35 13 ⟶ 14 29 35 19 2 6 19 13 , 14 5 11 35 19 ⟶ 14 29 35 19 2 6 19 19 , 14 5 11 35 2 ⟶ 14 29 35 19 2 6 19 2 , 14 5 11 35 7 ⟶ 14 29 35 19 2 6 19 7 , 14 5 11 35 20 ⟶ 14 29 35 19 2 6 19 20 , 14 5 11 35 21 ⟶ 14 29 35 19 2 6 19 21 , 14 5 11 35 22 ⟶ 14 29 35 19 2 6 19 22 , 15 5 11 35 13 ⟶ 15 29 35 19 2 6 19 13 , 15 5 11 35 19 ⟶ 15 29 35 19 2 6 19 19 , 15 5 11 35 2 ⟶ 15 29 35 19 2 6 19 2 , 15 5 11 35 7 ⟶ 15 29 35 19 2 6 19 7 , 15 5 11 35 20 ⟶ 15 29 35 19 2 6 19 20 , 15 5 11 35 21 ⟶ 15 29 35 19 2 6 19 21 , 15 5 11 35 22 ⟶ 15 29 35 19 2 6 19 22 , 16 5 11 35 13 ⟶ 16 29 35 19 2 6 19 13 , 16 5 11 35 19 ⟶ 16 29 35 19 2 6 19 19 , 16 5 11 35 2 ⟶ 16 29 35 19 2 6 19 2 , 16 5 11 35 7 ⟶ 16 29 35 19 2 6 19 7 , 16 5 11 35 20 ⟶ 16 29 35 19 2 6 19 20 , 16 5 11 35 21 ⟶ 16 29 35 19 2 6 19 21 , 16 5 11 35 22 ⟶ 16 29 35 19 2 6 19 22 , 17 5 11 35 13 ⟶ 17 29 35 19 2 6 19 13 , 17 5 11 35 19 ⟶ 17 29 35 19 2 6 19 19 , 17 5 11 35 2 ⟶ 17 29 35 19 2 6 19 2 , 17 5 11 35 7 ⟶ 17 29 35 19 2 6 19 7 , 17 5 11 35 20 ⟶ 17 29 35 19 2 6 19 20 , 17 5 11 35 21 ⟶ 17 29 35 19 2 6 19 21 , 17 5 11 35 22 ⟶ 17 29 35 19 2 6 19 22 , 0 1 21 35 13 ⟶ 0 29 35 19 2 4 , 0 1 21 35 19 ⟶ 0 29 35 19 2 6 , 0 1 21 35 2 ⟶ 0 29 35 19 2 3 , 0 1 21 35 7 ⟶ 0 29 35 19 2 9 , 0 1 21 35 20 ⟶ 0 29 35 19 2 10 , 0 1 21 35 21 ⟶ 0 29 35 19 2 11 , 0 1 21 35 22 ⟶ 0 29 35 19 2 12 , 13 1 21 35 13 ⟶ 13 29 35 19 2 4 , 13 1 21 35 19 ⟶ 13 29 35 19 2 6 , 13 1 21 35 2 ⟶ 13 29 35 19 2 3 , 13 1 21 35 7 ⟶ 13 29 35 19 2 9 , 13 1 21 35 20 ⟶ 13 29 35 19 2 10 , 13 1 21 35 21 ⟶ 13 29 35 19 2 11 , 13 1 21 35 22 ⟶ 13 29 35 19 2 12 , 4 1 21 35 13 ⟶ 4 29 35 19 2 4 , 4 1 21 35 19 ⟶ 4 29 35 19 2 6 , 4 1 21 35 2 ⟶ 4 29 35 19 2 3 , 4 1 21 35 7 ⟶ 4 29 35 19 2 9 , 4 1 21 35 20 ⟶ 4 29 35 19 2 10 , 4 1 21 35 21 ⟶ 4 29 35 19 2 11 , 4 1 21 35 22 ⟶ 4 29 35 19 2 12 , 14 1 21 35 13 ⟶ 14 29 35 19 2 4 , 14 1 21 35 19 ⟶ 14 29 35 19 2 6 , 14 1 21 35 2 ⟶ 14 29 35 19 2 3 , 14 1 21 35 7 ⟶ 14 29 35 19 2 9 , 14 1 21 35 20 ⟶ 14 29 35 19 2 10 , 14 1 21 35 21 ⟶ 14 29 35 19 2 11 , 14 1 21 35 22 ⟶ 14 29 35 19 2 12 , 15 1 21 35 13 ⟶ 15 29 35 19 2 4 , 15 1 21 35 19 ⟶ 15 29 35 19 2 6 , 15 1 21 35 2 ⟶ 15 29 35 19 2 3 , 15 1 21 35 7 ⟶ 15 29 35 19 2 9 , 15 1 21 35 20 ⟶ 15 29 35 19 2 10 , 15 1 21 35 21 ⟶ 15 29 35 19 2 11 , 15 1 21 35 22 ⟶ 15 29 35 19 2 12 , 16 1 21 35 13 ⟶ 16 29 35 19 2 4 , 16 1 21 35 19 ⟶ 16 29 35 19 2 6 , 16 1 21 35 2 ⟶ 16 29 35 19 2 3 , 16 1 21 35 7 ⟶ 16 29 35 19 2 9 , 16 1 21 35 20 ⟶ 16 29 35 19 2 10 , 16 1 21 35 21 ⟶ 16 29 35 19 2 11 , 16 1 21 35 22 ⟶ 16 29 35 19 2 12 , 17 1 21 35 13 ⟶ 17 29 35 19 2 4 , 17 1 21 35 19 ⟶ 17 29 35 19 2 6 , 17 1 21 35 2 ⟶ 17 29 35 19 2 3 , 17 1 21 35 7 ⟶ 17 29 35 19 2 9 , 17 1 21 35 20 ⟶ 17 29 35 19 2 10 , 17 1 21 35 21 ⟶ 17 29 35 19 2 11 , 17 1 21 35 22 ⟶ 17 29 35 19 2 12 , 0 1 21 35 13 ⟶ 0 18 32 35 2 6 13 , 0 1 21 35 19 ⟶ 0 18 32 35 2 6 19 , 0 1 21 35 2 ⟶ 0 18 32 35 2 6 2 , 0 1 21 35 7 ⟶ 0 18 32 35 2 6 7 , 0 1 21 35 20 ⟶ 0 18 32 35 2 6 20 , 0 1 21 35 21 ⟶ 0 18 32 35 2 6 21 , 0 1 21 35 22 ⟶ 0 18 32 35 2 6 22 , 13 1 21 35 13 ⟶ 13 18 32 35 2 6 13 , 13 1 21 35 19 ⟶ 13 18 32 35 2 6 19 , 13 1 21 35 2 ⟶ 13 18 32 35 2 6 2 , 13 1 21 35 7 ⟶ 13 18 32 35 2 6 7 , 13 1 21 35 20 ⟶ 13 18 32 35 2 6 20 , 13 1 21 35 21 ⟶ 13 18 32 35 2 6 21 , 13 1 21 35 22 ⟶ 13 18 32 35 2 6 22 , 4 1 21 35 13 ⟶ 4 18 32 35 2 6 13 , 4 1 21 35 19 ⟶ 4 18 32 35 2 6 19 , 4 1 21 35 2 ⟶ 4 18 32 35 2 6 2 , 4 1 21 35 7 ⟶ 4 18 32 35 2 6 7 , 4 1 21 35 20 ⟶ 4 18 32 35 2 6 20 , 4 1 21 35 21 ⟶ 4 18 32 35 2 6 21 , 4 1 21 35 22 ⟶ 4 18 32 35 2 6 22 , 14 1 21 35 13 ⟶ 14 18 32 35 2 6 13 , 14 1 21 35 19 ⟶ 14 18 32 35 2 6 19 , 14 1 21 35 2 ⟶ 14 18 32 35 2 6 2 , 14 1 21 35 7 ⟶ 14 18 32 35 2 6 7 , 14 1 21 35 20 ⟶ 14 18 32 35 2 6 20 , 14 1 21 35 21 ⟶ 14 18 32 35 2 6 21 , 14 1 21 35 22 ⟶ 14 18 32 35 2 6 22 , 15 1 21 35 13 ⟶ 15 18 32 35 2 6 13 , 15 1 21 35 19 ⟶ 15 18 32 35 2 6 19 , 15 1 21 35 2 ⟶ 15 18 32 35 2 6 2 , 15 1 21 35 7 ⟶ 15 18 32 35 2 6 7 , 15 1 21 35 20 ⟶ 15 18 32 35 2 6 20 , 15 1 21 35 21 ⟶ 15 18 32 35 2 6 21 , 15 1 21 35 22 ⟶ 15 18 32 35 2 6 22 , 16 1 21 35 13 ⟶ 16 18 32 35 2 6 13 , 16 1 21 35 19 ⟶ 16 18 32 35 2 6 19 , 16 1 21 35 2 ⟶ 16 18 32 35 2 6 2 , 16 1 21 35 7 ⟶ 16 18 32 35 2 6 7 , 16 1 21 35 20 ⟶ 16 18 32 35 2 6 20 , 16 1 21 35 21 ⟶ 16 18 32 35 2 6 21 , 16 1 21 35 22 ⟶ 16 18 32 35 2 6 22 , 17 1 21 35 13 ⟶ 17 18 32 35 2 6 13 , 17 1 21 35 19 ⟶ 17 18 32 35 2 6 19 , 17 1 21 35 2 ⟶ 17 18 32 35 2 6 2 , 17 1 21 35 7 ⟶ 17 18 32 35 2 6 7 , 17 1 21 35 20 ⟶ 17 18 32 35 2 6 20 , 17 1 21 35 21 ⟶ 17 18 32 35 2 6 21 , 17 1 21 35 22 ⟶ 17 18 32 35 2 6 22 , 0 5 3 11 16 ⟶ 0 5 9 8 11 16 , 0 5 3 11 35 ⟶ 0 5 9 8 11 35 , 0 5 3 11 30 ⟶ 0 5 9 8 11 30 , 0 5 3 11 37 ⟶ 0 5 9 8 11 37 , 0 5 3 11 27 ⟶ 0 5 9 8 11 27 , 0 5 3 11 31 ⟶ 0 5 9 8 11 31 , 0 5 3 11 38 ⟶ 0 5 9 8 11 38 , 13 5 3 11 16 ⟶ 13 5 9 8 11 16 , 13 5 3 11 35 ⟶ 13 5 9 8 11 35 , 13 5 3 11 30 ⟶ 13 5 9 8 11 30 , 13 5 3 11 37 ⟶ 13 5 9 8 11 37 , 13 5 3 11 27 ⟶ 13 5 9 8 11 27 , 13 5 3 11 31 ⟶ 13 5 9 8 11 31 , 13 5 3 11 38 ⟶ 13 5 9 8 11 38 , 4 5 3 11 16 ⟶ 4 5 9 8 11 16 , 4 5 3 11 35 ⟶ 4 5 9 8 11 35 , 4 5 3 11 30 ⟶ 4 5 9 8 11 30 , 4 5 3 11 37 ⟶ 4 5 9 8 11 37 , 4 5 3 11 27 ⟶ 4 5 9 8 11 27 , 4 5 3 11 31 ⟶ 4 5 9 8 11 31 , 4 5 3 11 38 ⟶ 4 5 9 8 11 38 , 14 5 3 11 16 ⟶ 14 5 9 8 11 16 , 14 5 3 11 35 ⟶ 14 5 9 8 11 35 , 14 5 3 11 30 ⟶ 14 5 9 8 11 30 , 14 5 3 11 37 ⟶ 14 5 9 8 11 37 , 14 5 3 11 27 ⟶ 14 5 9 8 11 27 , 14 5 3 11 31 ⟶ 14 5 9 8 11 31 , 14 5 3 11 38 ⟶ 14 5 9 8 11 38 , 15 5 3 11 16 ⟶ 15 5 9 8 11 16 , 15 5 3 11 35 ⟶ 15 5 9 8 11 35 , 15 5 3 11 30 ⟶ 15 5 9 8 11 30 , 15 5 3 11 37 ⟶ 15 5 9 8 11 37 , 15 5 3 11 27 ⟶ 15 5 9 8 11 27 , 15 5 3 11 31 ⟶ 15 5 9 8 11 31 , 15 5 3 11 38 ⟶ 15 5 9 8 11 38 , 16 5 3 11 16 ⟶ 16 5 9 8 11 16 , 16 5 3 11 35 ⟶ 16 5 9 8 11 35 , 16 5 3 11 30 ⟶ 16 5 9 8 11 30 , 16 5 3 11 37 ⟶ 16 5 9 8 11 37 , 16 5 3 11 27 ⟶ 16 5 9 8 11 27 , 16 5 3 11 31 ⟶ 16 5 9 8 11 31 , 16 5 3 11 38 ⟶ 16 5 9 8 11 38 , 17 5 3 11 16 ⟶ 17 5 9 8 11 16 , 17 5 3 11 35 ⟶ 17 5 9 8 11 35 , 17 5 3 11 30 ⟶ 17 5 9 8 11 30 , 17 5 3 11 37 ⟶ 17 5 9 8 11 37 , 17 5 3 11 27 ⟶ 17 5 9 8 11 27 , 17 5 3 11 31 ⟶ 17 5 9 8 11 31 , 17 5 3 11 38 ⟶ 17 5 9 8 11 38 , 0 1 2 11 16 ⟶ 0 18 8 6 21 16 , 0 1 2 11 35 ⟶ 0 18 8 6 21 35 , 0 1 2 11 30 ⟶ 0 18 8 6 21 30 , 0 1 2 11 37 ⟶ 0 18 8 6 21 37 , 0 1 2 11 27 ⟶ 0 18 8 6 21 27 , 0 1 2 11 31 ⟶ 0 18 8 6 21 31 , 0 1 2 11 38 ⟶ 0 18 8 6 21 38 , 13 1 2 11 16 ⟶ 13 18 8 6 21 16 , 13 1 2 11 35 ⟶ 13 18 8 6 21 35 , 13 1 2 11 30 ⟶ 13 18 8 6 21 30 , 13 1 2 11 37 ⟶ 13 18 8 6 21 37 , 13 1 2 11 27 ⟶ 13 18 8 6 21 27 , 13 1 2 11 31 ⟶ 13 18 8 6 21 31 , 13 1 2 11 38 ⟶ 13 18 8 6 21 38 , 4 1 2 11 16 ⟶ 4 18 8 6 21 16 , 4 1 2 11 35 ⟶ 4 18 8 6 21 35 , 4 1 2 11 30 ⟶ 4 18 8 6 21 30 , 4 1 2 11 37 ⟶ 4 18 8 6 21 37 , 4 1 2 11 27 ⟶ 4 18 8 6 21 27 , 4 1 2 11 31 ⟶ 4 18 8 6 21 31 , 4 1 2 11 38 ⟶ 4 18 8 6 21 38 , 14 1 2 11 16 ⟶ 14 18 8 6 21 16 , 14 1 2 11 35 ⟶ 14 18 8 6 21 35 , 14 1 2 11 30 ⟶ 14 18 8 6 21 30 , 14 1 2 11 37 ⟶ 14 18 8 6 21 37 , 14 1 2 11 27 ⟶ 14 18 8 6 21 27 , 14 1 2 11 31 ⟶ 14 18 8 6 21 31 , 14 1 2 11 38 ⟶ 14 18 8 6 21 38 , 15 1 2 11 16 ⟶ 15 18 8 6 21 16 , 15 1 2 11 35 ⟶ 15 18 8 6 21 35 , 15 1 2 11 30 ⟶ 15 18 8 6 21 30 , 15 1 2 11 37 ⟶ 15 18 8 6 21 37 , 15 1 2 11 27 ⟶ 15 18 8 6 21 27 , 15 1 2 11 31 ⟶ 15 18 8 6 21 31 , 15 1 2 11 38 ⟶ 15 18 8 6 21 38 , 16 1 2 11 16 ⟶ 16 18 8 6 21 16 , 16 1 2 11 35 ⟶ 16 18 8 6 21 35 , 16 1 2 11 30 ⟶ 16 18 8 6 21 30 , 16 1 2 11 37 ⟶ 16 18 8 6 21 37 , 16 1 2 11 27 ⟶ 16 18 8 6 21 27 , 16 1 2 11 31 ⟶ 16 18 8 6 21 31 , 16 1 2 11 38 ⟶ 16 18 8 6 21 38 , 17 1 2 11 16 ⟶ 17 18 8 6 21 16 , 17 1 2 11 35 ⟶ 17 18 8 6 21 35 , 17 1 2 11 30 ⟶ 17 18 8 6 21 30 , 17 1 2 11 37 ⟶ 17 18 8 6 21 37 , 17 1 2 11 27 ⟶ 17 18 8 6 21 27 , 17 1 2 11 31 ⟶ 17 18 8 6 21 31 , 17 1 2 11 38 ⟶ 17 18 8 6 21 38 , 0 1 2 11 16 ⟶ 18 14 18 8 6 21 16 , 0 1 2 11 35 ⟶ 18 14 18 8 6 21 35 , 0 1 2 11 30 ⟶ 18 14 18 8 6 21 30 , 0 1 2 11 37 ⟶ 18 14 18 8 6 21 37 , 0 1 2 11 27 ⟶ 18 14 18 8 6 21 27 , 0 1 2 11 31 ⟶ 18 14 18 8 6 21 31 , 0 1 2 11 38 ⟶ 18 14 18 8 6 21 38 , 13 1 2 11 16 ⟶ 7 14 18 8 6 21 16 , 13 1 2 11 35 ⟶ 7 14 18 8 6 21 35 , 13 1 2 11 30 ⟶ 7 14 18 8 6 21 30 , 13 1 2 11 37 ⟶ 7 14 18 8 6 21 37 , 13 1 2 11 27 ⟶ 7 14 18 8 6 21 27 , 13 1 2 11 31 ⟶ 7 14 18 8 6 21 31 , 13 1 2 11 38 ⟶ 7 14 18 8 6 21 38 , 4 1 2 11 16 ⟶ 9 14 18 8 6 21 16 , 4 1 2 11 35 ⟶ 9 14 18 8 6 21 35 , 4 1 2 11 30 ⟶ 9 14 18 8 6 21 30 , 4 1 2 11 37 ⟶ 9 14 18 8 6 21 37 , 4 1 2 11 27 ⟶ 9 14 18 8 6 21 27 , 4 1 2 11 31 ⟶ 9 14 18 8 6 21 31 , 4 1 2 11 38 ⟶ 9 14 18 8 6 21 38 , 14 1 2 11 16 ⟶ 40 14 18 8 6 21 16 , 14 1 2 11 35 ⟶ 40 14 18 8 6 21 35 , 14 1 2 11 30 ⟶ 40 14 18 8 6 21 30 , 14 1 2 11 37 ⟶ 40 14 18 8 6 21 37 , 14 1 2 11 27 ⟶ 40 14 18 8 6 21 27 , 14 1 2 11 31 ⟶ 40 14 18 8 6 21 31 , 14 1 2 11 38 ⟶ 40 14 18 8 6 21 38 , 15 1 2 11 16 ⟶ 41 14 18 8 6 21 16 , 15 1 2 11 35 ⟶ 41 14 18 8 6 21 35 , 15 1 2 11 30 ⟶ 41 14 18 8 6 21 30 , 15 1 2 11 37 ⟶ 41 14 18 8 6 21 37 , 15 1 2 11 27 ⟶ 41 14 18 8 6 21 27 , 15 1 2 11 31 ⟶ 41 14 18 8 6 21 31 , 15 1 2 11 38 ⟶ 41 14 18 8 6 21 38 , 16 1 2 11 16 ⟶ 37 14 18 8 6 21 16 , 16 1 2 11 35 ⟶ 37 14 18 8 6 21 35 , 16 1 2 11 30 ⟶ 37 14 18 8 6 21 30 , 16 1 2 11 37 ⟶ 37 14 18 8 6 21 37 , 16 1 2 11 27 ⟶ 37 14 18 8 6 21 27 , 16 1 2 11 31 ⟶ 37 14 18 8 6 21 31 , 16 1 2 11 38 ⟶ 37 14 18 8 6 21 38 , 17 1 2 11 16 ⟶ 42 14 18 8 6 21 16 , 17 1 2 11 35 ⟶ 42 14 18 8 6 21 35 , 17 1 2 11 30 ⟶ 42 14 18 8 6 21 30 , 17 1 2 11 37 ⟶ 42 14 18 8 6 21 37 , 17 1 2 11 27 ⟶ 42 14 18 8 6 21 27 , 17 1 2 11 31 ⟶ 42 14 18 8 6 21 31 , 17 1 2 11 38 ⟶ 42 14 18 8 6 21 38 , 0 1 2 3 3 4 ⟶ 23 41 40 8 6 2 4 5 4 , 0 1 2 3 3 6 ⟶ 23 41 40 8 6 2 4 5 6 , 0 1 2 3 3 3 ⟶ 23 41 40 8 6 2 4 5 3 , 0 1 2 3 3 9 ⟶ 23 41 40 8 6 2 4 5 9 , 0 1 2 3 3 10 ⟶ 23 41 40 8 6 2 4 5 10 , 0 1 2 3 3 11 ⟶ 23 41 40 8 6 2 4 5 11 , 0 1 2 3 3 12 ⟶ 23 41 40 8 6 2 4 5 12 , 13 1 2 3 3 4 ⟶ 20 41 40 8 6 2 4 5 4 , 13 1 2 3 3 6 ⟶ 20 41 40 8 6 2 4 5 6 , 13 1 2 3 3 3 ⟶ 20 41 40 8 6 2 4 5 3 , 13 1 2 3 3 9 ⟶ 20 41 40 8 6 2 4 5 9 , 13 1 2 3 3 10 ⟶ 20 41 40 8 6 2 4 5 10 , 13 1 2 3 3 11 ⟶ 20 41 40 8 6 2 4 5 11 , 13 1 2 3 3 12 ⟶ 20 41 40 8 6 2 4 5 12 , 4 1 2 3 3 4 ⟶ 10 41 40 8 6 2 4 5 4 , 4 1 2 3 3 6 ⟶ 10 41 40 8 6 2 4 5 6 , 4 1 2 3 3 3 ⟶ 10 41 40 8 6 2 4 5 3 , 4 1 2 3 3 9 ⟶ 10 41 40 8 6 2 4 5 9 , 4 1 2 3 3 10 ⟶ 10 41 40 8 6 2 4 5 10 , 4 1 2 3 3 11 ⟶ 10 41 40 8 6 2 4 5 11 , 4 1 2 3 3 12 ⟶ 10 41 40 8 6 2 4 5 12 , 14 1 2 3 3 4 ⟶ 25 41 40 8 6 2 4 5 4 , 14 1 2 3 3 6 ⟶ 25 41 40 8 6 2 4 5 6 , 14 1 2 3 3 3 ⟶ 25 41 40 8 6 2 4 5 3 , 14 1 2 3 3 9 ⟶ 25 41 40 8 6 2 4 5 9 , 14 1 2 3 3 10 ⟶ 25 41 40 8 6 2 4 5 10 , 14 1 2 3 3 11 ⟶ 25 41 40 8 6 2 4 5 11 , 14 1 2 3 3 12 ⟶ 25 41 40 8 6 2 4 5 12 , 15 1 2 3 3 4 ⟶ 26 41 40 8 6 2 4 5 4 , 15 1 2 3 3 6 ⟶ 26 41 40 8 6 2 4 5 6 , 15 1 2 3 3 3 ⟶ 26 41 40 8 6 2 4 5 3 , 15 1 2 3 3 9 ⟶ 26 41 40 8 6 2 4 5 9 , 15 1 2 3 3 10 ⟶ 26 41 40 8 6 2 4 5 10 , 15 1 2 3 3 11 ⟶ 26 41 40 8 6 2 4 5 11 , 15 1 2 3 3 12 ⟶ 26 41 40 8 6 2 4 5 12 , 16 1 2 3 3 4 ⟶ 27 41 40 8 6 2 4 5 4 , 16 1 2 3 3 6 ⟶ 27 41 40 8 6 2 4 5 6 , 16 1 2 3 3 3 ⟶ 27 41 40 8 6 2 4 5 3 , 16 1 2 3 3 9 ⟶ 27 41 40 8 6 2 4 5 9 , 16 1 2 3 3 10 ⟶ 27 41 40 8 6 2 4 5 10 , 16 1 2 3 3 11 ⟶ 27 41 40 8 6 2 4 5 11 , 16 1 2 3 3 12 ⟶ 27 41 40 8 6 2 4 5 12 , 17 1 2 3 3 4 ⟶ 28 41 40 8 6 2 4 5 4 , 17 1 2 3 3 6 ⟶ 28 41 40 8 6 2 4 5 6 , 17 1 2 3 3 3 ⟶ 28 41 40 8 6 2 4 5 3 , 17 1 2 3 3 9 ⟶ 28 41 40 8 6 2 4 5 9 , 17 1 2 3 3 10 ⟶ 28 41 40 8 6 2 4 5 10 , 17 1 2 3 3 11 ⟶ 28 41 40 8 6 2 4 5 11 , 17 1 2 3 3 12 ⟶ 28 41 40 8 6 2 4 5 12 , 0 29 16 5 3 4 ⟶ 0 29 30 4 18 8 4 , 0 29 16 5 3 6 ⟶ 0 29 30 4 18 8 6 , 0 29 16 5 3 3 ⟶ 0 29 30 4 18 8 3 , 0 29 16 5 3 9 ⟶ 0 29 30 4 18 8 9 , 0 29 16 5 3 10 ⟶ 0 29 30 4 18 8 10 , 0 29 16 5 3 11 ⟶ 0 29 30 4 18 8 11 , 0 29 16 5 3 12 ⟶ 0 29 30 4 18 8 12 , 13 29 16 5 3 4 ⟶ 13 29 30 4 18 8 4 , 13 29 16 5 3 6 ⟶ 13 29 30 4 18 8 6 , 13 29 16 5 3 3 ⟶ 13 29 30 4 18 8 3 , 13 29 16 5 3 9 ⟶ 13 29 30 4 18 8 9 , 13 29 16 5 3 10 ⟶ 13 29 30 4 18 8 10 , 13 29 16 5 3 11 ⟶ 13 29 30 4 18 8 11 , 13 29 16 5 3 12 ⟶ 13 29 30 4 18 8 12 , 4 29 16 5 3 4 ⟶ 4 29 30 4 18 8 4 , 4 29 16 5 3 6 ⟶ 4 29 30 4 18 8 6 , 4 29 16 5 3 3 ⟶ 4 29 30 4 18 8 3 , 4 29 16 5 3 9 ⟶ 4 29 30 4 18 8 9 , 4 29 16 5 3 10 ⟶ 4 29 30 4 18 8 10 , 4 29 16 5 3 11 ⟶ 4 29 30 4 18 8 11 , 4 29 16 5 3 12 ⟶ 4 29 30 4 18 8 12 , 14 29 16 5 3 4 ⟶ 14 29 30 4 18 8 4 , 14 29 16 5 3 6 ⟶ 14 29 30 4 18 8 6 , 14 29 16 5 3 3 ⟶ 14 29 30 4 18 8 3 , 14 29 16 5 3 9 ⟶ 14 29 30 4 18 8 9 , 14 29 16 5 3 10 ⟶ 14 29 30 4 18 8 10 , 14 29 16 5 3 11 ⟶ 14 29 30 4 18 8 11 , 14 29 16 5 3 12 ⟶ 14 29 30 4 18 8 12 , 15 29 16 5 3 4 ⟶ 15 29 30 4 18 8 4 , 15 29 16 5 3 6 ⟶ 15 29 30 4 18 8 6 , 15 29 16 5 3 3 ⟶ 15 29 30 4 18 8 3 , 15 29 16 5 3 9 ⟶ 15 29 30 4 18 8 9 , 15 29 16 5 3 10 ⟶ 15 29 30 4 18 8 10 , 15 29 16 5 3 11 ⟶ 15 29 30 4 18 8 11 , 15 29 16 5 3 12 ⟶ 15 29 30 4 18 8 12 , 16 29 16 5 3 4 ⟶ 16 29 30 4 18 8 4 , 16 29 16 5 3 6 ⟶ 16 29 30 4 18 8 6 , 16 29 16 5 3 3 ⟶ 16 29 30 4 18 8 3 , 16 29 16 5 3 9 ⟶ 16 29 30 4 18 8 9 , 16 29 16 5 3 10 ⟶ 16 29 30 4 18 8 10 , 16 29 16 5 3 11 ⟶ 16 29 30 4 18 8 11 , 16 29 16 5 3 12 ⟶ 16 29 30 4 18 8 12 , 17 29 16 5 3 4 ⟶ 17 29 30 4 18 8 4 , 17 29 16 5 3 6 ⟶ 17 29 30 4 18 8 6 , 17 29 16 5 3 3 ⟶ 17 29 30 4 18 8 3 , 17 29 16 5 3 9 ⟶ 17 29 30 4 18 8 9 , 17 29 16 5 3 10 ⟶ 17 29 30 4 18 8 10 , 17 29 16 5 3 11 ⟶ 17 29 30 4 18 8 11 , 17 29 16 5 3 12 ⟶ 17 29 30 4 18 8 12 , 5 11 16 1 2 4 ⟶ 29 35 2 3 4 0 18 40 14 , 5 11 16 1 2 6 ⟶ 29 35 2 3 4 0 18 40 39 , 5 11 16 1 2 3 ⟶ 29 35 2 3 4 0 18 40 8 , 5 11 16 1 2 9 ⟶ 29 35 2 3 4 0 18 40 40 , 5 11 16 1 2 10 ⟶ 29 35 2 3 4 0 18 40 25 , 5 11 16 1 2 11 ⟶ 29 35 2 3 4 0 18 40 32 , 5 11 16 1 2 12 ⟶ 29 35 2 3 4 0 18 40 44 , 2 11 16 1 2 4 ⟶ 21 35 2 3 4 0 18 40 14 , 2 11 16 1 2 6 ⟶ 21 35 2 3 4 0 18 40 39 , 2 11 16 1 2 3 ⟶ 21 35 2 3 4 0 18 40 8 , 2 11 16 1 2 9 ⟶ 21 35 2 3 4 0 18 40 40 , 2 11 16 1 2 10 ⟶ 21 35 2 3 4 0 18 40 25 , 2 11 16 1 2 11 ⟶ 21 35 2 3 4 0 18 40 32 , 2 11 16 1 2 12 ⟶ 21 35 2 3 4 0 18 40 44 , 3 11 16 1 2 4 ⟶ 11 35 2 3 4 0 18 40 14 , 3 11 16 1 2 6 ⟶ 11 35 2 3 4 0 18 40 39 , 3 11 16 1 2 3 ⟶ 11 35 2 3 4 0 18 40 8 , 3 11 16 1 2 9 ⟶ 11 35 2 3 4 0 18 40 40 , 3 11 16 1 2 10 ⟶ 11 35 2 3 4 0 18 40 25 , 3 11 16 1 2 11 ⟶ 11 35 2 3 4 0 18 40 32 , 3 11 16 1 2 12 ⟶ 11 35 2 3 4 0 18 40 44 , 8 11 16 1 2 4 ⟶ 32 35 2 3 4 0 18 40 14 , 8 11 16 1 2 6 ⟶ 32 35 2 3 4 0 18 40 39 , 8 11 16 1 2 3 ⟶ 32 35 2 3 4 0 18 40 8 , 8 11 16 1 2 9 ⟶ 32 35 2 3 4 0 18 40 40 , 8 11 16 1 2 10 ⟶ 32 35 2 3 4 0 18 40 25 , 8 11 16 1 2 11 ⟶ 32 35 2 3 4 0 18 40 32 , 8 11 16 1 2 12 ⟶ 32 35 2 3 4 0 18 40 44 , 36 11 16 1 2 4 ⟶ 33 35 2 3 4 0 18 40 14 , 36 11 16 1 2 6 ⟶ 33 35 2 3 4 0 18 40 39 , 36 11 16 1 2 3 ⟶ 33 35 2 3 4 0 18 40 8 , 36 11 16 1 2 9 ⟶ 33 35 2 3 4 0 18 40 40 , 36 11 16 1 2 10 ⟶ 33 35 2 3 4 0 18 40 25 , 36 11 16 1 2 11 ⟶ 33 35 2 3 4 0 18 40 32 , 36 11 16 1 2 12 ⟶ 33 35 2 3 4 0 18 40 44 , 30 11 16 1 2 4 ⟶ 31 35 2 3 4 0 18 40 14 , 30 11 16 1 2 6 ⟶ 31 35 2 3 4 0 18 40 39 , 30 11 16 1 2 3 ⟶ 31 35 2 3 4 0 18 40 8 , 30 11 16 1 2 9 ⟶ 31 35 2 3 4 0 18 40 40 , 30 11 16 1 2 10 ⟶ 31 35 2 3 4 0 18 40 25 , 30 11 16 1 2 11 ⟶ 31 35 2 3 4 0 18 40 32 , 30 11 16 1 2 12 ⟶ 31 35 2 3 4 0 18 40 44 , 45 11 16 1 2 4 ⟶ 34 35 2 3 4 0 18 40 14 , 45 11 16 1 2 6 ⟶ 34 35 2 3 4 0 18 40 39 , 45 11 16 1 2 3 ⟶ 34 35 2 3 4 0 18 40 8 , 45 11 16 1 2 9 ⟶ 34 35 2 3 4 0 18 40 40 , 45 11 16 1 2 10 ⟶ 34 35 2 3 4 0 18 40 25 , 45 11 16 1 2 11 ⟶ 34 35 2 3 4 0 18 40 32 , 45 11 16 1 2 12 ⟶ 34 35 2 3 4 0 18 40 44 , 0 29 16 1 2 4 ⟶ 0 18 32 35 13 18 8 4 , 0 29 16 1 2 6 ⟶ 0 18 32 35 13 18 8 6 , 0 29 16 1 2 3 ⟶ 0 18 32 35 13 18 8 3 , 0 29 16 1 2 9 ⟶ 0 18 32 35 13 18 8 9 , 0 29 16 1 2 10 ⟶ 0 18 32 35 13 18 8 10 , 0 29 16 1 2 11 ⟶ 0 18 32 35 13 18 8 11 , 0 29 16 1 2 12 ⟶ 0 18 32 35 13 18 8 12 , 13 29 16 1 2 4 ⟶ 13 18 32 35 13 18 8 4 , 13 29 16 1 2 6 ⟶ 13 18 32 35 13 18 8 6 , 13 29 16 1 2 3 ⟶ 13 18 32 35 13 18 8 3 , 13 29 16 1 2 9 ⟶ 13 18 32 35 13 18 8 9 , 13 29 16 1 2 10 ⟶ 13 18 32 35 13 18 8 10 , 13 29 16 1 2 11 ⟶ 13 18 32 35 13 18 8 11 , 13 29 16 1 2 12 ⟶ 13 18 32 35 13 18 8 12 , 4 29 16 1 2 4 ⟶ 4 18 32 35 13 18 8 4 , 4 29 16 1 2 6 ⟶ 4 18 32 35 13 18 8 6 , 4 29 16 1 2 3 ⟶ 4 18 32 35 13 18 8 3 , 4 29 16 1 2 9 ⟶ 4 18 32 35 13 18 8 9 , 4 29 16 1 2 10 ⟶ 4 18 32 35 13 18 8 10 , 4 29 16 1 2 11 ⟶ 4 18 32 35 13 18 8 11 , 4 29 16 1 2 12 ⟶ 4 18 32 35 13 18 8 12 , 14 29 16 1 2 4 ⟶ 14 18 32 35 13 18 8 4 , 14 29 16 1 2 6 ⟶ 14 18 32 35 13 18 8 6 , 14 29 16 1 2 3 ⟶ 14 18 32 35 13 18 8 3 , 14 29 16 1 2 9 ⟶ 14 18 32 35 13 18 8 9 , 14 29 16 1 2 10 ⟶ 14 18 32 35 13 18 8 10 , 14 29 16 1 2 11 ⟶ 14 18 32 35 13 18 8 11 , 14 29 16 1 2 12 ⟶ 14 18 32 35 13 18 8 12 , 15 29 16 1 2 4 ⟶ 15 18 32 35 13 18 8 4 , 15 29 16 1 2 6 ⟶ 15 18 32 35 13 18 8 6 , 15 29 16 1 2 3 ⟶ 15 18 32 35 13 18 8 3 , 15 29 16 1 2 9 ⟶ 15 18 32 35 13 18 8 9 , 15 29 16 1 2 10 ⟶ 15 18 32 35 13 18 8 10 , 15 29 16 1 2 11 ⟶ 15 18 32 35 13 18 8 11 , 15 29 16 1 2 12 ⟶ 15 18 32 35 13 18 8 12 , 16 29 16 1 2 4 ⟶ 16 18 32 35 13 18 8 4 , 16 29 16 1 2 6 ⟶ 16 18 32 35 13 18 8 6 , 16 29 16 1 2 3 ⟶ 16 18 32 35 13 18 8 3 , 16 29 16 1 2 9 ⟶ 16 18 32 35 13 18 8 9 , 16 29 16 1 2 10 ⟶ 16 18 32 35 13 18 8 10 , 16 29 16 1 2 11 ⟶ 16 18 32 35 13 18 8 11 , 16 29 16 1 2 12 ⟶ 16 18 32 35 13 18 8 12 , 17 29 16 1 2 4 ⟶ 17 18 32 35 13 18 8 4 , 17 29 16 1 2 6 ⟶ 17 18 32 35 13 18 8 6 , 17 29 16 1 2 3 ⟶ 17 18 32 35 13 18 8 3 , 17 29 16 1 2 9 ⟶ 17 18 32 35 13 18 8 9 , 17 29 16 1 2 10 ⟶ 17 18 32 35 13 18 8 10 , 17 29 16 1 2 11 ⟶ 17 18 32 35 13 18 8 11 , 17 29 16 1 2 12 ⟶ 17 18 32 35 13 18 8 12 , 0 0 29 37 8 4 ⟶ 0 0 18 32 27 36 4 , 0 0 29 37 8 6 ⟶ 0 0 18 32 27 36 6 , 0 0 29 37 8 3 ⟶ 0 0 18 32 27 36 3 , 0 0 29 37 8 9 ⟶ 0 0 18 32 27 36 9 , 0 0 29 37 8 10 ⟶ 0 0 18 32 27 36 10 , 0 0 29 37 8 11 ⟶ 0 0 18 32 27 36 11 , 0 0 29 37 8 12 ⟶ 0 0 18 32 27 36 12 , 13 0 29 37 8 4 ⟶ 13 0 18 32 27 36 4 , 13 0 29 37 8 6 ⟶ 13 0 18 32 27 36 6 , 13 0 29 37 8 3 ⟶ 13 0 18 32 27 36 3 , 13 0 29 37 8 9 ⟶ 13 0 18 32 27 36 9 , 13 0 29 37 8 10 ⟶ 13 0 18 32 27 36 10 , 13 0 29 37 8 11 ⟶ 13 0 18 32 27 36 11 , 13 0 29 37 8 12 ⟶ 13 0 18 32 27 36 12 , 4 0 29 37 8 4 ⟶ 4 0 18 32 27 36 4 , 4 0 29 37 8 6 ⟶ 4 0 18 32 27 36 6 , 4 0 29 37 8 3 ⟶ 4 0 18 32 27 36 3 , 4 0 29 37 8 9 ⟶ 4 0 18 32 27 36 9 , 4 0 29 37 8 10 ⟶ 4 0 18 32 27 36 10 , 4 0 29 37 8 11 ⟶ 4 0 18 32 27 36 11 , 4 0 29 37 8 12 ⟶ 4 0 18 32 27 36 12 , 14 0 29 37 8 4 ⟶ 14 0 18 32 27 36 4 , 14 0 29 37 8 6 ⟶ 14 0 18 32 27 36 6 , 14 0 29 37 8 3 ⟶ 14 0 18 32 27 36 3 , 14 0 29 37 8 9 ⟶ 14 0 18 32 27 36 9 , 14 0 29 37 8 10 ⟶ 14 0 18 32 27 36 10 , 14 0 29 37 8 11 ⟶ 14 0 18 32 27 36 11 , 14 0 29 37 8 12 ⟶ 14 0 18 32 27 36 12 , 15 0 29 37 8 4 ⟶ 15 0 18 32 27 36 4 , 15 0 29 37 8 6 ⟶ 15 0 18 32 27 36 6 , 15 0 29 37 8 3 ⟶ 15 0 18 32 27 36 3 , 15 0 29 37 8 9 ⟶ 15 0 18 32 27 36 9 , 15 0 29 37 8 10 ⟶ 15 0 18 32 27 36 10 , 15 0 29 37 8 11 ⟶ 15 0 18 32 27 36 11 , 15 0 29 37 8 12 ⟶ 15 0 18 32 27 36 12 , 16 0 29 37 8 4 ⟶ 16 0 18 32 27 36 4 , 16 0 29 37 8 6 ⟶ 16 0 18 32 27 36 6 , 16 0 29 37 8 3 ⟶ 16 0 18 32 27 36 3 , 16 0 29 37 8 9 ⟶ 16 0 18 32 27 36 9 , 16 0 29 37 8 10 ⟶ 16 0 18 32 27 36 10 , 16 0 29 37 8 11 ⟶ 16 0 18 32 27 36 11 , 16 0 29 37 8 12 ⟶ 16 0 18 32 27 36 12 , 17 0 29 37 8 4 ⟶ 17 0 18 32 27 36 4 , 17 0 29 37 8 6 ⟶ 17 0 18 32 27 36 6 , 17 0 29 37 8 3 ⟶ 17 0 18 32 27 36 3 , 17 0 29 37 8 9 ⟶ 17 0 18 32 27 36 9 , 17 0 29 37 8 10 ⟶ 17 0 18 32 27 36 10 , 17 0 29 37 8 11 ⟶ 17 0 18 32 27 36 11 , 17 0 29 37 8 12 ⟶ 17 0 18 32 27 36 12 , 29 30 4 23 36 4 ⟶ 29 35 13 18 8 10 36 4 , 29 30 4 23 36 6 ⟶ 29 35 13 18 8 10 36 6 , 29 30 4 23 36 3 ⟶ 29 35 13 18 8 10 36 3 , 29 30 4 23 36 9 ⟶ 29 35 13 18 8 10 36 9 , 29 30 4 23 36 10 ⟶ 29 35 13 18 8 10 36 10 , 29 30 4 23 36 11 ⟶ 29 35 13 18 8 10 36 11 , 29 30 4 23 36 12 ⟶ 29 35 13 18 8 10 36 12 , 21 30 4 23 36 4 ⟶ 21 35 13 18 8 10 36 4 , 21 30 4 23 36 6 ⟶ 21 35 13 18 8 10 36 6 , 21 30 4 23 36 3 ⟶ 21 35 13 18 8 10 36 3 , 21 30 4 23 36 9 ⟶ 21 35 13 18 8 10 36 9 , 21 30 4 23 36 10 ⟶ 21 35 13 18 8 10 36 10 , 21 30 4 23 36 11 ⟶ 21 35 13 18 8 10 36 11 , 21 30 4 23 36 12 ⟶ 21 35 13 18 8 10 36 12 , 11 30 4 23 36 4 ⟶ 11 35 13 18 8 10 36 4 , 11 30 4 23 36 6 ⟶ 11 35 13 18 8 10 36 6 , 11 30 4 23 36 3 ⟶ 11 35 13 18 8 10 36 3 , 11 30 4 23 36 9 ⟶ 11 35 13 18 8 10 36 9 , 11 30 4 23 36 10 ⟶ 11 35 13 18 8 10 36 10 , 11 30 4 23 36 11 ⟶ 11 35 13 18 8 10 36 11 , 11 30 4 23 36 12 ⟶ 11 35 13 18 8 10 36 12 , 32 30 4 23 36 4 ⟶ 32 35 13 18 8 10 36 4 , 32 30 4 23 36 6 ⟶ 32 35 13 18 8 10 36 6 , 32 30 4 23 36 3 ⟶ 32 35 13 18 8 10 36 3 , 32 30 4 23 36 9 ⟶ 32 35 13 18 8 10 36 9 , 32 30 4 23 36 10 ⟶ 32 35 13 18 8 10 36 10 , 32 30 4 23 36 11 ⟶ 32 35 13 18 8 10 36 11 , 32 30 4 23 36 12 ⟶ 32 35 13 18 8 10 36 12 , 33 30 4 23 36 4 ⟶ 33 35 13 18 8 10 36 4 , 33 30 4 23 36 6 ⟶ 33 35 13 18 8 10 36 6 , 33 30 4 23 36 3 ⟶ 33 35 13 18 8 10 36 3 , 33 30 4 23 36 9 ⟶ 33 35 13 18 8 10 36 9 , 33 30 4 23 36 10 ⟶ 33 35 13 18 8 10 36 10 , 33 30 4 23 36 11 ⟶ 33 35 13 18 8 10 36 11 , 33 30 4 23 36 12 ⟶ 33 35 13 18 8 10 36 12 , 31 30 4 23 36 4 ⟶ 31 35 13 18 8 10 36 4 , 31 30 4 23 36 6 ⟶ 31 35 13 18 8 10 36 6 , 31 30 4 23 36 3 ⟶ 31 35 13 18 8 10 36 3 , 31 30 4 23 36 9 ⟶ 31 35 13 18 8 10 36 9 , 31 30 4 23 36 10 ⟶ 31 35 13 18 8 10 36 10 , 31 30 4 23 36 11 ⟶ 31 35 13 18 8 10 36 11 , 31 30 4 23 36 12 ⟶ 31 35 13 18 8 10 36 12 , 34 30 4 23 36 4 ⟶ 34 35 13 18 8 10 36 4 , 34 30 4 23 36 6 ⟶ 34 35 13 18 8 10 36 6 , 34 30 4 23 36 3 ⟶ 34 35 13 18 8 10 36 3 , 34 30 4 23 36 9 ⟶ 34 35 13 18 8 10 36 9 , 34 30 4 23 36 10 ⟶ 34 35 13 18 8 10 36 10 , 34 30 4 23 36 11 ⟶ 34 35 13 18 8 10 36 11 , 34 30 4 23 36 12 ⟶ 34 35 13 18 8 10 36 12 , 0 29 16 23 36 4 ⟶ 0 0 18 40 25 33 30 4 , 0 29 16 23 36 6 ⟶ 0 0 18 40 25 33 30 6 , 0 29 16 23 36 3 ⟶ 0 0 18 40 25 33 30 3 , 0 29 16 23 36 9 ⟶ 0 0 18 40 25 33 30 9 , 0 29 16 23 36 10 ⟶ 0 0 18 40 25 33 30 10 , 0 29 16 23 36 11 ⟶ 0 0 18 40 25 33 30 11 , 0 29 16 23 36 12 ⟶ 0 0 18 40 25 33 30 12 , 13 29 16 23 36 4 ⟶ 13 0 18 40 25 33 30 4 , 13 29 16 23 36 6 ⟶ 13 0 18 40 25 33 30 6 , 13 29 16 23 36 3 ⟶ 13 0 18 40 25 33 30 3 , 13 29 16 23 36 9 ⟶ 13 0 18 40 25 33 30 9 , 13 29 16 23 36 10 ⟶ 13 0 18 40 25 33 30 10 , 13 29 16 23 36 11 ⟶ 13 0 18 40 25 33 30 11 , 13 29 16 23 36 12 ⟶ 13 0 18 40 25 33 30 12 , 4 29 16 23 36 4 ⟶ 4 0 18 40 25 33 30 4 , 4 29 16 23 36 6 ⟶ 4 0 18 40 25 33 30 6 , 4 29 16 23 36 3 ⟶ 4 0 18 40 25 33 30 3 , 4 29 16 23 36 9 ⟶ 4 0 18 40 25 33 30 9 , 4 29 16 23 36 10 ⟶ 4 0 18 40 25 33 30 10 , 4 29 16 23 36 11 ⟶ 4 0 18 40 25 33 30 11 , 4 29 16 23 36 12 ⟶ 4 0 18 40 25 33 30 12 , 14 29 16 23 36 4 ⟶ 14 0 18 40 25 33 30 4 , 14 29 16 23 36 6 ⟶ 14 0 18 40 25 33 30 6 , 14 29 16 23 36 3 ⟶ 14 0 18 40 25 33 30 3 , 14 29 16 23 36 9 ⟶ 14 0 18 40 25 33 30 9 , 14 29 16 23 36 10 ⟶ 14 0 18 40 25 33 30 10 , 14 29 16 23 36 11 ⟶ 14 0 18 40 25 33 30 11 , 14 29 16 23 36 12 ⟶ 14 0 18 40 25 33 30 12 , 15 29 16 23 36 4 ⟶ 15 0 18 40 25 33 30 4 , 15 29 16 23 36 6 ⟶ 15 0 18 40 25 33 30 6 , 15 29 16 23 36 3 ⟶ 15 0 18 40 25 33 30 3 , 15 29 16 23 36 9 ⟶ 15 0 18 40 25 33 30 9 , 15 29 16 23 36 10 ⟶ 15 0 18 40 25 33 30 10 , 15 29 16 23 36 11 ⟶ 15 0 18 40 25 33 30 11 , 15 29 16 23 36 12 ⟶ 15 0 18 40 25 33 30 12 , 16 29 16 23 36 4 ⟶ 16 0 18 40 25 33 30 4 , 16 29 16 23 36 6 ⟶ 16 0 18 40 25 33 30 6 , 16 29 16 23 36 3 ⟶ 16 0 18 40 25 33 30 3 , 16 29 16 23 36 9 ⟶ 16 0 18 40 25 33 30 9 , 16 29 16 23 36 10 ⟶ 16 0 18 40 25 33 30 10 , 16 29 16 23 36 11 ⟶ 16 0 18 40 25 33 30 11 , 16 29 16 23 36 12 ⟶ 16 0 18 40 25 33 30 12 , 17 29 16 23 36 4 ⟶ 17 0 18 40 25 33 30 4 , 17 29 16 23 36 6 ⟶ 17 0 18 40 25 33 30 6 , 17 29 16 23 36 3 ⟶ 17 0 18 40 25 33 30 3 , 17 29 16 23 36 9 ⟶ 17 0 18 40 25 33 30 9 , 17 29 16 23 36 10 ⟶ 17 0 18 40 25 33 30 10 , 17 29 16 23 36 11 ⟶ 17 0 18 40 25 33 30 11 , 17 29 16 23 36 12 ⟶ 17 0 18 40 25 33 30 12 , 0 0 5 11 30 4 ⟶ 0 18 8 11 16 5 4 , 0 0 5 11 30 6 ⟶ 0 18 8 11 16 5 6 , 0 0 5 11 30 3 ⟶ 0 18 8 11 16 5 3 , 0 0 5 11 30 9 ⟶ 0 18 8 11 16 5 9 , 0 0 5 11 30 10 ⟶ 0 18 8 11 16 5 10 , 0 0 5 11 30 11 ⟶ 0 18 8 11 16 5 11 , 0 0 5 11 30 12 ⟶ 0 18 8 11 16 5 12 , 13 0 5 11 30 4 ⟶ 13 18 8 11 16 5 4 , 13 0 5 11 30 6 ⟶ 13 18 8 11 16 5 6 , 13 0 5 11 30 3 ⟶ 13 18 8 11 16 5 3 , 13 0 5 11 30 9 ⟶ 13 18 8 11 16 5 9 , 13 0 5 11 30 10 ⟶ 13 18 8 11 16 5 10 , 13 0 5 11 30 11 ⟶ 13 18 8 11 16 5 11 , 13 0 5 11 30 12 ⟶ 13 18 8 11 16 5 12 , 4 0 5 11 30 4 ⟶ 4 18 8 11 16 5 4 , 4 0 5 11 30 6 ⟶ 4 18 8 11 16 5 6 , 4 0 5 11 30 3 ⟶ 4 18 8 11 16 5 3 , 4 0 5 11 30 9 ⟶ 4 18 8 11 16 5 9 , 4 0 5 11 30 10 ⟶ 4 18 8 11 16 5 10 , 4 0 5 11 30 11 ⟶ 4 18 8 11 16 5 11 , 4 0 5 11 30 12 ⟶ 4 18 8 11 16 5 12 , 14 0 5 11 30 4 ⟶ 14 18 8 11 16 5 4 , 14 0 5 11 30 6 ⟶ 14 18 8 11 16 5 6 , 14 0 5 11 30 3 ⟶ 14 18 8 11 16 5 3 , 14 0 5 11 30 9 ⟶ 14 18 8 11 16 5 9 , 14 0 5 11 30 10 ⟶ 14 18 8 11 16 5 10 , 14 0 5 11 30 11 ⟶ 14 18 8 11 16 5 11 , 14 0 5 11 30 12 ⟶ 14 18 8 11 16 5 12 , 15 0 5 11 30 4 ⟶ 15 18 8 11 16 5 4 , 15 0 5 11 30 6 ⟶ 15 18 8 11 16 5 6 , 15 0 5 11 30 3 ⟶ 15 18 8 11 16 5 3 , 15 0 5 11 30 9 ⟶ 15 18 8 11 16 5 9 , 15 0 5 11 30 10 ⟶ 15 18 8 11 16 5 10 , 15 0 5 11 30 11 ⟶ 15 18 8 11 16 5 11 , 15 0 5 11 30 12 ⟶ 15 18 8 11 16 5 12 , 16 0 5 11 30 4 ⟶ 16 18 8 11 16 5 4 , 16 0 5 11 30 6 ⟶ 16 18 8 11 16 5 6 , 16 0 5 11 30 3 ⟶ 16 18 8 11 16 5 3 , 16 0 5 11 30 9 ⟶ 16 18 8 11 16 5 9 , 16 0 5 11 30 10 ⟶ 16 18 8 11 16 5 10 , 16 0 5 11 30 11 ⟶ 16 18 8 11 16 5 11 , 16 0 5 11 30 12 ⟶ 16 18 8 11 16 5 12 , 17 0 5 11 30 4 ⟶ 17 18 8 11 16 5 4 , 17 0 5 11 30 6 ⟶ 17 18 8 11 16 5 6 , 17 0 5 11 30 3 ⟶ 17 18 8 11 16 5 3 , 17 0 5 11 30 9 ⟶ 17 18 8 11 16 5 9 , 17 0 5 11 30 10 ⟶ 17 18 8 11 16 5 10 , 17 0 5 11 30 11 ⟶ 17 18 8 11 16 5 11 , 17 0 5 11 30 12 ⟶ 17 18 8 11 16 5 12 , 1 21 30 11 30 4 ⟶ 29 31 37 8 6 2 4 , 1 21 30 11 30 6 ⟶ 29 31 37 8 6 2 6 , 1 21 30 11 30 3 ⟶ 29 31 37 8 6 2 3 , 1 21 30 11 30 9 ⟶ 29 31 37 8 6 2 9 , 1 21 30 11 30 10 ⟶ 29 31 37 8 6 2 10 , 1 21 30 11 30 11 ⟶ 29 31 37 8 6 2 11 , 1 21 30 11 30 12 ⟶ 29 31 37 8 6 2 12 , 19 21 30 11 30 4 ⟶ 21 31 37 8 6 2 4 , 19 21 30 11 30 6 ⟶ 21 31 37 8 6 2 6 , 19 21 30 11 30 3 ⟶ 21 31 37 8 6 2 3 , 19 21 30 11 30 9 ⟶ 21 31 37 8 6 2 9 , 19 21 30 11 30 10 ⟶ 21 31 37 8 6 2 10 , 19 21 30 11 30 11 ⟶ 21 31 37 8 6 2 11 , 19 21 30 11 30 12 ⟶ 21 31 37 8 6 2 12 , 6 21 30 11 30 4 ⟶ 11 31 37 8 6 2 4 , 6 21 30 11 30 6 ⟶ 11 31 37 8 6 2 6 , 6 21 30 11 30 3 ⟶ 11 31 37 8 6 2 3 , 6 21 30 11 30 9 ⟶ 11 31 37 8 6 2 9 , 6 21 30 11 30 10 ⟶ 11 31 37 8 6 2 10 , 6 21 30 11 30 11 ⟶ 11 31 37 8 6 2 11 , 6 21 30 11 30 12 ⟶ 11 31 37 8 6 2 12 , 39 21 30 11 30 4 ⟶ 32 31 37 8 6 2 4 , 39 21 30 11 30 6 ⟶ 32 31 37 8 6 2 6 , 39 21 30 11 30 3 ⟶ 32 31 37 8 6 2 3 , 39 21 30 11 30 9 ⟶ 32 31 37 8 6 2 9 , 39 21 30 11 30 10 ⟶ 32 31 37 8 6 2 10 , 39 21 30 11 30 11 ⟶ 32 31 37 8 6 2 11 , 39 21 30 11 30 12 ⟶ 32 31 37 8 6 2 12 , 24 21 30 11 30 4 ⟶ 33 31 37 8 6 2 4 , 24 21 30 11 30 6 ⟶ 33 31 37 8 6 2 6 , 24 21 30 11 30 3 ⟶ 33 31 37 8 6 2 3 , 24 21 30 11 30 9 ⟶ 33 31 37 8 6 2 9 , 24 21 30 11 30 10 ⟶ 33 31 37 8 6 2 10 , 24 21 30 11 30 11 ⟶ 33 31 37 8 6 2 11 , 24 21 30 11 30 12 ⟶ 33 31 37 8 6 2 12 , 35 21 30 11 30 4 ⟶ 31 31 37 8 6 2 4 , 35 21 30 11 30 6 ⟶ 31 31 37 8 6 2 6 , 35 21 30 11 30 3 ⟶ 31 31 37 8 6 2 3 , 35 21 30 11 30 9 ⟶ 31 31 37 8 6 2 9 , 35 21 30 11 30 10 ⟶ 31 31 37 8 6 2 10 , 35 21 30 11 30 11 ⟶ 31 31 37 8 6 2 11 , 35 21 30 11 30 12 ⟶ 31 31 37 8 6 2 12 , 43 21 30 11 30 4 ⟶ 34 31 37 8 6 2 4 , 43 21 30 11 30 6 ⟶ 34 31 37 8 6 2 6 , 43 21 30 11 30 3 ⟶ 34 31 37 8 6 2 3 , 43 21 30 11 30 9 ⟶ 34 31 37 8 6 2 9 , 43 21 30 11 30 10 ⟶ 34 31 37 8 6 2 10 , 43 21 30 11 30 11 ⟶ 34 31 37 8 6 2 11 , 43 21 30 11 30 12 ⟶ 34 31 37 8 6 2 12 , 5 9 39 21 30 4 ⟶ 18 32 35 19 2 3 4 , 5 9 39 21 30 6 ⟶ 18 32 35 19 2 3 6 , 5 9 39 21 30 3 ⟶ 18 32 35 19 2 3 3 , 5 9 39 21 30 9 ⟶ 18 32 35 19 2 3 9 , 5 9 39 21 30 10 ⟶ 18 32 35 19 2 3 10 , 5 9 39 21 30 11 ⟶ 18 32 35 19 2 3 11 , 5 9 39 21 30 12 ⟶ 18 32 35 19 2 3 12 , 2 9 39 21 30 4 ⟶ 7 32 35 19 2 3 4 , 2 9 39 21 30 6 ⟶ 7 32 35 19 2 3 6 , 2 9 39 21 30 3 ⟶ 7 32 35 19 2 3 3 , 2 9 39 21 30 9 ⟶ 7 32 35 19 2 3 9 , 2 9 39 21 30 10 ⟶ 7 32 35 19 2 3 10 , 2 9 39 21 30 11 ⟶ 7 32 35 19 2 3 11 , 2 9 39 21 30 12 ⟶ 7 32 35 19 2 3 12 , 3 9 39 21 30 4 ⟶ 9 32 35 19 2 3 4 , 3 9 39 21 30 6 ⟶ 9 32 35 19 2 3 6 , 3 9 39 21 30 3 ⟶ 9 32 35 19 2 3 3 , 3 9 39 21 30 9 ⟶ 9 32 35 19 2 3 9 , 3 9 39 21 30 10 ⟶ 9 32 35 19 2 3 10 , 3 9 39 21 30 11 ⟶ 9 32 35 19 2 3 11 , 3 9 39 21 30 12 ⟶ 9 32 35 19 2 3 12 , 8 9 39 21 30 4 ⟶ 40 32 35 19 2 3 4 , 8 9 39 21 30 6 ⟶ 40 32 35 19 2 3 6 , 8 9 39 21 30 3 ⟶ 40 32 35 19 2 3 3 , 8 9 39 21 30 9 ⟶ 40 32 35 19 2 3 9 , 8 9 39 21 30 10 ⟶ 40 32 35 19 2 3 10 , 8 9 39 21 30 11 ⟶ 40 32 35 19 2 3 11 , 8 9 39 21 30 12 ⟶ 40 32 35 19 2 3 12 , 36 9 39 21 30 4 ⟶ 41 32 35 19 2 3 4 , 36 9 39 21 30 6 ⟶ 41 32 35 19 2 3 6 , 36 9 39 21 30 3 ⟶ 41 32 35 19 2 3 3 , 36 9 39 21 30 9 ⟶ 41 32 35 19 2 3 9 , 36 9 39 21 30 10 ⟶ 41 32 35 19 2 3 10 , 36 9 39 21 30 11 ⟶ 41 32 35 19 2 3 11 , 36 9 39 21 30 12 ⟶ 41 32 35 19 2 3 12 , 30 9 39 21 30 4 ⟶ 37 32 35 19 2 3 4 , 30 9 39 21 30 6 ⟶ 37 32 35 19 2 3 6 , 30 9 39 21 30 3 ⟶ 37 32 35 19 2 3 3 , 30 9 39 21 30 9 ⟶ 37 32 35 19 2 3 9 , 30 9 39 21 30 10 ⟶ 37 32 35 19 2 3 10 , 30 9 39 21 30 11 ⟶ 37 32 35 19 2 3 11 , 30 9 39 21 30 12 ⟶ 37 32 35 19 2 3 12 , 45 9 39 21 30 4 ⟶ 42 32 35 19 2 3 4 , 45 9 39 21 30 6 ⟶ 42 32 35 19 2 3 6 , 45 9 39 21 30 3 ⟶ 42 32 35 19 2 3 3 , 45 9 39 21 30 9 ⟶ 42 32 35 19 2 3 9 , 45 9 39 21 30 10 ⟶ 42 32 35 19 2 3 10 , 45 9 39 21 30 11 ⟶ 42 32 35 19 2 3 11 , 45 9 39 21 30 12 ⟶ 42 32 35 19 2 3 12 , 23 15 0 29 30 4 ⟶ 23 15 0 18 32 30 4 , 23 15 0 29 30 6 ⟶ 23 15 0 18 32 30 6 , 23 15 0 29 30 3 ⟶ 23 15 0 18 32 30 3 , 23 15 0 29 30 9 ⟶ 23 15 0 18 32 30 9 , 23 15 0 29 30 10 ⟶ 23 15 0 18 32 30 10 , 23 15 0 29 30 11 ⟶ 23 15 0 18 32 30 11 , 23 15 0 29 30 12 ⟶ 23 15 0 18 32 30 12 , 20 15 0 29 30 4 ⟶ 20 15 0 18 32 30 4 , 20 15 0 29 30 6 ⟶ 20 15 0 18 32 30 6 , 20 15 0 29 30 3 ⟶ 20 15 0 18 32 30 3 , 20 15 0 29 30 9 ⟶ 20 15 0 18 32 30 9 , 20 15 0 29 30 10 ⟶ 20 15 0 18 32 30 10 , 20 15 0 29 30 11 ⟶ 20 15 0 18 32 30 11 , 20 15 0 29 30 12 ⟶ 20 15 0 18 32 30 12 , 10 15 0 29 30 4 ⟶ 10 15 0 18 32 30 4 , 10 15 0 29 30 6 ⟶ 10 15 0 18 32 30 6 , 10 15 0 29 30 3 ⟶ 10 15 0 18 32 30 3 , 10 15 0 29 30 9 ⟶ 10 15 0 18 32 30 9 , 10 15 0 29 30 10 ⟶ 10 15 0 18 32 30 10 , 10 15 0 29 30 11 ⟶ 10 15 0 18 32 30 11 , 10 15 0 29 30 12 ⟶ 10 15 0 18 32 30 12 , 25 15 0 29 30 4 ⟶ 25 15 0 18 32 30 4 , 25 15 0 29 30 6 ⟶ 25 15 0 18 32 30 6 , 25 15 0 29 30 3 ⟶ 25 15 0 18 32 30 3 , 25 15 0 29 30 9 ⟶ 25 15 0 18 32 30 9 , 25 15 0 29 30 10 ⟶ 25 15 0 18 32 30 10 , 25 15 0 29 30 11 ⟶ 25 15 0 18 32 30 11 , 25 15 0 29 30 12 ⟶ 25 15 0 18 32 30 12 , 26 15 0 29 30 4 ⟶ 26 15 0 18 32 30 4 , 26 15 0 29 30 6 ⟶ 26 15 0 18 32 30 6 , 26 15 0 29 30 3 ⟶ 26 15 0 18 32 30 3 , 26 15 0 29 30 9 ⟶ 26 15 0 18 32 30 9 , 26 15 0 29 30 10 ⟶ 26 15 0 18 32 30 10 , 26 15 0 29 30 11 ⟶ 26 15 0 18 32 30 11 , 26 15 0 29 30 12 ⟶ 26 15 0 18 32 30 12 , 27 15 0 29 30 4 ⟶ 27 15 0 18 32 30 4 , 27 15 0 29 30 6 ⟶ 27 15 0 18 32 30 6 , 27 15 0 29 30 3 ⟶ 27 15 0 18 32 30 3 , 27 15 0 29 30 9 ⟶ 27 15 0 18 32 30 9 , 27 15 0 29 30 10 ⟶ 27 15 0 18 32 30 10 , 27 15 0 29 30 11 ⟶ 27 15 0 18 32 30 11 , 27 15 0 29 30 12 ⟶ 27 15 0 18 32 30 12 , 28 15 0 29 30 4 ⟶ 28 15 0 18 32 30 4 , 28 15 0 29 30 6 ⟶ 28 15 0 18 32 30 6 , 28 15 0 29 30 3 ⟶ 28 15 0 18 32 30 3 , 28 15 0 29 30 9 ⟶ 28 15 0 18 32 30 9 , 28 15 0 29 30 10 ⟶ 28 15 0 18 32 30 10 , 28 15 0 29 30 11 ⟶ 28 15 0 18 32 30 11 , 28 15 0 29 30 12 ⟶ 28 15 0 18 32 30 12 , 1 7 14 29 30 4 ⟶ 0 0 0 18 32 35 2 4 , 1 7 14 29 30 6 ⟶ 0 0 0 18 32 35 2 6 , 1 7 14 29 30 3 ⟶ 0 0 0 18 32 35 2 3 , 1 7 14 29 30 9 ⟶ 0 0 0 18 32 35 2 9 , 1 7 14 29 30 10 ⟶ 0 0 0 18 32 35 2 10 , 1 7 14 29 30 11 ⟶ 0 0 0 18 32 35 2 11 , 1 7 14 29 30 12 ⟶ 0 0 0 18 32 35 2 12 , 19 7 14 29 30 4 ⟶ 13 0 0 18 32 35 2 4 , 19 7 14 29 30 6 ⟶ 13 0 0 18 32 35 2 6 , 19 7 14 29 30 3 ⟶ 13 0 0 18 32 35 2 3 , 19 7 14 29 30 9 ⟶ 13 0 0 18 32 35 2 9 , 19 7 14 29 30 10 ⟶ 13 0 0 18 32 35 2 10 , 19 7 14 29 30 11 ⟶ 13 0 0 18 32 35 2 11 , 19 7 14 29 30 12 ⟶ 13 0 0 18 32 35 2 12 , 6 7 14 29 30 4 ⟶ 4 0 0 18 32 35 2 4 , 6 7 14 29 30 6 ⟶ 4 0 0 18 32 35 2 6 , 6 7 14 29 30 3 ⟶ 4 0 0 18 32 35 2 3 , 6 7 14 29 30 9 ⟶ 4 0 0 18 32 35 2 9 , 6 7 14 29 30 10 ⟶ 4 0 0 18 32 35 2 10 , 6 7 14 29 30 11 ⟶ 4 0 0 18 32 35 2 11 , 6 7 14 29 30 12 ⟶ 4 0 0 18 32 35 2 12 , 39 7 14 29 30 4 ⟶ 14 0 0 18 32 35 2 4 , 39 7 14 29 30 6 ⟶ 14 0 0 18 32 35 2 6 , 39 7 14 29 30 3 ⟶ 14 0 0 18 32 35 2 3 , 39 7 14 29 30 9 ⟶ 14 0 0 18 32 35 2 9 , 39 7 14 29 30 10 ⟶ 14 0 0 18 32 35 2 10 , 39 7 14 29 30 11 ⟶ 14 0 0 18 32 35 2 11 , 39 7 14 29 30 12 ⟶ 14 0 0 18 32 35 2 12 , 24 7 14 29 30 4 ⟶ 15 0 0 18 32 35 2 4 , 24 7 14 29 30 6 ⟶ 15 0 0 18 32 35 2 6 , 24 7 14 29 30 3 ⟶ 15 0 0 18 32 35 2 3 , 24 7 14 29 30 9 ⟶ 15 0 0 18 32 35 2 9 , 24 7 14 29 30 10 ⟶ 15 0 0 18 32 35 2 10 , 24 7 14 29 30 11 ⟶ 15 0 0 18 32 35 2 11 , 24 7 14 29 30 12 ⟶ 15 0 0 18 32 35 2 12 , 35 7 14 29 30 4 ⟶ 16 0 0 18 32 35 2 4 , 35 7 14 29 30 6 ⟶ 16 0 0 18 32 35 2 6 , 35 7 14 29 30 3 ⟶ 16 0 0 18 32 35 2 3 , 35 7 14 29 30 9 ⟶ 16 0 0 18 32 35 2 9 , 35 7 14 29 30 10 ⟶ 16 0 0 18 32 35 2 10 , 35 7 14 29 30 11 ⟶ 16 0 0 18 32 35 2 11 , 35 7 14 29 30 12 ⟶ 16 0 0 18 32 35 2 12 , 43 7 14 29 30 4 ⟶ 17 0 0 18 32 35 2 4 , 43 7 14 29 30 6 ⟶ 17 0 0 18 32 35 2 6 , 43 7 14 29 30 3 ⟶ 17 0 0 18 32 35 2 3 , 43 7 14 29 30 9 ⟶ 17 0 0 18 32 35 2 9 , 43 7 14 29 30 10 ⟶ 17 0 0 18 32 35 2 10 , 43 7 14 29 30 11 ⟶ 17 0 0 18 32 35 2 11 , 43 7 14 29 30 12 ⟶ 17 0 0 18 32 35 2 12 , 1 20 15 29 30 4 ⟶ 1 21 16 18 25 36 4 , 1 20 15 29 30 6 ⟶ 1 21 16 18 25 36 6 , 1 20 15 29 30 3 ⟶ 1 21 16 18 25 36 3 , 1 20 15 29 30 9 ⟶ 1 21 16 18 25 36 9 , 1 20 15 29 30 10 ⟶ 1 21 16 18 25 36 10 , 1 20 15 29 30 11 ⟶ 1 21 16 18 25 36 11 , 1 20 15 29 30 12 ⟶ 1 21 16 18 25 36 12 , 19 20 15 29 30 4 ⟶ 19 21 16 18 25 36 4 , 19 20 15 29 30 6 ⟶ 19 21 16 18 25 36 6 , 19 20 15 29 30 3 ⟶ 19 21 16 18 25 36 3 , 19 20 15 29 30 9 ⟶ 19 21 16 18 25 36 9 , 19 20 15 29 30 10 ⟶ 19 21 16 18 25 36 10 , 19 20 15 29 30 11 ⟶ 19 21 16 18 25 36 11 , 19 20 15 29 30 12 ⟶ 19 21 16 18 25 36 12 , 6 20 15 29 30 4 ⟶ 6 21 16 18 25 36 4 , 6 20 15 29 30 6 ⟶ 6 21 16 18 25 36 6 , 6 20 15 29 30 3 ⟶ 6 21 16 18 25 36 3 , 6 20 15 29 30 9 ⟶ 6 21 16 18 25 36 9 , 6 20 15 29 30 10 ⟶ 6 21 16 18 25 36 10 , 6 20 15 29 30 11 ⟶ 6 21 16 18 25 36 11 , 6 20 15 29 30 12 ⟶ 6 21 16 18 25 36 12 , 39 20 15 29 30 4 ⟶ 39 21 16 18 25 36 4 , 39 20 15 29 30 6 ⟶ 39 21 16 18 25 36 6 , 39 20 15 29 30 3 ⟶ 39 21 16 18 25 36 3 , 39 20 15 29 30 9 ⟶ 39 21 16 18 25 36 9 , 39 20 15 29 30 10 ⟶ 39 21 16 18 25 36 10 , 39 20 15 29 30 11 ⟶ 39 21 16 18 25 36 11 , 39 20 15 29 30 12 ⟶ 39 21 16 18 25 36 12 , 24 20 15 29 30 4 ⟶ 24 21 16 18 25 36 4 , 24 20 15 29 30 6 ⟶ 24 21 16 18 25 36 6 , 24 20 15 29 30 3 ⟶ 24 21 16 18 25 36 3 , 24 20 15 29 30 9 ⟶ 24 21 16 18 25 36 9 , 24 20 15 29 30 10 ⟶ 24 21 16 18 25 36 10 , 24 20 15 29 30 11 ⟶ 24 21 16 18 25 36 11 , 24 20 15 29 30 12 ⟶ 24 21 16 18 25 36 12 , 35 20 15 29 30 4 ⟶ 35 21 16 18 25 36 4 , 35 20 15 29 30 6 ⟶ 35 21 16 18 25 36 6 , 35 20 15 29 30 3 ⟶ 35 21 16 18 25 36 3 , 35 20 15 29 30 9 ⟶ 35 21 16 18 25 36 9 , 35 20 15 29 30 10 ⟶ 35 21 16 18 25 36 10 , 35 20 15 29 30 11 ⟶ 35 21 16 18 25 36 11 , 35 20 15 29 30 12 ⟶ 35 21 16 18 25 36 12 , 43 20 15 29 30 4 ⟶ 43 21 16 18 25 36 4 , 43 20 15 29 30 6 ⟶ 43 21 16 18 25 36 6 , 43 20 15 29 30 3 ⟶ 43 21 16 18 25 36 3 , 43 20 15 29 30 9 ⟶ 43 21 16 18 25 36 9 , 43 20 15 29 30 10 ⟶ 43 21 16 18 25 36 10 , 43 20 15 29 30 11 ⟶ 43 21 16 18 25 36 11 , 43 20 15 29 30 12 ⟶ 43 21 16 18 25 36 12 , 0 29 37 32 30 4 ⟶ 0 29 31 37 8 3 4 , 0 29 37 32 30 6 ⟶ 0 29 31 37 8 3 6 , 0 29 37 32 30 3 ⟶ 0 29 31 37 8 3 3 , 0 29 37 32 30 9 ⟶ 0 29 31 37 8 3 9 , 0 29 37 32 30 10 ⟶ 0 29 31 37 8 3 10 , 0 29 37 32 30 11 ⟶ 0 29 31 37 8 3 11 , 0 29 37 32 30 12 ⟶ 0 29 31 37 8 3 12 , 13 29 37 32 30 4 ⟶ 13 29 31 37 8 3 4 , 13 29 37 32 30 6 ⟶ 13 29 31 37 8 3 6 , 13 29 37 32 30 3 ⟶ 13 29 31 37 8 3 3 , 13 29 37 32 30 9 ⟶ 13 29 31 37 8 3 9 , 13 29 37 32 30 10 ⟶ 13 29 31 37 8 3 10 , 13 29 37 32 30 11 ⟶ 13 29 31 37 8 3 11 , 13 29 37 32 30 12 ⟶ 13 29 31 37 8 3 12 , 4 29 37 32 30 4 ⟶ 4 29 31 37 8 3 4 , 4 29 37 32 30 6 ⟶ 4 29 31 37 8 3 6 , 4 29 37 32 30 3 ⟶ 4 29 31 37 8 3 3 , 4 29 37 32 30 9 ⟶ 4 29 31 37 8 3 9 , 4 29 37 32 30 10 ⟶ 4 29 31 37 8 3 10 , 4 29 37 32 30 11 ⟶ 4 29 31 37 8 3 11 , 4 29 37 32 30 12 ⟶ 4 29 31 37 8 3 12 , 14 29 37 32 30 4 ⟶ 14 29 31 37 8 3 4 , 14 29 37 32 30 6 ⟶ 14 29 31 37 8 3 6 , 14 29 37 32 30 3 ⟶ 14 29 31 37 8 3 3 , 14 29 37 32 30 9 ⟶ 14 29 31 37 8 3 9 , 14 29 37 32 30 10 ⟶ 14 29 31 37 8 3 10 , 14 29 37 32 30 11 ⟶ 14 29 31 37 8 3 11 , 14 29 37 32 30 12 ⟶ 14 29 31 37 8 3 12 , 15 29 37 32 30 4 ⟶ 15 29 31 37 8 3 4 , 15 29 37 32 30 6 ⟶ 15 29 31 37 8 3 6 , 15 29 37 32 30 3 ⟶ 15 29 31 37 8 3 3 , 15 29 37 32 30 9 ⟶ 15 29 31 37 8 3 9 , 15 29 37 32 30 10 ⟶ 15 29 31 37 8 3 10 , 15 29 37 32 30 11 ⟶ 15 29 31 37 8 3 11 , 15 29 37 32 30 12 ⟶ 15 29 31 37 8 3 12 , 16 29 37 32 30 4 ⟶ 16 29 31 37 8 3 4 , 16 29 37 32 30 6 ⟶ 16 29 31 37 8 3 6 , 16 29 37 32 30 3 ⟶ 16 29 31 37 8 3 3 , 16 29 37 32 30 9 ⟶ 16 29 31 37 8 3 9 , 16 29 37 32 30 10 ⟶ 16 29 31 37 8 3 10 , 16 29 37 32 30 11 ⟶ 16 29 31 37 8 3 11 , 16 29 37 32 30 12 ⟶ 16 29 31 37 8 3 12 , 17 29 37 32 30 4 ⟶ 17 29 31 37 8 3 4 , 17 29 37 32 30 6 ⟶ 17 29 31 37 8 3 6 , 17 29 37 32 30 3 ⟶ 17 29 31 37 8 3 3 , 17 29 37 32 30 9 ⟶ 17 29 31 37 8 3 9 , 17 29 37 32 30 10 ⟶ 17 29 31 37 8 3 10 , 17 29 37 32 30 11 ⟶ 17 29 31 37 8 3 11 , 17 29 37 32 30 12 ⟶ 17 29 31 37 8 3 12 , 1 7 32 31 30 4 ⟶ 0 18 40 32 35 2 11 16 , 1 7 32 31 30 6 ⟶ 0 18 40 32 35 2 11 35 , 1 7 32 31 30 3 ⟶ 0 18 40 32 35 2 11 30 , 1 7 32 31 30 9 ⟶ 0 18 40 32 35 2 11 37 , 1 7 32 31 30 10 ⟶ 0 18 40 32 35 2 11 27 , 1 7 32 31 30 11 ⟶ 0 18 40 32 35 2 11 31 , 1 7 32 31 30 12 ⟶ 0 18 40 32 35 2 11 38 , 19 7 32 31 30 4 ⟶ 13 18 40 32 35 2 11 16 , 19 7 32 31 30 6 ⟶ 13 18 40 32 35 2 11 35 , 19 7 32 31 30 3 ⟶ 13 18 40 32 35 2 11 30 , 19 7 32 31 30 9 ⟶ 13 18 40 32 35 2 11 37 , 19 7 32 31 30 10 ⟶ 13 18 40 32 35 2 11 27 , 19 7 32 31 30 11 ⟶ 13 18 40 32 35 2 11 31 , 19 7 32 31 30 12 ⟶ 13 18 40 32 35 2 11 38 , 6 7 32 31 30 4 ⟶ 4 18 40 32 35 2 11 16 , 6 7 32 31 30 6 ⟶ 4 18 40 32 35 2 11 35 , 6 7 32 31 30 3 ⟶ 4 18 40 32 35 2 11 30 , 6 7 32 31 30 9 ⟶ 4 18 40 32 35 2 11 37 , 6 7 32 31 30 10 ⟶ 4 18 40 32 35 2 11 27 , 6 7 32 31 30 11 ⟶ 4 18 40 32 35 2 11 31 , 6 7 32 31 30 12 ⟶ 4 18 40 32 35 2 11 38 , 39 7 32 31 30 4 ⟶ 14 18 40 32 35 2 11 16 , 39 7 32 31 30 6 ⟶ 14 18 40 32 35 2 11 35 , 39 7 32 31 30 3 ⟶ 14 18 40 32 35 2 11 30 , 39 7 32 31 30 9 ⟶ 14 18 40 32 35 2 11 37 , 39 7 32 31 30 10 ⟶ 14 18 40 32 35 2 11 27 , 39 7 32 31 30 11 ⟶ 14 18 40 32 35 2 11 31 , 39 7 32 31 30 12 ⟶ 14 18 40 32 35 2 11 38 , 24 7 32 31 30 4 ⟶ 15 18 40 32 35 2 11 16 , 24 7 32 31 30 6 ⟶ 15 18 40 32 35 2 11 35 , 24 7 32 31 30 3 ⟶ 15 18 40 32 35 2 11 30 , 24 7 32 31 30 9 ⟶ 15 18 40 32 35 2 11 37 , 24 7 32 31 30 10 ⟶ 15 18 40 32 35 2 11 27 , 24 7 32 31 30 11 ⟶ 15 18 40 32 35 2 11 31 , 24 7 32 31 30 12 ⟶ 15 18 40 32 35 2 11 38 , 35 7 32 31 30 4 ⟶ 16 18 40 32 35 2 11 16 , 35 7 32 31 30 6 ⟶ 16 18 40 32 35 2 11 35 , 35 7 32 31 30 3 ⟶ 16 18 40 32 35 2 11 30 , 35 7 32 31 30 9 ⟶ 16 18 40 32 35 2 11 37 , 35 7 32 31 30 10 ⟶ 16 18 40 32 35 2 11 27 , 35 7 32 31 30 11 ⟶ 16 18 40 32 35 2 11 31 , 35 7 32 31 30 12 ⟶ 16 18 40 32 35 2 11 38 , 43 7 32 31 30 4 ⟶ 17 18 40 32 35 2 11 16 , 43 7 32 31 30 6 ⟶ 17 18 40 32 35 2 11 35 , 43 7 32 31 30 3 ⟶ 17 18 40 32 35 2 11 30 , 43 7 32 31 30 9 ⟶ 17 18 40 32 35 2 11 37 , 43 7 32 31 30 10 ⟶ 17 18 40 32 35 2 11 27 , 43 7 32 31 30 11 ⟶ 17 18 40 32 35 2 11 31 , 43 7 32 31 30 12 ⟶ 17 18 40 32 35 2 11 38 , 1 21 31 30 6 13 ⟶ 1 21 35 21 27 36 4 , 1 21 31 30 6 19 ⟶ 1 21 35 21 27 36 6 , 1 21 31 30 6 2 ⟶ 1 21 35 21 27 36 3 , 1 21 31 30 6 7 ⟶ 1 21 35 21 27 36 9 , 1 21 31 30 6 20 ⟶ 1 21 35 21 27 36 10 , 1 21 31 30 6 21 ⟶ 1 21 35 21 27 36 11 , 1 21 31 30 6 22 ⟶ 1 21 35 21 27 36 12 , 19 21 31 30 6 13 ⟶ 19 21 35 21 27 36 4 , 19 21 31 30 6 19 ⟶ 19 21 35 21 27 36 6 , 19 21 31 30 6 2 ⟶ 19 21 35 21 27 36 3 , 19 21 31 30 6 7 ⟶ 19 21 35 21 27 36 9 , 19 21 31 30 6 20 ⟶ 19 21 35 21 27 36 10 , 19 21 31 30 6 21 ⟶ 19 21 35 21 27 36 11 , 19 21 31 30 6 22 ⟶ 19 21 35 21 27 36 12 , 6 21 31 30 6 13 ⟶ 6 21 35 21 27 36 4 , 6 21 31 30 6 19 ⟶ 6 21 35 21 27 36 6 , 6 21 31 30 6 2 ⟶ 6 21 35 21 27 36 3 , 6 21 31 30 6 7 ⟶ 6 21 35 21 27 36 9 , 6 21 31 30 6 20 ⟶ 6 21 35 21 27 36 10 , 6 21 31 30 6 21 ⟶ 6 21 35 21 27 36 11 , 6 21 31 30 6 22 ⟶ 6 21 35 21 27 36 12 , 39 21 31 30 6 13 ⟶ 39 21 35 21 27 36 4 , 39 21 31 30 6 19 ⟶ 39 21 35 21 27 36 6 , 39 21 31 30 6 2 ⟶ 39 21 35 21 27 36 3 , 39 21 31 30 6 7 ⟶ 39 21 35 21 27 36 9 , 39 21 31 30 6 20 ⟶ 39 21 35 21 27 36 10 , 39 21 31 30 6 21 ⟶ 39 21 35 21 27 36 11 , 39 21 31 30 6 22 ⟶ 39 21 35 21 27 36 12 , 24 21 31 30 6 13 ⟶ 24 21 35 21 27 36 4 , 24 21 31 30 6 19 ⟶ 24 21 35 21 27 36 6 , 24 21 31 30 6 2 ⟶ 24 21 35 21 27 36 3 , 24 21 31 30 6 7 ⟶ 24 21 35 21 27 36 9 , 24 21 31 30 6 20 ⟶ 24 21 35 21 27 36 10 , 24 21 31 30 6 21 ⟶ 24 21 35 21 27 36 11 , 24 21 31 30 6 22 ⟶ 24 21 35 21 27 36 12 , 35 21 31 30 6 13 ⟶ 35 21 35 21 27 36 4 , 35 21 31 30 6 19 ⟶ 35 21 35 21 27 36 6 , 35 21 31 30 6 2 ⟶ 35 21 35 21 27 36 3 , 35 21 31 30 6 7 ⟶ 35 21 35 21 27 36 9 , 35 21 31 30 6 20 ⟶ 35 21 35 21 27 36 10 , 35 21 31 30 6 21 ⟶ 35 21 35 21 27 36 11 , 35 21 31 30 6 22 ⟶ 35 21 35 21 27 36 12 , 43 21 31 30 6 13 ⟶ 43 21 35 21 27 36 4 , 43 21 31 30 6 19 ⟶ 43 21 35 21 27 36 6 , 43 21 31 30 6 2 ⟶ 43 21 35 21 27 36 3 , 43 21 31 30 6 7 ⟶ 43 21 35 21 27 36 9 , 43 21 31 30 6 20 ⟶ 43 21 35 21 27 36 10 , 43 21 31 30 6 21 ⟶ 43 21 35 21 27 36 11 , 43 21 31 30 6 22 ⟶ 43 21 35 21 27 36 12 , 5 4 0 1 19 13 ⟶ 5 4 0 18 39 19 13 , 5 4 0 1 19 19 ⟶ 5 4 0 18 39 19 19 , 5 4 0 1 19 2 ⟶ 5 4 0 18 39 19 2 , 5 4 0 1 19 7 ⟶ 5 4 0 18 39 19 7 , 5 4 0 1 19 20 ⟶ 5 4 0 18 39 19 20 , 5 4 0 1 19 21 ⟶ 5 4 0 18 39 19 21 , 5 4 0 1 19 22 ⟶ 5 4 0 18 39 19 22 , 2 4 0 1 19 13 ⟶ 2 4 0 18 39 19 13 , 2 4 0 1 19 19 ⟶ 2 4 0 18 39 19 19 , 2 4 0 1 19 2 ⟶ 2 4 0 18 39 19 2 , 2 4 0 1 19 7 ⟶ 2 4 0 18 39 19 7 , 2 4 0 1 19 20 ⟶ 2 4 0 18 39 19 20 , 2 4 0 1 19 21 ⟶ 2 4 0 18 39 19 21 , 2 4 0 1 19 22 ⟶ 2 4 0 18 39 19 22 , 3 4 0 1 19 13 ⟶ 3 4 0 18 39 19 13 , 3 4 0 1 19 19 ⟶ 3 4 0 18 39 19 19 , 3 4 0 1 19 2 ⟶ 3 4 0 18 39 19 2 , 3 4 0 1 19 7 ⟶ 3 4 0 18 39 19 7 , 3 4 0 1 19 20 ⟶ 3 4 0 18 39 19 20 , 3 4 0 1 19 21 ⟶ 3 4 0 18 39 19 21 , 3 4 0 1 19 22 ⟶ 3 4 0 18 39 19 22 , 8 4 0 1 19 13 ⟶ 8 4 0 18 39 19 13 , 8 4 0 1 19 19 ⟶ 8 4 0 18 39 19 19 , 8 4 0 1 19 2 ⟶ 8 4 0 18 39 19 2 , 8 4 0 1 19 7 ⟶ 8 4 0 18 39 19 7 , 8 4 0 1 19 20 ⟶ 8 4 0 18 39 19 20 , 8 4 0 1 19 21 ⟶ 8 4 0 18 39 19 21 , 8 4 0 1 19 22 ⟶ 8 4 0 18 39 19 22 , 36 4 0 1 19 13 ⟶ 36 4 0 18 39 19 13 , 36 4 0 1 19 19 ⟶ 36 4 0 18 39 19 19 , 36 4 0 1 19 2 ⟶ 36 4 0 18 39 19 2 , 36 4 0 1 19 7 ⟶ 36 4 0 18 39 19 7 , 36 4 0 1 19 20 ⟶ 36 4 0 18 39 19 20 , 36 4 0 1 19 21 ⟶ 36 4 0 18 39 19 21 , 36 4 0 1 19 22 ⟶ 36 4 0 18 39 19 22 , 30 4 0 1 19 13 ⟶ 30 4 0 18 39 19 13 , 30 4 0 1 19 19 ⟶ 30 4 0 18 39 19 19 , 30 4 0 1 19 2 ⟶ 30 4 0 18 39 19 2 , 30 4 0 1 19 7 ⟶ 30 4 0 18 39 19 7 , 30 4 0 1 19 20 ⟶ 30 4 0 18 39 19 20 , 30 4 0 1 19 21 ⟶ 30 4 0 18 39 19 21 , 30 4 0 1 19 22 ⟶ 30 4 0 18 39 19 22 , 45 4 0 1 19 13 ⟶ 45 4 0 18 39 19 13 , 45 4 0 1 19 19 ⟶ 45 4 0 18 39 19 19 , 45 4 0 1 19 2 ⟶ 45 4 0 18 39 19 2 , 45 4 0 1 19 7 ⟶ 45 4 0 18 39 19 7 , 45 4 0 1 19 20 ⟶ 45 4 0 18 39 19 20 , 45 4 0 1 19 21 ⟶ 45 4 0 18 39 19 21 , 45 4 0 1 19 22 ⟶ 45 4 0 18 39 19 22 , 23 41 14 1 19 13 ⟶ 23 15 0 18 39 19 13 , 23 41 14 1 19 19 ⟶ 23 15 0 18 39 19 19 , 23 41 14 1 19 2 ⟶ 23 15 0 18 39 19 2 , 23 41 14 1 19 7 ⟶ 23 15 0 18 39 19 7 , 23 41 14 1 19 20 ⟶ 23 15 0 18 39 19 20 , 23 41 14 1 19 21 ⟶ 23 15 0 18 39 19 21 , 23 41 14 1 19 22 ⟶ 23 15 0 18 39 19 22 , 20 41 14 1 19 13 ⟶ 20 15 0 18 39 19 13 , 20 41 14 1 19 19 ⟶ 20 15 0 18 39 19 19 , 20 41 14 1 19 2 ⟶ 20 15 0 18 39 19 2 , 20 41 14 1 19 7 ⟶ 20 15 0 18 39 19 7 , 20 41 14 1 19 20 ⟶ 20 15 0 18 39 19 20 , 20 41 14 1 19 21 ⟶ 20 15 0 18 39 19 21 , 20 41 14 1 19 22 ⟶ 20 15 0 18 39 19 22 , 10 41 14 1 19 13 ⟶ 10 15 0 18 39 19 13 , 10 41 14 1 19 19 ⟶ 10 15 0 18 39 19 19 , 10 41 14 1 19 2 ⟶ 10 15 0 18 39 19 2 , 10 41 14 1 19 7 ⟶ 10 15 0 18 39 19 7 , 10 41 14 1 19 20 ⟶ 10 15 0 18 39 19 20 , 10 41 14 1 19 21 ⟶ 10 15 0 18 39 19 21 , 10 41 14 1 19 22 ⟶ 10 15 0 18 39 19 22 , 25 41 14 1 19 13 ⟶ 25 15 0 18 39 19 13 , 25 41 14 1 19 19 ⟶ 25 15 0 18 39 19 19 , 25 41 14 1 19 2 ⟶ 25 15 0 18 39 19 2 , 25 41 14 1 19 7 ⟶ 25 15 0 18 39 19 7 , 25 41 14 1 19 20 ⟶ 25 15 0 18 39 19 20 , 25 41 14 1 19 21 ⟶ 25 15 0 18 39 19 21 , 25 41 14 1 19 22 ⟶ 25 15 0 18 39 19 22 , 26 41 14 1 19 13 ⟶ 26 15 0 18 39 19 13 , 26 41 14 1 19 19 ⟶ 26 15 0 18 39 19 19 , 26 41 14 1 19 2 ⟶ 26 15 0 18 39 19 2 , 26 41 14 1 19 7 ⟶ 26 15 0 18 39 19 7 , 26 41 14 1 19 20 ⟶ 26 15 0 18 39 19 20 , 26 41 14 1 19 21 ⟶ 26 15 0 18 39 19 21 , 26 41 14 1 19 22 ⟶ 26 15 0 18 39 19 22 , 27 41 14 1 19 13 ⟶ 27 15 0 18 39 19 13 , 27 41 14 1 19 19 ⟶ 27 15 0 18 39 19 19 , 27 41 14 1 19 2 ⟶ 27 15 0 18 39 19 2 , 27 41 14 1 19 7 ⟶ 27 15 0 18 39 19 7 , 27 41 14 1 19 20 ⟶ 27 15 0 18 39 19 20 , 27 41 14 1 19 21 ⟶ 27 15 0 18 39 19 21 , 27 41 14 1 19 22 ⟶ 27 15 0 18 39 19 22 , 28 41 14 1 19 13 ⟶ 28 15 0 18 39 19 13 , 28 41 14 1 19 19 ⟶ 28 15 0 18 39 19 19 , 28 41 14 1 19 2 ⟶ 28 15 0 18 39 19 2 , 28 41 14 1 19 7 ⟶ 28 15 0 18 39 19 7 , 28 41 14 1 19 20 ⟶ 28 15 0 18 39 19 20 , 28 41 14 1 19 21 ⟶ 28 15 0 18 39 19 21 , 28 41 14 1 19 22 ⟶ 28 15 0 18 39 19 22 , 0 29 37 39 19 13 ⟶ 0 18 40 32 35 19 13 , 0 29 37 39 19 19 ⟶ 0 18 40 32 35 19 19 , 0 29 37 39 19 2 ⟶ 0 18 40 32 35 19 2 , 0 29 37 39 19 7 ⟶ 0 18 40 32 35 19 7 , 0 29 37 39 19 20 ⟶ 0 18 40 32 35 19 20 , 0 29 37 39 19 21 ⟶ 0 18 40 32 35 19 21 , 0 29 37 39 19 22 ⟶ 0 18 40 32 35 19 22 , 13 29 37 39 19 13 ⟶ 13 18 40 32 35 19 13 , 13 29 37 39 19 19 ⟶ 13 18 40 32 35 19 19 , 13 29 37 39 19 2 ⟶ 13 18 40 32 35 19 2 , 13 29 37 39 19 7 ⟶ 13 18 40 32 35 19 7 , 13 29 37 39 19 20 ⟶ 13 18 40 32 35 19 20 , 13 29 37 39 19 21 ⟶ 13 18 40 32 35 19 21 , 13 29 37 39 19 22 ⟶ 13 18 40 32 35 19 22 , 4 29 37 39 19 13 ⟶ 4 18 40 32 35 19 13 , 4 29 37 39 19 19 ⟶ 4 18 40 32 35 19 19 , 4 29 37 39 19 2 ⟶ 4 18 40 32 35 19 2 , 4 29 37 39 19 7 ⟶ 4 18 40 32 35 19 7 , 4 29 37 39 19 20 ⟶ 4 18 40 32 35 19 20 , 4 29 37 39 19 21 ⟶ 4 18 40 32 35 19 21 , 4 29 37 39 19 22 ⟶ 4 18 40 32 35 19 22 , 14 29 37 39 19 13 ⟶ 14 18 40 32 35 19 13 , 14 29 37 39 19 19 ⟶ 14 18 40 32 35 19 19 , 14 29 37 39 19 2 ⟶ 14 18 40 32 35 19 2 , 14 29 37 39 19 7 ⟶ 14 18 40 32 35 19 7 , 14 29 37 39 19 20 ⟶ 14 18 40 32 35 19 20 , 14 29 37 39 19 21 ⟶ 14 18 40 32 35 19 21 , 14 29 37 39 19 22 ⟶ 14 18 40 32 35 19 22 , 15 29 37 39 19 13 ⟶ 15 18 40 32 35 19 13 , 15 29 37 39 19 19 ⟶ 15 18 40 32 35 19 19 , 15 29 37 39 19 2 ⟶ 15 18 40 32 35 19 2 , 15 29 37 39 19 7 ⟶ 15 18 40 32 35 19 7 , 15 29 37 39 19 20 ⟶ 15 18 40 32 35 19 20 , 15 29 37 39 19 21 ⟶ 15 18 40 32 35 19 21 , 15 29 37 39 19 22 ⟶ 15 18 40 32 35 19 22 , 16 29 37 39 19 13 ⟶ 16 18 40 32 35 19 13 , 16 29 37 39 19 19 ⟶ 16 18 40 32 35 19 19 , 16 29 37 39 19 2 ⟶ 16 18 40 32 35 19 2 , 16 29 37 39 19 7 ⟶ 16 18 40 32 35 19 7 , 16 29 37 39 19 20 ⟶ 16 18 40 32 35 19 20 , 16 29 37 39 19 21 ⟶ 16 18 40 32 35 19 21 , 16 29 37 39 19 22 ⟶ 16 18 40 32 35 19 22 , 17 29 37 39 19 13 ⟶ 17 18 40 32 35 19 13 , 17 29 37 39 19 19 ⟶ 17 18 40 32 35 19 19 , 17 29 37 39 19 2 ⟶ 17 18 40 32 35 19 2 , 17 29 37 39 19 7 ⟶ 17 18 40 32 35 19 7 , 17 29 37 39 19 20 ⟶ 17 18 40 32 35 19 20 , 17 29 37 39 19 21 ⟶ 17 18 40 32 35 19 21 , 17 29 37 39 19 22 ⟶ 17 18 40 32 35 19 22 , 5 11 30 11 35 13 ⟶ 5 6 21 37 32 35 2 4 , 5 11 30 11 35 19 ⟶ 5 6 21 37 32 35 2 6 , 5 11 30 11 35 2 ⟶ 5 6 21 37 32 35 2 3 , 5 11 30 11 35 7 ⟶ 5 6 21 37 32 35 2 9 , 5 11 30 11 35 20 ⟶ 5 6 21 37 32 35 2 10 , 5 11 30 11 35 21 ⟶ 5 6 21 37 32 35 2 11 , 5 11 30 11 35 22 ⟶ 5 6 21 37 32 35 2 12 , 2 11 30 11 35 13 ⟶ 2 6 21 37 32 35 2 4 , 2 11 30 11 35 19 ⟶ 2 6 21 37 32 35 2 6 , 2 11 30 11 35 2 ⟶ 2 6 21 37 32 35 2 3 , 2 11 30 11 35 7 ⟶ 2 6 21 37 32 35 2 9 , 2 11 30 11 35 20 ⟶ 2 6 21 37 32 35 2 10 , 2 11 30 11 35 21 ⟶ 2 6 21 37 32 35 2 11 , 2 11 30 11 35 22 ⟶ 2 6 21 37 32 35 2 12 , 3 11 30 11 35 13 ⟶ 3 6 21 37 32 35 2 4 , 3 11 30 11 35 19 ⟶ 3 6 21 37 32 35 2 6 , 3 11 30 11 35 2 ⟶ 3 6 21 37 32 35 2 3 , 3 11 30 11 35 7 ⟶ 3 6 21 37 32 35 2 9 , 3 11 30 11 35 20 ⟶ 3 6 21 37 32 35 2 10 , 3 11 30 11 35 21 ⟶ 3 6 21 37 32 35 2 11 , 3 11 30 11 35 22 ⟶ 3 6 21 37 32 35 2 12 , 8 11 30 11 35 13 ⟶ 8 6 21 37 32 35 2 4 , 8 11 30 11 35 19 ⟶ 8 6 21 37 32 35 2 6 , 8 11 30 11 35 2 ⟶ 8 6 21 37 32 35 2 3 , 8 11 30 11 35 7 ⟶ 8 6 21 37 32 35 2 9 , 8 11 30 11 35 20 ⟶ 8 6 21 37 32 35 2 10 , 8 11 30 11 35 21 ⟶ 8 6 21 37 32 35 2 11 , 8 11 30 11 35 22 ⟶ 8 6 21 37 32 35 2 12 , 36 11 30 11 35 13 ⟶ 36 6 21 37 32 35 2 4 , 36 11 30 11 35 19 ⟶ 36 6 21 37 32 35 2 6 , 36 11 30 11 35 2 ⟶ 36 6 21 37 32 35 2 3 , 36 11 30 11 35 7 ⟶ 36 6 21 37 32 35 2 9 , 36 11 30 11 35 20 ⟶ 36 6 21 37 32 35 2 10 , 36 11 30 11 35 21 ⟶ 36 6 21 37 32 35 2 11 , 36 11 30 11 35 22 ⟶ 36 6 21 37 32 35 2 12 , 30 11 30 11 35 13 ⟶ 30 6 21 37 32 35 2 4 , 30 11 30 11 35 19 ⟶ 30 6 21 37 32 35 2 6 , 30 11 30 11 35 2 ⟶ 30 6 21 37 32 35 2 3 , 30 11 30 11 35 7 ⟶ 30 6 21 37 32 35 2 9 , 30 11 30 11 35 20 ⟶ 30 6 21 37 32 35 2 10 , 30 11 30 11 35 21 ⟶ 30 6 21 37 32 35 2 11 , 30 11 30 11 35 22 ⟶ 30 6 21 37 32 35 2 12 , 45 11 30 11 35 13 ⟶ 45 6 21 37 32 35 2 4 , 45 11 30 11 35 19 ⟶ 45 6 21 37 32 35 2 6 , 45 11 30 11 35 2 ⟶ 45 6 21 37 32 35 2 3 , 45 11 30 11 35 7 ⟶ 45 6 21 37 32 35 2 9 , 45 11 30 11 35 20 ⟶ 45 6 21 37 32 35 2 10 , 45 11 30 11 35 21 ⟶ 45 6 21 37 32 35 2 11 , 45 11 30 11 35 22 ⟶ 45 6 21 37 32 35 2 12 , 0 1 21 31 35 13 ⟶ 0 0 18 32 35 19 21 35 13 , 0 1 21 31 35 19 ⟶ 0 0 18 32 35 19 21 35 19 , 0 1 21 31 35 2 ⟶ 0 0 18 32 35 19 21 35 2 , 0 1 21 31 35 7 ⟶ 0 0 18 32 35 19 21 35 7 , 0 1 21 31 35 20 ⟶ 0 0 18 32 35 19 21 35 20 , 0 1 21 31 35 21 ⟶ 0 0 18 32 35 19 21 35 21 , 0 1 21 31 35 22 ⟶ 0 0 18 32 35 19 21 35 22 , 13 1 21 31 35 13 ⟶ 13 0 18 32 35 19 21 35 13 , 13 1 21 31 35 19 ⟶ 13 0 18 32 35 19 21 35 19 , 13 1 21 31 35 2 ⟶ 13 0 18 32 35 19 21 35 2 , 13 1 21 31 35 7 ⟶ 13 0 18 32 35 19 21 35 7 , 13 1 21 31 35 20 ⟶ 13 0 18 32 35 19 21 35 20 , 13 1 21 31 35 21 ⟶ 13 0 18 32 35 19 21 35 21 , 13 1 21 31 35 22 ⟶ 13 0 18 32 35 19 21 35 22 , 4 1 21 31 35 13 ⟶ 4 0 18 32 35 19 21 35 13 , 4 1 21 31 35 19 ⟶ 4 0 18 32 35 19 21 35 19 , 4 1 21 31 35 2 ⟶ 4 0 18 32 35 19 21 35 2 , 4 1 21 31 35 7 ⟶ 4 0 18 32 35 19 21 35 7 , 4 1 21 31 35 20 ⟶ 4 0 18 32 35 19 21 35 20 , 4 1 21 31 35 21 ⟶ 4 0 18 32 35 19 21 35 21 , 4 1 21 31 35 22 ⟶ 4 0 18 32 35 19 21 35 22 , 14 1 21 31 35 13 ⟶ 14 0 18 32 35 19 21 35 13 , 14 1 21 31 35 19 ⟶ 14 0 18 32 35 19 21 35 19 , 14 1 21 31 35 2 ⟶ 14 0 18 32 35 19 21 35 2 , 14 1 21 31 35 7 ⟶ 14 0 18 32 35 19 21 35 7 , 14 1 21 31 35 20 ⟶ 14 0 18 32 35 19 21 35 20 , 14 1 21 31 35 21 ⟶ 14 0 18 32 35 19 21 35 21 , 14 1 21 31 35 22 ⟶ 14 0 18 32 35 19 21 35 22 , 15 1 21 31 35 13 ⟶ 15 0 18 32 35 19 21 35 13 , 15 1 21 31 35 19 ⟶ 15 0 18 32 35 19 21 35 19 , 15 1 21 31 35 2 ⟶ 15 0 18 32 35 19 21 35 2 , 15 1 21 31 35 7 ⟶ 15 0 18 32 35 19 21 35 7 , 15 1 21 31 35 20 ⟶ 15 0 18 32 35 19 21 35 20 , 15 1 21 31 35 21 ⟶ 15 0 18 32 35 19 21 35 21 , 15 1 21 31 35 22 ⟶ 15 0 18 32 35 19 21 35 22 , 16 1 21 31 35 13 ⟶ 16 0 18 32 35 19 21 35 13 , 16 1 21 31 35 19 ⟶ 16 0 18 32 35 19 21 35 19 , 16 1 21 31 35 2 ⟶ 16 0 18 32 35 19 21 35 2 , 16 1 21 31 35 7 ⟶ 16 0 18 32 35 19 21 35 7 , 16 1 21 31 35 20 ⟶ 16 0 18 32 35 19 21 35 20 , 16 1 21 31 35 21 ⟶ 16 0 18 32 35 19 21 35 21 , 16 1 21 31 35 22 ⟶ 16 0 18 32 35 19 21 35 22 , 17 1 21 31 35 13 ⟶ 17 0 18 32 35 19 21 35 13 , 17 1 21 31 35 19 ⟶ 17 0 18 32 35 19 21 35 19 , 17 1 21 31 35 2 ⟶ 17 0 18 32 35 19 21 35 2 , 17 1 21 31 35 7 ⟶ 17 0 18 32 35 19 21 35 7 , 17 1 21 31 35 20 ⟶ 17 0 18 32 35 19 21 35 20 , 17 1 21 31 35 21 ⟶ 17 0 18 32 35 19 21 35 21 , 17 1 21 31 35 22 ⟶ 17 0 18 32 35 19 21 35 22 , 29 30 4 5 11 16 ⟶ 29 30 4 18 40 8 11 16 , 29 30 4 5 11 35 ⟶ 29 30 4 18 40 8 11 35 , 29 30 4 5 11 30 ⟶ 29 30 4 18 40 8 11 30 , 29 30 4 5 11 37 ⟶ 29 30 4 18 40 8 11 37 , 29 30 4 5 11 27 ⟶ 29 30 4 18 40 8 11 27 , 29 30 4 5 11 31 ⟶ 29 30 4 18 40 8 11 31 , 29 30 4 5 11 38 ⟶ 29 30 4 18 40 8 11 38 , 21 30 4 5 11 16 ⟶ 21 30 4 18 40 8 11 16 , 21 30 4 5 11 35 ⟶ 21 30 4 18 40 8 11 35 , 21 30 4 5 11 30 ⟶ 21 30 4 18 40 8 11 30 , 21 30 4 5 11 37 ⟶ 21 30 4 18 40 8 11 37 , 21 30 4 5 11 27 ⟶ 21 30 4 18 40 8 11 27 , 21 30 4 5 11 31 ⟶ 21 30 4 18 40 8 11 31 , 21 30 4 5 11 38 ⟶ 21 30 4 18 40 8 11 38 , 11 30 4 5 11 16 ⟶ 11 30 4 18 40 8 11 16 , 11 30 4 5 11 35 ⟶ 11 30 4 18 40 8 11 35 , 11 30 4 5 11 30 ⟶ 11 30 4 18 40 8 11 30 , 11 30 4 5 11 37 ⟶ 11 30 4 18 40 8 11 37 , 11 30 4 5 11 27 ⟶ 11 30 4 18 40 8 11 27 , 11 30 4 5 11 31 ⟶ 11 30 4 18 40 8 11 31 , 11 30 4 5 11 38 ⟶ 11 30 4 18 40 8 11 38 , 32 30 4 5 11 16 ⟶ 32 30 4 18 40 8 11 16 , 32 30 4 5 11 35 ⟶ 32 30 4 18 40 8 11 35 , 32 30 4 5 11 30 ⟶ 32 30 4 18 40 8 11 30 , 32 30 4 5 11 37 ⟶ 32 30 4 18 40 8 11 37 , 32 30 4 5 11 27 ⟶ 32 30 4 18 40 8 11 27 , 32 30 4 5 11 31 ⟶ 32 30 4 18 40 8 11 31 , 32 30 4 5 11 38 ⟶ 32 30 4 18 40 8 11 38 , 33 30 4 5 11 16 ⟶ 33 30 4 18 40 8 11 16 , 33 30 4 5 11 35 ⟶ 33 30 4 18 40 8 11 35 , 33 30 4 5 11 30 ⟶ 33 30 4 18 40 8 11 30 , 33 30 4 5 11 37 ⟶ 33 30 4 18 40 8 11 37 , 33 30 4 5 11 27 ⟶ 33 30 4 18 40 8 11 27 , 33 30 4 5 11 31 ⟶ 33 30 4 18 40 8 11 31 , 33 30 4 5 11 38 ⟶ 33 30 4 18 40 8 11 38 , 31 30 4 5 11 16 ⟶ 31 30 4 18 40 8 11 16 , 31 30 4 5 11 35 ⟶ 31 30 4 18 40 8 11 35 , 31 30 4 5 11 30 ⟶ 31 30 4 18 40 8 11 30 , 31 30 4 5 11 37 ⟶ 31 30 4 18 40 8 11 37 , 31 30 4 5 11 27 ⟶ 31 30 4 18 40 8 11 27 , 31 30 4 5 11 31 ⟶ 31 30 4 18 40 8 11 31 , 31 30 4 5 11 38 ⟶ 31 30 4 18 40 8 11 38 , 34 30 4 5 11 16 ⟶ 34 30 4 18 40 8 11 16 , 34 30 4 5 11 35 ⟶ 34 30 4 18 40 8 11 35 , 34 30 4 5 11 30 ⟶ 34 30 4 18 40 8 11 30 , 34 30 4 5 11 37 ⟶ 34 30 4 18 40 8 11 37 , 34 30 4 5 11 27 ⟶ 34 30 4 18 40 8 11 27 , 34 30 4 5 11 31 ⟶ 34 30 4 18 40 8 11 31 , 34 30 4 5 11 38 ⟶ 34 30 4 18 40 8 11 38 , 23 41 14 5 11 16 ⟶ 23 41 14 18 8 11 16 , 23 41 14 5 11 35 ⟶ 23 41 14 18 8 11 35 , 23 41 14 5 11 30 ⟶ 23 41 14 18 8 11 30 , 23 41 14 5 11 37 ⟶ 23 41 14 18 8 11 37 , 23 41 14 5 11 27 ⟶ 23 41 14 18 8 11 27 , 23 41 14 5 11 31 ⟶ 23 41 14 18 8 11 31 , 23 41 14 5 11 38 ⟶ 23 41 14 18 8 11 38 , 20 41 14 5 11 16 ⟶ 20 41 14 18 8 11 16 , 20 41 14 5 11 35 ⟶ 20 41 14 18 8 11 35 , 20 41 14 5 11 30 ⟶ 20 41 14 18 8 11 30 , 20 41 14 5 11 37 ⟶ 20 41 14 18 8 11 37 , 20 41 14 5 11 27 ⟶ 20 41 14 18 8 11 27 , 20 41 14 5 11 31 ⟶ 20 41 14 18 8 11 31 , 20 41 14 5 11 38 ⟶ 20 41 14 18 8 11 38 , 10 41 14 5 11 16 ⟶ 10 41 14 18 8 11 16 , 10 41 14 5 11 35 ⟶ 10 41 14 18 8 11 35 , 10 41 14 5 11 30 ⟶ 10 41 14 18 8 11 30 , 10 41 14 5 11 37 ⟶ 10 41 14 18 8 11 37 , 10 41 14 5 11 27 ⟶ 10 41 14 18 8 11 27 , 10 41 14 5 11 31 ⟶ 10 41 14 18 8 11 31 , 10 41 14 5 11 38 ⟶ 10 41 14 18 8 11 38 , 25 41 14 5 11 16 ⟶ 25 41 14 18 8 11 16 , 25 41 14 5 11 35 ⟶ 25 41 14 18 8 11 35 , 25 41 14 5 11 30 ⟶ 25 41 14 18 8 11 30 , 25 41 14 5 11 37 ⟶ 25 41 14 18 8 11 37 , 25 41 14 5 11 27 ⟶ 25 41 14 18 8 11 27 , 25 41 14 5 11 31 ⟶ 25 41 14 18 8 11 31 , 25 41 14 5 11 38 ⟶ 25 41 14 18 8 11 38 , 26 41 14 5 11 16 ⟶ 26 41 14 18 8 11 16 , 26 41 14 5 11 35 ⟶ 26 41 14 18 8 11 35 , 26 41 14 5 11 30 ⟶ 26 41 14 18 8 11 30 , 26 41 14 5 11 37 ⟶ 26 41 14 18 8 11 37 , 26 41 14 5 11 27 ⟶ 26 41 14 18 8 11 27 , 26 41 14 5 11 31 ⟶ 26 41 14 18 8 11 31 , 26 41 14 5 11 38 ⟶ 26 41 14 18 8 11 38 , 27 41 14 5 11 16 ⟶ 27 41 14 18 8 11 16 , 27 41 14 5 11 35 ⟶ 27 41 14 18 8 11 35 , 27 41 14 5 11 30 ⟶ 27 41 14 18 8 11 30 , 27 41 14 5 11 37 ⟶ 27 41 14 18 8 11 37 , 27 41 14 5 11 27 ⟶ 27 41 14 18 8 11 27 , 27 41 14 5 11 31 ⟶ 27 41 14 18 8 11 31 , 27 41 14 5 11 38 ⟶ 27 41 14 18 8 11 38 , 28 41 14 5 11 16 ⟶ 28 41 14 18 8 11 16 , 28 41 14 5 11 35 ⟶ 28 41 14 18 8 11 35 , 28 41 14 5 11 30 ⟶ 28 41 14 18 8 11 30 , 28 41 14 5 11 37 ⟶ 28 41 14 18 8 11 37 , 28 41 14 5 11 27 ⟶ 28 41 14 18 8 11 27 , 28 41 14 5 11 31 ⟶ 28 41 14 18 8 11 31 , 28 41 14 5 11 38 ⟶ 28 41 14 18 8 11 38 , 0 1 2 11 31 16 ⟶ 1 13 5 9 32 31 16 , 0 1 2 11 31 35 ⟶ 1 13 5 9 32 31 35 , 0 1 2 11 31 30 ⟶ 1 13 5 9 32 31 30 , 0 1 2 11 31 37 ⟶ 1 13 5 9 32 31 37 , 0 1 2 11 31 27 ⟶ 1 13 5 9 32 31 27 , 0 1 2 11 31 31 ⟶ 1 13 5 9 32 31 31 , 0 1 2 11 31 38 ⟶ 1 13 5 9 32 31 38 , 13 1 2 11 31 16 ⟶ 19 13 5 9 32 31 16 , 13 1 2 11 31 35 ⟶ 19 13 5 9 32 31 35 , 13 1 2 11 31 30 ⟶ 19 13 5 9 32 31 30 , 13 1 2 11 31 37 ⟶ 19 13 5 9 32 31 37 , 13 1 2 11 31 27 ⟶ 19 13 5 9 32 31 27 , 13 1 2 11 31 31 ⟶ 19 13 5 9 32 31 31 , 13 1 2 11 31 38 ⟶ 19 13 5 9 32 31 38 , 4 1 2 11 31 16 ⟶ 6 13 5 9 32 31 16 , 4 1 2 11 31 35 ⟶ 6 13 5 9 32 31 35 , 4 1 2 11 31 30 ⟶ 6 13 5 9 32 31 30 , 4 1 2 11 31 37 ⟶ 6 13 5 9 32 31 37 , 4 1 2 11 31 27 ⟶ 6 13 5 9 32 31 27 , 4 1 2 11 31 31 ⟶ 6 13 5 9 32 31 31 , 4 1 2 11 31 38 ⟶ 6 13 5 9 32 31 38 , 14 1 2 11 31 16 ⟶ 39 13 5 9 32 31 16 , 14 1 2 11 31 35 ⟶ 39 13 5 9 32 31 35 , 14 1 2 11 31 30 ⟶ 39 13 5 9 32 31 30 , 14 1 2 11 31 37 ⟶ 39 13 5 9 32 31 37 , 14 1 2 11 31 27 ⟶ 39 13 5 9 32 31 27 , 14 1 2 11 31 31 ⟶ 39 13 5 9 32 31 31 , 14 1 2 11 31 38 ⟶ 39 13 5 9 32 31 38 , 15 1 2 11 31 16 ⟶ 24 13 5 9 32 31 16 , 15 1 2 11 31 35 ⟶ 24 13 5 9 32 31 35 , 15 1 2 11 31 30 ⟶ 24 13 5 9 32 31 30 , 15 1 2 11 31 37 ⟶ 24 13 5 9 32 31 37 , 15 1 2 11 31 27 ⟶ 24 13 5 9 32 31 27 , 15 1 2 11 31 31 ⟶ 24 13 5 9 32 31 31 , 15 1 2 11 31 38 ⟶ 24 13 5 9 32 31 38 , 16 1 2 11 31 16 ⟶ 35 13 5 9 32 31 16 , 16 1 2 11 31 35 ⟶ 35 13 5 9 32 31 35 , 16 1 2 11 31 30 ⟶ 35 13 5 9 32 31 30 , 16 1 2 11 31 37 ⟶ 35 13 5 9 32 31 37 , 16 1 2 11 31 27 ⟶ 35 13 5 9 32 31 27 , 16 1 2 11 31 31 ⟶ 35 13 5 9 32 31 31 , 16 1 2 11 31 38 ⟶ 35 13 5 9 32 31 38 , 17 1 2 11 31 16 ⟶ 43 13 5 9 32 31 16 , 17 1 2 11 31 35 ⟶ 43 13 5 9 32 31 35 , 17 1 2 11 31 30 ⟶ 43 13 5 9 32 31 30 , 17 1 2 11 31 37 ⟶ 43 13 5 9 32 31 37 , 17 1 2 11 31 27 ⟶ 43 13 5 9 32 31 27 , 17 1 2 11 31 31 ⟶ 43 13 5 9 32 31 31 , 17 1 2 11 31 38 ⟶ 43 13 5 9 32 31 38 , 0 1 21 30 3 3 4 ⟶ 23 15 5 11 35 2 3 4 , 0 1 21 30 3 3 6 ⟶ 23 15 5 11 35 2 3 6 , 0 1 21 30 3 3 3 ⟶ 23 15 5 11 35 2 3 3 , 0 1 21 30 3 3 9 ⟶ 23 15 5 11 35 2 3 9 , 0 1 21 30 3 3 10 ⟶ 23 15 5 11 35 2 3 10 , 0 1 21 30 3 3 11 ⟶ 23 15 5 11 35 2 3 11 , 0 1 21 30 3 3 12 ⟶ 23 15 5 11 35 2 3 12 , 13 1 21 30 3 3 4 ⟶ 20 15 5 11 35 2 3 4 , 13 1 21 30 3 3 6 ⟶ 20 15 5 11 35 2 3 6 , 13 1 21 30 3 3 3 ⟶ 20 15 5 11 35 2 3 3 , 13 1 21 30 3 3 9 ⟶ 20 15 5 11 35 2 3 9 , 13 1 21 30 3 3 10 ⟶ 20 15 5 11 35 2 3 10 , 13 1 21 30 3 3 11 ⟶ 20 15 5 11 35 2 3 11 , 13 1 21 30 3 3 12 ⟶ 20 15 5 11 35 2 3 12 , 4 1 21 30 3 3 4 ⟶ 10 15 5 11 35 2 3 4 , 4 1 21 30 3 3 6 ⟶ 10 15 5 11 35 2 3 6 , 4 1 21 30 3 3 3 ⟶ 10 15 5 11 35 2 3 3 , 4 1 21 30 3 3 9 ⟶ 10 15 5 11 35 2 3 9 , 4 1 21 30 3 3 10 ⟶ 10 15 5 11 35 2 3 10 , 4 1 21 30 3 3 11 ⟶ 10 15 5 11 35 2 3 11 , 4 1 21 30 3 3 12 ⟶ 10 15 5 11 35 2 3 12 , 14 1 21 30 3 3 4 ⟶ 25 15 5 11 35 2 3 4 , 14 1 21 30 3 3 6 ⟶ 25 15 5 11 35 2 3 6 , 14 1 21 30 3 3 3 ⟶ 25 15 5 11 35 2 3 3 , 14 1 21 30 3 3 9 ⟶ 25 15 5 11 35 2 3 9 , 14 1 21 30 3 3 10 ⟶ 25 15 5 11 35 2 3 10 , 14 1 21 30 3 3 11 ⟶ 25 15 5 11 35 2 3 11 , 14 1 21 30 3 3 12 ⟶ 25 15 5 11 35 2 3 12 , 15 1 21 30 3 3 4 ⟶ 26 15 5 11 35 2 3 4 , 15 1 21 30 3 3 6 ⟶ 26 15 5 11 35 2 3 6 , 15 1 21 30 3 3 3 ⟶ 26 15 5 11 35 2 3 3 , 15 1 21 30 3 3 9 ⟶ 26 15 5 11 35 2 3 9 , 15 1 21 30 3 3 10 ⟶ 26 15 5 11 35 2 3 10 , 15 1 21 30 3 3 11 ⟶ 26 15 5 11 35 2 3 11 , 15 1 21 30 3 3 12 ⟶ 26 15 5 11 35 2 3 12 , 16 1 21 30 3 3 4 ⟶ 27 15 5 11 35 2 3 4 , 16 1 21 30 3 3 6 ⟶ 27 15 5 11 35 2 3 6 , 16 1 21 30 3 3 3 ⟶ 27 15 5 11 35 2 3 3 , 16 1 21 30 3 3 9 ⟶ 27 15 5 11 35 2 3 9 , 16 1 21 30 3 3 10 ⟶ 27 15 5 11 35 2 3 10 , 16 1 21 30 3 3 11 ⟶ 27 15 5 11 35 2 3 11 , 16 1 21 30 3 3 12 ⟶ 27 15 5 11 35 2 3 12 , 17 1 21 30 3 3 4 ⟶ 28 15 5 11 35 2 3 4 , 17 1 21 30 3 3 6 ⟶ 28 15 5 11 35 2 3 6 , 17 1 21 30 3 3 3 ⟶ 28 15 5 11 35 2 3 3 , 17 1 21 30 3 3 9 ⟶ 28 15 5 11 35 2 3 9 , 17 1 21 30 3 3 10 ⟶ 28 15 5 11 35 2 3 10 , 17 1 21 30 3 3 11 ⟶ 28 15 5 11 35 2 3 11 , 17 1 21 30 3 3 12 ⟶ 28 15 5 11 35 2 3 12 , 1 20 15 1 2 3 4 ⟶ 1 20 36 9 14 5 9 39 13 , 1 20 15 1 2 3 6 ⟶ 1 20 36 9 14 5 9 39 19 , 1 20 15 1 2 3 3 ⟶ 1 20 36 9 14 5 9 39 2 , 1 20 15 1 2 3 9 ⟶ 1 20 36 9 14 5 9 39 7 , 1 20 15 1 2 3 10 ⟶ 1 20 36 9 14 5 9 39 20 , 1 20 15 1 2 3 11 ⟶ 1 20 36 9 14 5 9 39 21 , 1 20 15 1 2 3 12 ⟶ 1 20 36 9 14 5 9 39 22 , 19 20 15 1 2 3 4 ⟶ 19 20 36 9 14 5 9 39 13 , 19 20 15 1 2 3 6 ⟶ 19 20 36 9 14 5 9 39 19 , 19 20 15 1 2 3 3 ⟶ 19 20 36 9 14 5 9 39 2 , 19 20 15 1 2 3 9 ⟶ 19 20 36 9 14 5 9 39 7 , 19 20 15 1 2 3 10 ⟶ 19 20 36 9 14 5 9 39 20 , 19 20 15 1 2 3 11 ⟶ 19 20 36 9 14 5 9 39 21 , 19 20 15 1 2 3 12 ⟶ 19 20 36 9 14 5 9 39 22 , 6 20 15 1 2 3 4 ⟶ 6 20 36 9 14 5 9 39 13 , 6 20 15 1 2 3 6 ⟶ 6 20 36 9 14 5 9 39 19 , 6 20 15 1 2 3 3 ⟶ 6 20 36 9 14 5 9 39 2 , 6 20 15 1 2 3 9 ⟶ 6 20 36 9 14 5 9 39 7 , 6 20 15 1 2 3 10 ⟶ 6 20 36 9 14 5 9 39 20 , 6 20 15 1 2 3 11 ⟶ 6 20 36 9 14 5 9 39 21 , 6 20 15 1 2 3 12 ⟶ 6 20 36 9 14 5 9 39 22 , 39 20 15 1 2 3 4 ⟶ 39 20 36 9 14 5 9 39 13 , 39 20 15 1 2 3 6 ⟶ 39 20 36 9 14 5 9 39 19 , 39 20 15 1 2 3 3 ⟶ 39 20 36 9 14 5 9 39 2 , 39 20 15 1 2 3 9 ⟶ 39 20 36 9 14 5 9 39 7 , 39 20 15 1 2 3 10 ⟶ 39 20 36 9 14 5 9 39 20 , 39 20 15 1 2 3 11 ⟶ 39 20 36 9 14 5 9 39 21 , 39 20 15 1 2 3 12 ⟶ 39 20 36 9 14 5 9 39 22 , 24 20 15 1 2 3 4 ⟶ 24 20 36 9 14 5 9 39 13 , 24 20 15 1 2 3 6 ⟶ 24 20 36 9 14 5 9 39 19 , 24 20 15 1 2 3 3 ⟶ 24 20 36 9 14 5 9 39 2 , 24 20 15 1 2 3 9 ⟶ 24 20 36 9 14 5 9 39 7 , 24 20 15 1 2 3 10 ⟶ 24 20 36 9 14 5 9 39 20 , 24 20 15 1 2 3 11 ⟶ 24 20 36 9 14 5 9 39 21 , 24 20 15 1 2 3 12 ⟶ 24 20 36 9 14 5 9 39 22 , 35 20 15 1 2 3 4 ⟶ 35 20 36 9 14 5 9 39 13 , 35 20 15 1 2 3 6 ⟶ 35 20 36 9 14 5 9 39 19 , 35 20 15 1 2 3 3 ⟶ 35 20 36 9 14 5 9 39 2 , 35 20 15 1 2 3 9 ⟶ 35 20 36 9 14 5 9 39 7 , 35 20 15 1 2 3 10 ⟶ 35 20 36 9 14 5 9 39 20 , 35 20 15 1 2 3 11 ⟶ 35 20 36 9 14 5 9 39 21 , 35 20 15 1 2 3 12 ⟶ 35 20 36 9 14 5 9 39 22 , 43 20 15 1 2 3 4 ⟶ 43 20 36 9 14 5 9 39 13 , 43 20 15 1 2 3 6 ⟶ 43 20 36 9 14 5 9 39 19 , 43 20 15 1 2 3 3 ⟶ 43 20 36 9 14 5 9 39 2 , 43 20 15 1 2 3 9 ⟶ 43 20 36 9 14 5 9 39 7 , 43 20 15 1 2 3 10 ⟶ 43 20 36 9 14 5 9 39 20 , 43 20 15 1 2 3 11 ⟶ 43 20 36 9 14 5 9 39 21 , 43 20 15 1 2 3 12 ⟶ 43 20 36 9 14 5 9 39 22 , 5 4 1 13 5 3 4 ⟶ 5 4 0 0 18 8 6 2 4 , 5 4 1 13 5 3 6 ⟶ 5 4 0 0 18 8 6 2 6 , 5 4 1 13 5 3 3 ⟶ 5 4 0 0 18 8 6 2 3 , 5 4 1 13 5 3 9 ⟶ 5 4 0 0 18 8 6 2 9 , 5 4 1 13 5 3 10 ⟶ 5 4 0 0 18 8 6 2 10 , 5 4 1 13 5 3 11 ⟶ 5 4 0 0 18 8 6 2 11 , 5 4 1 13 5 3 12 ⟶ 5 4 0 0 18 8 6 2 12 , 2 4 1 13 5 3 4 ⟶ 2 4 0 0 18 8 6 2 4 , 2 4 1 13 5 3 6 ⟶ 2 4 0 0 18 8 6 2 6 , 2 4 1 13 5 3 3 ⟶ 2 4 0 0 18 8 6 2 3 , 2 4 1 13 5 3 9 ⟶ 2 4 0 0 18 8 6 2 9 , 2 4 1 13 5 3 10 ⟶ 2 4 0 0 18 8 6 2 10 , 2 4 1 13 5 3 11 ⟶ 2 4 0 0 18 8 6 2 11 , 2 4 1 13 5 3 12 ⟶ 2 4 0 0 18 8 6 2 12 , 3 4 1 13 5 3 4 ⟶ 3 4 0 0 18 8 6 2 4 , 3 4 1 13 5 3 6 ⟶ 3 4 0 0 18 8 6 2 6 , 3 4 1 13 5 3 3 ⟶ 3 4 0 0 18 8 6 2 3 , 3 4 1 13 5 3 9 ⟶ 3 4 0 0 18 8 6 2 9 , 3 4 1 13 5 3 10 ⟶ 3 4 0 0 18 8 6 2 10 , 3 4 1 13 5 3 11 ⟶ 3 4 0 0 18 8 6 2 11 , 3 4 1 13 5 3 12 ⟶ 3 4 0 0 18 8 6 2 12 , 8 4 1 13 5 3 4 ⟶ 8 4 0 0 18 8 6 2 4 , 8 4 1 13 5 3 6 ⟶ 8 4 0 0 18 8 6 2 6 , 8 4 1 13 5 3 3 ⟶ 8 4 0 0 18 8 6 2 3 , 8 4 1 13 5 3 9 ⟶ 8 4 0 0 18 8 6 2 9 , 8 4 1 13 5 3 10 ⟶ 8 4 0 0 18 8 6 2 10 , 8 4 1 13 5 3 11 ⟶ 8 4 0 0 18 8 6 2 11 , 8 4 1 13 5 3 12 ⟶ 8 4 0 0 18 8 6 2 12 , 36 4 1 13 5 3 4 ⟶ 36 4 0 0 18 8 6 2 4 , 36 4 1 13 5 3 6 ⟶ 36 4 0 0 18 8 6 2 6 , 36 4 1 13 5 3 3 ⟶ 36 4 0 0 18 8 6 2 3 , 36 4 1 13 5 3 9 ⟶ 36 4 0 0 18 8 6 2 9 , 36 4 1 13 5 3 10 ⟶ 36 4 0 0 18 8 6 2 10 , 36 4 1 13 5 3 11 ⟶ 36 4 0 0 18 8 6 2 11 , 36 4 1 13 5 3 12 ⟶ 36 4 0 0 18 8 6 2 12 , 30 4 1 13 5 3 4 ⟶ 30 4 0 0 18 8 6 2 4 , 30 4 1 13 5 3 6 ⟶ 30 4 0 0 18 8 6 2 6 , 30 4 1 13 5 3 3 ⟶ 30 4 0 0 18 8 6 2 3 , 30 4 1 13 5 3 9 ⟶ 30 4 0 0 18 8 6 2 9 , 30 4 1 13 5 3 10 ⟶ 30 4 0 0 18 8 6 2 10 , 30 4 1 13 5 3 11 ⟶ 30 4 0 0 18 8 6 2 11 , 30 4 1 13 5 3 12 ⟶ 30 4 0 0 18 8 6 2 12 , 45 4 1 13 5 3 4 ⟶ 45 4 0 0 18 8 6 2 4 , 45 4 1 13 5 3 6 ⟶ 45 4 0 0 18 8 6 2 6 , 45 4 1 13 5 3 3 ⟶ 45 4 0 0 18 8 6 2 3 , 45 4 1 13 5 3 9 ⟶ 45 4 0 0 18 8 6 2 9 , 45 4 1 13 5 3 10 ⟶ 45 4 0 0 18 8 6 2 10 , 45 4 1 13 5 3 11 ⟶ 45 4 0 0 18 8 6 2 11 , 45 4 1 13 5 3 12 ⟶ 45 4 0 0 18 8 6 2 12 , 29 30 9 14 5 3 4 ⟶ 29 16 18 8 9 8 3 4 , 29 30 9 14 5 3 6 ⟶ 29 16 18 8 9 8 3 6 , 29 30 9 14 5 3 3 ⟶ 29 16 18 8 9 8 3 3 , 29 30 9 14 5 3 9 ⟶ 29 16 18 8 9 8 3 9 , 29 30 9 14 5 3 10 ⟶ 29 16 18 8 9 8 3 10 , 29 30 9 14 5 3 11 ⟶ 29 16 18 8 9 8 3 11 , 29 30 9 14 5 3 12 ⟶ 29 16 18 8 9 8 3 12 , 21 30 9 14 5 3 4 ⟶ 21 16 18 8 9 8 3 4 , 21 30 9 14 5 3 6 ⟶ 21 16 18 8 9 8 3 6 , 21 30 9 14 5 3 3 ⟶ 21 16 18 8 9 8 3 3 , 21 30 9 14 5 3 9 ⟶ 21 16 18 8 9 8 3 9 , 21 30 9 14 5 3 10 ⟶ 21 16 18 8 9 8 3 10 , 21 30 9 14 5 3 11 ⟶ 21 16 18 8 9 8 3 11 , 21 30 9 14 5 3 12 ⟶ 21 16 18 8 9 8 3 12 , 11 30 9 14 5 3 4 ⟶ 11 16 18 8 9 8 3 4 , 11 30 9 14 5 3 6 ⟶ 11 16 18 8 9 8 3 6 , 11 30 9 14 5 3 3 ⟶ 11 16 18 8 9 8 3 3 , 11 30 9 14 5 3 9 ⟶ 11 16 18 8 9 8 3 9 , 11 30 9 14 5 3 10 ⟶ 11 16 18 8 9 8 3 10 , 11 30 9 14 5 3 11 ⟶ 11 16 18 8 9 8 3 11 , 11 30 9 14 5 3 12 ⟶ 11 16 18 8 9 8 3 12 , 32 30 9 14 5 3 4 ⟶ 32 16 18 8 9 8 3 4 , 32 30 9 14 5 3 6 ⟶ 32 16 18 8 9 8 3 6 , 32 30 9 14 5 3 3 ⟶ 32 16 18 8 9 8 3 3 , 32 30 9 14 5 3 9 ⟶ 32 16 18 8 9 8 3 9 , 32 30 9 14 5 3 10 ⟶ 32 16 18 8 9 8 3 10 , 32 30 9 14 5 3 11 ⟶ 32 16 18 8 9 8 3 11 , 32 30 9 14 5 3 12 ⟶ 32 16 18 8 9 8 3 12 , 33 30 9 14 5 3 4 ⟶ 33 16 18 8 9 8 3 4 , 33 30 9 14 5 3 6 ⟶ 33 16 18 8 9 8 3 6 , 33 30 9 14 5 3 3 ⟶ 33 16 18 8 9 8 3 3 , 33 30 9 14 5 3 9 ⟶ 33 16 18 8 9 8 3 9 , 33 30 9 14 5 3 10 ⟶ 33 16 18 8 9 8 3 10 , 33 30 9 14 5 3 11 ⟶ 33 16 18 8 9 8 3 11 , 33 30 9 14 5 3 12 ⟶ 33 16 18 8 9 8 3 12 , 31 30 9 14 5 3 4 ⟶ 31 16 18 8 9 8 3 4 , 31 30 9 14 5 3 6 ⟶ 31 16 18 8 9 8 3 6 , 31 30 9 14 5 3 3 ⟶ 31 16 18 8 9 8 3 3 , 31 30 9 14 5 3 9 ⟶ 31 16 18 8 9 8 3 9 , 31 30 9 14 5 3 10 ⟶ 31 16 18 8 9 8 3 10 , 31 30 9 14 5 3 11 ⟶ 31 16 18 8 9 8 3 11 , 31 30 9 14 5 3 12 ⟶ 31 16 18 8 9 8 3 12 , 34 30 9 14 5 3 4 ⟶ 34 16 18 8 9 8 3 4 , 34 30 9 14 5 3 6 ⟶ 34 16 18 8 9 8 3 6 , 34 30 9 14 5 3 3 ⟶ 34 16 18 8 9 8 3 3 , 34 30 9 14 5 3 9 ⟶ 34 16 18 8 9 8 3 9 , 34 30 9 14 5 3 10 ⟶ 34 16 18 8 9 8 3 10 , 34 30 9 14 5 3 11 ⟶ 34 16 18 8 9 8 3 11 , 34 30 9 14 5 3 12 ⟶ 34 16 18 8 9 8 3 12 , 23 41 14 29 30 3 4 ⟶ 29 16 1 7 8 10 36 4 , 23 41 14 29 30 3 6 ⟶ 29 16 1 7 8 10 36 6 , 23 41 14 29 30 3 3 ⟶ 29 16 1 7 8 10 36 3 , 23 41 14 29 30 3 9 ⟶ 29 16 1 7 8 10 36 9 , 23 41 14 29 30 3 10 ⟶ 29 16 1 7 8 10 36 10 , 23 41 14 29 30 3 11 ⟶ 29 16 1 7 8 10 36 11 , 23 41 14 29 30 3 12 ⟶ 29 16 1 7 8 10 36 12 , 20 41 14 29 30 3 4 ⟶ 21 16 1 7 8 10 36 4 , 20 41 14 29 30 3 6 ⟶ 21 16 1 7 8 10 36 6 , 20 41 14 29 30 3 3 ⟶ 21 16 1 7 8 10 36 3 , 20 41 14 29 30 3 9 ⟶ 21 16 1 7 8 10 36 9 , 20 41 14 29 30 3 10 ⟶ 21 16 1 7 8 10 36 10 , 20 41 14 29 30 3 11 ⟶ 21 16 1 7 8 10 36 11 , 20 41 14 29 30 3 12 ⟶ 21 16 1 7 8 10 36 12 , 10 41 14 29 30 3 4 ⟶ 11 16 1 7 8 10 36 4 , 10 41 14 29 30 3 6 ⟶ 11 16 1 7 8 10 36 6 , 10 41 14 29 30 3 3 ⟶ 11 16 1 7 8 10 36 3 , 10 41 14 29 30 3 9 ⟶ 11 16 1 7 8 10 36 9 , 10 41 14 29 30 3 10 ⟶ 11 16 1 7 8 10 36 10 , 10 41 14 29 30 3 11 ⟶ 11 16 1 7 8 10 36 11 , 10 41 14 29 30 3 12 ⟶ 11 16 1 7 8 10 36 12 , 25 41 14 29 30 3 4 ⟶ 32 16 1 7 8 10 36 4 , 25 41 14 29 30 3 6 ⟶ 32 16 1 7 8 10 36 6 , 25 41 14 29 30 3 3 ⟶ 32 16 1 7 8 10 36 3 , 25 41 14 29 30 3 9 ⟶ 32 16 1 7 8 10 36 9 , 25 41 14 29 30 3 10 ⟶ 32 16 1 7 8 10 36 10 , 25 41 14 29 30 3 11 ⟶ 32 16 1 7 8 10 36 11 , 25 41 14 29 30 3 12 ⟶ 32 16 1 7 8 10 36 12 , 26 41 14 29 30 3 4 ⟶ 33 16 1 7 8 10 36 4 , 26 41 14 29 30 3 6 ⟶ 33 16 1 7 8 10 36 6 , 26 41 14 29 30 3 3 ⟶ 33 16 1 7 8 10 36 3 , 26 41 14 29 30 3 9 ⟶ 33 16 1 7 8 10 36 9 , 26 41 14 29 30 3 10 ⟶ 33 16 1 7 8 10 36 10 , 26 41 14 29 30 3 11 ⟶ 33 16 1 7 8 10 36 11 , 26 41 14 29 30 3 12 ⟶ 33 16 1 7 8 10 36 12 , 27 41 14 29 30 3 4 ⟶ 31 16 1 7 8 10 36 4 , 27 41 14 29 30 3 6 ⟶ 31 16 1 7 8 10 36 6 , 27 41 14 29 30 3 3 ⟶ 31 16 1 7 8 10 36 3 , 27 41 14 29 30 3 9 ⟶ 31 16 1 7 8 10 36 9 , 27 41 14 29 30 3 10 ⟶ 31 16 1 7 8 10 36 10 , 27 41 14 29 30 3 11 ⟶ 31 16 1 7 8 10 36 11 , 27 41 14 29 30 3 12 ⟶ 31 16 1 7 8 10 36 12 , 28 41 14 29 30 3 4 ⟶ 34 16 1 7 8 10 36 4 , 28 41 14 29 30 3 6 ⟶ 34 16 1 7 8 10 36 6 , 28 41 14 29 30 3 3 ⟶ 34 16 1 7 8 10 36 3 , 28 41 14 29 30 3 9 ⟶ 34 16 1 7 8 10 36 9 , 28 41 14 29 30 3 10 ⟶ 34 16 1 7 8 10 36 10 , 28 41 14 29 30 3 11 ⟶ 34 16 1 7 8 10 36 11 , 28 41 14 29 30 3 12 ⟶ 34 16 1 7 8 10 36 12 , 23 41 32 31 30 3 4 ⟶ 29 31 37 8 3 6 20 24 13 , 23 41 32 31 30 3 6 ⟶ 29 31 37 8 3 6 20 24 19 , 23 41 32 31 30 3 3 ⟶ 29 31 37 8 3 6 20 24 2 , 23 41 32 31 30 3 9 ⟶ 29 31 37 8 3 6 20 24 7 , 23 41 32 31 30 3 10 ⟶ 29 31 37 8 3 6 20 24 20 , 23 41 32 31 30 3 11 ⟶ 29 31 37 8 3 6 20 24 21 , 23 41 32 31 30 3 12 ⟶ 29 31 37 8 3 6 20 24 22 , 20 41 32 31 30 3 4 ⟶ 21 31 37 8 3 6 20 24 13 , 20 41 32 31 30 3 6 ⟶ 21 31 37 8 3 6 20 24 19 , 20 41 32 31 30 3 3 ⟶ 21 31 37 8 3 6 20 24 2 , 20 41 32 31 30 3 9 ⟶ 21 31 37 8 3 6 20 24 7 , 20 41 32 31 30 3 10 ⟶ 21 31 37 8 3 6 20 24 20 , 20 41 32 31 30 3 11 ⟶ 21 31 37 8 3 6 20 24 21 , 20 41 32 31 30 3 12 ⟶ 21 31 37 8 3 6 20 24 22 , 10 41 32 31 30 3 4 ⟶ 11 31 37 8 3 6 20 24 13 , 10 41 32 31 30 3 6 ⟶ 11 31 37 8 3 6 20 24 19 , 10 41 32 31 30 3 3 ⟶ 11 31 37 8 3 6 20 24 2 , 10 41 32 31 30 3 9 ⟶ 11 31 37 8 3 6 20 24 7 , 10 41 32 31 30 3 10 ⟶ 11 31 37 8 3 6 20 24 20 , 10 41 32 31 30 3 11 ⟶ 11 31 37 8 3 6 20 24 21 , 10 41 32 31 30 3 12 ⟶ 11 31 37 8 3 6 20 24 22 , 25 41 32 31 30 3 4 ⟶ 32 31 37 8 3 6 20 24 13 , 25 41 32 31 30 3 6 ⟶ 32 31 37 8 3 6 20 24 19 , 25 41 32 31 30 3 3 ⟶ 32 31 37 8 3 6 20 24 2 , 25 41 32 31 30 3 9 ⟶ 32 31 37 8 3 6 20 24 7 , 25 41 32 31 30 3 10 ⟶ 32 31 37 8 3 6 20 24 20 , 25 41 32 31 30 3 11 ⟶ 32 31 37 8 3 6 20 24 21 , 25 41 32 31 30 3 12 ⟶ 32 31 37 8 3 6 20 24 22 , 26 41 32 31 30 3 4 ⟶ 33 31 37 8 3 6 20 24 13 , 26 41 32 31 30 3 6 ⟶ 33 31 37 8 3 6 20 24 19 , 26 41 32 31 30 3 3 ⟶ 33 31 37 8 3 6 20 24 2 , 26 41 32 31 30 3 9 ⟶ 33 31 37 8 3 6 20 24 7 , 26 41 32 31 30 3 10 ⟶ 33 31 37 8 3 6 20 24 20 , 26 41 32 31 30 3 11 ⟶ 33 31 37 8 3 6 20 24 21 , 26 41 32 31 30 3 12 ⟶ 33 31 37 8 3 6 20 24 22 , 27 41 32 31 30 3 4 ⟶ 31 31 37 8 3 6 20 24 13 , 27 41 32 31 30 3 6 ⟶ 31 31 37 8 3 6 20 24 19 , 27 41 32 31 30 3 3 ⟶ 31 31 37 8 3 6 20 24 2 , 27 41 32 31 30 3 9 ⟶ 31 31 37 8 3 6 20 24 7 , 27 41 32 31 30 3 10 ⟶ 31 31 37 8 3 6 20 24 20 , 27 41 32 31 30 3 11 ⟶ 31 31 37 8 3 6 20 24 21 , 27 41 32 31 30 3 12 ⟶ 31 31 37 8 3 6 20 24 22 , 28 41 32 31 30 3 4 ⟶ 34 31 37 8 3 6 20 24 13 , 28 41 32 31 30 3 6 ⟶ 34 31 37 8 3 6 20 24 19 , 28 41 32 31 30 3 3 ⟶ 34 31 37 8 3 6 20 24 2 , 28 41 32 31 30 3 9 ⟶ 34 31 37 8 3 6 20 24 7 , 28 41 32 31 30 3 10 ⟶ 34 31 37 8 3 6 20 24 20 , 28 41 32 31 30 3 11 ⟶ 34 31 37 8 3 6 20 24 21 , 28 41 32 31 30 3 12 ⟶ 34 31 37 8 3 6 20 24 22 , 0 1 2 4 1 2 4 ⟶ 5 6 19 13 0 18 8 6 13 , 0 1 2 4 1 2 6 ⟶ 5 6 19 13 0 18 8 6 19 , 0 1 2 4 1 2 3 ⟶ 5 6 19 13 0 18 8 6 2 , 0 1 2 4 1 2 9 ⟶ 5 6 19 13 0 18 8 6 7 , 0 1 2 4 1 2 10 ⟶ 5 6 19 13 0 18 8 6 20 , 0 1 2 4 1 2 11 ⟶ 5 6 19 13 0 18 8 6 21 , 0 1 2 4 1 2 12 ⟶ 5 6 19 13 0 18 8 6 22 , 13 1 2 4 1 2 4 ⟶ 2 6 19 13 0 18 8 6 13 , 13 1 2 4 1 2 6 ⟶ 2 6 19 13 0 18 8 6 19 , 13 1 2 4 1 2 3 ⟶ 2 6 19 13 0 18 8 6 2 , 13 1 2 4 1 2 9 ⟶ 2 6 19 13 0 18 8 6 7 , 13 1 2 4 1 2 10 ⟶ 2 6 19 13 0 18 8 6 20 , 13 1 2 4 1 2 11 ⟶ 2 6 19 13 0 18 8 6 21 , 13 1 2 4 1 2 12 ⟶ 2 6 19 13 0 18 8 6 22 , 4 1 2 4 1 2 4 ⟶ 3 6 19 13 0 18 8 6 13 , 4 1 2 4 1 2 6 ⟶ 3 6 19 13 0 18 8 6 19 , 4 1 2 4 1 2 3 ⟶ 3 6 19 13 0 18 8 6 2 , 4 1 2 4 1 2 9 ⟶ 3 6 19 13 0 18 8 6 7 , 4 1 2 4 1 2 10 ⟶ 3 6 19 13 0 18 8 6 20 , 4 1 2 4 1 2 11 ⟶ 3 6 19 13 0 18 8 6 21 , 4 1 2 4 1 2 12 ⟶ 3 6 19 13 0 18 8 6 22 , 14 1 2 4 1 2 4 ⟶ 8 6 19 13 0 18 8 6 13 , 14 1 2 4 1 2 6 ⟶ 8 6 19 13 0 18 8 6 19 , 14 1 2 4 1 2 3 ⟶ 8 6 19 13 0 18 8 6 2 , 14 1 2 4 1 2 9 ⟶ 8 6 19 13 0 18 8 6 7 , 14 1 2 4 1 2 10 ⟶ 8 6 19 13 0 18 8 6 20 , 14 1 2 4 1 2 11 ⟶ 8 6 19 13 0 18 8 6 21 , 14 1 2 4 1 2 12 ⟶ 8 6 19 13 0 18 8 6 22 , 15 1 2 4 1 2 4 ⟶ 36 6 19 13 0 18 8 6 13 , 15 1 2 4 1 2 6 ⟶ 36 6 19 13 0 18 8 6 19 , 15 1 2 4 1 2 3 ⟶ 36 6 19 13 0 18 8 6 2 , 15 1 2 4 1 2 9 ⟶ 36 6 19 13 0 18 8 6 7 , 15 1 2 4 1 2 10 ⟶ 36 6 19 13 0 18 8 6 20 , 15 1 2 4 1 2 11 ⟶ 36 6 19 13 0 18 8 6 21 , 15 1 2 4 1 2 12 ⟶ 36 6 19 13 0 18 8 6 22 , 16 1 2 4 1 2 4 ⟶ 30 6 19 13 0 18 8 6 13 , 16 1 2 4 1 2 6 ⟶ 30 6 19 13 0 18 8 6 19 , 16 1 2 4 1 2 3 ⟶ 30 6 19 13 0 18 8 6 2 , 16 1 2 4 1 2 9 ⟶ 30 6 19 13 0 18 8 6 7 , 16 1 2 4 1 2 10 ⟶ 30 6 19 13 0 18 8 6 20 , 16 1 2 4 1 2 11 ⟶ 30 6 19 13 0 18 8 6 21 , 16 1 2 4 1 2 12 ⟶ 30 6 19 13 0 18 8 6 22 , 17 1 2 4 1 2 4 ⟶ 45 6 19 13 0 18 8 6 13 , 17 1 2 4 1 2 6 ⟶ 45 6 19 13 0 18 8 6 19 , 17 1 2 4 1 2 3 ⟶ 45 6 19 13 0 18 8 6 2 , 17 1 2 4 1 2 9 ⟶ 45 6 19 13 0 18 8 6 7 , 17 1 2 4 1 2 10 ⟶ 45 6 19 13 0 18 8 6 20 , 17 1 2 4 1 2 11 ⟶ 45 6 19 13 0 18 8 6 21 , 17 1 2 4 1 2 12 ⟶ 45 6 19 13 0 18 8 6 22 , 29 30 4 0 1 2 4 ⟶ 0 0 18 8 11 35 20 36 4 , 29 30 4 0 1 2 6 ⟶ 0 0 18 8 11 35 20 36 6 , 29 30 4 0 1 2 3 ⟶ 0 0 18 8 11 35 20 36 3 , 29 30 4 0 1 2 9 ⟶ 0 0 18 8 11 35 20 36 9 , 29 30 4 0 1 2 10 ⟶ 0 0 18 8 11 35 20 36 10 , 29 30 4 0 1 2 11 ⟶ 0 0 18 8 11 35 20 36 11 , 29 30 4 0 1 2 12 ⟶ 0 0 18 8 11 35 20 36 12 , 21 30 4 0 1 2 4 ⟶ 13 0 18 8 11 35 20 36 4 , 21 30 4 0 1 2 6 ⟶ 13 0 18 8 11 35 20 36 6 , 21 30 4 0 1 2 3 ⟶ 13 0 18 8 11 35 20 36 3 , 21 30 4 0 1 2 9 ⟶ 13 0 18 8 11 35 20 36 9 , 21 30 4 0 1 2 10 ⟶ 13 0 18 8 11 35 20 36 10 , 21 30 4 0 1 2 11 ⟶ 13 0 18 8 11 35 20 36 11 , 21 30 4 0 1 2 12 ⟶ 13 0 18 8 11 35 20 36 12 , 11 30 4 0 1 2 4 ⟶ 4 0 18 8 11 35 20 36 4 , 11 30 4 0 1 2 6 ⟶ 4 0 18 8 11 35 20 36 6 , 11 30 4 0 1 2 3 ⟶ 4 0 18 8 11 35 20 36 3 , 11 30 4 0 1 2 9 ⟶ 4 0 18 8 11 35 20 36 9 , 11 30 4 0 1 2 10 ⟶ 4 0 18 8 11 35 20 36 10 , 11 30 4 0 1 2 11 ⟶ 4 0 18 8 11 35 20 36 11 , 11 30 4 0 1 2 12 ⟶ 4 0 18 8 11 35 20 36 12 , 32 30 4 0 1 2 4 ⟶ 14 0 18 8 11 35 20 36 4 , 32 30 4 0 1 2 6 ⟶ 14 0 18 8 11 35 20 36 6 , 32 30 4 0 1 2 3 ⟶ 14 0 18 8 11 35 20 36 3 , 32 30 4 0 1 2 9 ⟶ 14 0 18 8 11 35 20 36 9 , 32 30 4 0 1 2 10 ⟶ 14 0 18 8 11 35 20 36 10 , 32 30 4 0 1 2 11 ⟶ 14 0 18 8 11 35 20 36 11 , 32 30 4 0 1 2 12 ⟶ 14 0 18 8 11 35 20 36 12 , 33 30 4 0 1 2 4 ⟶ 15 0 18 8 11 35 20 36 4 , 33 30 4 0 1 2 6 ⟶ 15 0 18 8 11 35 20 36 6 , 33 30 4 0 1 2 3 ⟶ 15 0 18 8 11 35 20 36 3 , 33 30 4 0 1 2 9 ⟶ 15 0 18 8 11 35 20 36 9 , 33 30 4 0 1 2 10 ⟶ 15 0 18 8 11 35 20 36 10 , 33 30 4 0 1 2 11 ⟶ 15 0 18 8 11 35 20 36 11 , 33 30 4 0 1 2 12 ⟶ 15 0 18 8 11 35 20 36 12 , 31 30 4 0 1 2 4 ⟶ 16 0 18 8 11 35 20 36 4 , 31 30 4 0 1 2 6 ⟶ 16 0 18 8 11 35 20 36 6 , 31 30 4 0 1 2 3 ⟶ 16 0 18 8 11 35 20 36 3 , 31 30 4 0 1 2 9 ⟶ 16 0 18 8 11 35 20 36 9 , 31 30 4 0 1 2 10 ⟶ 16 0 18 8 11 35 20 36 10 , 31 30 4 0 1 2 11 ⟶ 16 0 18 8 11 35 20 36 11 , 31 30 4 0 1 2 12 ⟶ 16 0 18 8 11 35 20 36 12 , 34 30 4 0 1 2 4 ⟶ 17 0 18 8 11 35 20 36 4 , 34 30 4 0 1 2 6 ⟶ 17 0 18 8 11 35 20 36 6 , 34 30 4 0 1 2 3 ⟶ 17 0 18 8 11 35 20 36 3 , 34 30 4 0 1 2 9 ⟶ 17 0 18 8 11 35 20 36 9 , 34 30 4 0 1 2 10 ⟶ 17 0 18 8 11 35 20 36 10 , 34 30 4 0 1 2 11 ⟶ 17 0 18 8 11 35 20 36 11 , 34 30 4 0 1 2 12 ⟶ 17 0 18 8 11 35 20 36 12 , 29 31 31 16 1 2 4 ⟶ 29 37 32 35 21 16 5 4 , 29 31 31 16 1 2 6 ⟶ 29 37 32 35 21 16 5 6 , 29 31 31 16 1 2 3 ⟶ 29 37 32 35 21 16 5 3 , 29 31 31 16 1 2 9 ⟶ 29 37 32 35 21 16 5 9 , 29 31 31 16 1 2 10 ⟶ 29 37 32 35 21 16 5 10 , 29 31 31 16 1 2 11 ⟶ 29 37 32 35 21 16 5 11 , 29 31 31 16 1 2 12 ⟶ 29 37 32 35 21 16 5 12 , 21 31 31 16 1 2 4 ⟶ 21 37 32 35 21 16 5 4 , 21 31 31 16 1 2 6 ⟶ 21 37 32 35 21 16 5 6 , 21 31 31 16 1 2 3 ⟶ 21 37 32 35 21 16 5 3 , 21 31 31 16 1 2 9 ⟶ 21 37 32 35 21 16 5 9 , 21 31 31 16 1 2 10 ⟶ 21 37 32 35 21 16 5 10 , 21 31 31 16 1 2 11 ⟶ 21 37 32 35 21 16 5 11 , 21 31 31 16 1 2 12 ⟶ 21 37 32 35 21 16 5 12 , 11 31 31 16 1 2 4 ⟶ 11 37 32 35 21 16 5 4 , 11 31 31 16 1 2 6 ⟶ 11 37 32 35 21 16 5 6 , 11 31 31 16 1 2 3 ⟶ 11 37 32 35 21 16 5 3 , 11 31 31 16 1 2 9 ⟶ 11 37 32 35 21 16 5 9 , 11 31 31 16 1 2 10 ⟶ 11 37 32 35 21 16 5 10 , 11 31 31 16 1 2 11 ⟶ 11 37 32 35 21 16 5 11 , 11 31 31 16 1 2 12 ⟶ 11 37 32 35 21 16 5 12 , 32 31 31 16 1 2 4 ⟶ 32 37 32 35 21 16 5 4 , 32 31 31 16 1 2 6 ⟶ 32 37 32 35 21 16 5 6 , 32 31 31 16 1 2 3 ⟶ 32 37 32 35 21 16 5 3 , 32 31 31 16 1 2 9 ⟶ 32 37 32 35 21 16 5 9 , 32 31 31 16 1 2 10 ⟶ 32 37 32 35 21 16 5 10 , 32 31 31 16 1 2 11 ⟶ 32 37 32 35 21 16 5 11 , 32 31 31 16 1 2 12 ⟶ 32 37 32 35 21 16 5 12 , 33 31 31 16 1 2 4 ⟶ 33 37 32 35 21 16 5 4 , 33 31 31 16 1 2 6 ⟶ 33 37 32 35 21 16 5 6 , 33 31 31 16 1 2 3 ⟶ 33 37 32 35 21 16 5 3 , 33 31 31 16 1 2 9 ⟶ 33 37 32 35 21 16 5 9 , 33 31 31 16 1 2 10 ⟶ 33 37 32 35 21 16 5 10 , 33 31 31 16 1 2 11 ⟶ 33 37 32 35 21 16 5 11 , 33 31 31 16 1 2 12 ⟶ 33 37 32 35 21 16 5 12 , 31 31 31 16 1 2 4 ⟶ 31 37 32 35 21 16 5 4 , 31 31 31 16 1 2 6 ⟶ 31 37 32 35 21 16 5 6 , 31 31 31 16 1 2 3 ⟶ 31 37 32 35 21 16 5 3 , 31 31 31 16 1 2 9 ⟶ 31 37 32 35 21 16 5 9 , 31 31 31 16 1 2 10 ⟶ 31 37 32 35 21 16 5 10 , 31 31 31 16 1 2 11 ⟶ 31 37 32 35 21 16 5 11 , 31 31 31 16 1 2 12 ⟶ 31 37 32 35 21 16 5 12 , 34 31 31 16 1 2 4 ⟶ 34 37 32 35 21 16 5 4 , 34 31 31 16 1 2 6 ⟶ 34 37 32 35 21 16 5 6 , 34 31 31 16 1 2 3 ⟶ 34 37 32 35 21 16 5 3 , 34 31 31 16 1 2 9 ⟶ 34 37 32 35 21 16 5 9 , 34 31 31 16 1 2 10 ⟶ 34 37 32 35 21 16 5 10 , 34 31 31 16 1 2 11 ⟶ 34 37 32 35 21 16 5 11 , 34 31 31 16 1 2 12 ⟶ 34 37 32 35 21 16 5 12 , 0 29 35 7 39 2 4 ⟶ 0 18 40 32 35 2 6 13 , 0 29 35 7 39 2 6 ⟶ 0 18 40 32 35 2 6 19 , 0 29 35 7 39 2 3 ⟶ 0 18 40 32 35 2 6 2 , 0 29 35 7 39 2 9 ⟶ 0 18 40 32 35 2 6 7 , 0 29 35 7 39 2 10 ⟶ 0 18 40 32 35 2 6 20 , 0 29 35 7 39 2 11 ⟶ 0 18 40 32 35 2 6 21 , 0 29 35 7 39 2 12 ⟶ 0 18 40 32 35 2 6 22 , 13 29 35 7 39 2 4 ⟶ 13 18 40 32 35 2 6 13 , 13 29 35 7 39 2 6 ⟶ 13 18 40 32 35 2 6 19 , 13 29 35 7 39 2 3 ⟶ 13 18 40 32 35 2 6 2 , 13 29 35 7 39 2 9 ⟶ 13 18 40 32 35 2 6 7 , 13 29 35 7 39 2 10 ⟶ 13 18 40 32 35 2 6 20 , 13 29 35 7 39 2 11 ⟶ 13 18 40 32 35 2 6 21 , 13 29 35 7 39 2 12 ⟶ 13 18 40 32 35 2 6 22 , 4 29 35 7 39 2 4 ⟶ 4 18 40 32 35 2 6 13 , 4 29 35 7 39 2 6 ⟶ 4 18 40 32 35 2 6 19 , 4 29 35 7 39 2 3 ⟶ 4 18 40 32 35 2 6 2 , 4 29 35 7 39 2 9 ⟶ 4 18 40 32 35 2 6 7 , 4 29 35 7 39 2 10 ⟶ 4 18 40 32 35 2 6 20 , 4 29 35 7 39 2 11 ⟶ 4 18 40 32 35 2 6 21 , 4 29 35 7 39 2 12 ⟶ 4 18 40 32 35 2 6 22 , 14 29 35 7 39 2 4 ⟶ 14 18 40 32 35 2 6 13 , 14 29 35 7 39 2 6 ⟶ 14 18 40 32 35 2 6 19 , 14 29 35 7 39 2 3 ⟶ 14 18 40 32 35 2 6 2 , 14 29 35 7 39 2 9 ⟶ 14 18 40 32 35 2 6 7 , 14 29 35 7 39 2 10 ⟶ 14 18 40 32 35 2 6 20 , 14 29 35 7 39 2 11 ⟶ 14 18 40 32 35 2 6 21 , 14 29 35 7 39 2 12 ⟶ 14 18 40 32 35 2 6 22 , 15 29 35 7 39 2 4 ⟶ 15 18 40 32 35 2 6 13 , 15 29 35 7 39 2 6 ⟶ 15 18 40 32 35 2 6 19 , 15 29 35 7 39 2 3 ⟶ 15 18 40 32 35 2 6 2 , 15 29 35 7 39 2 9 ⟶ 15 18 40 32 35 2 6 7 , 15 29 35 7 39 2 10 ⟶ 15 18 40 32 35 2 6 20 , 15 29 35 7 39 2 11 ⟶ 15 18 40 32 35 2 6 21 , 15 29 35 7 39 2 12 ⟶ 15 18 40 32 35 2 6 22 , 16 29 35 7 39 2 4 ⟶ 16 18 40 32 35 2 6 13 , 16 29 35 7 39 2 6 ⟶ 16 18 40 32 35 2 6 19 , 16 29 35 7 39 2 3 ⟶ 16 18 40 32 35 2 6 2 , 16 29 35 7 39 2 9 ⟶ 16 18 40 32 35 2 6 7 , 16 29 35 7 39 2 10 ⟶ 16 18 40 32 35 2 6 20 , 16 29 35 7 39 2 11 ⟶ 16 18 40 32 35 2 6 21 , 16 29 35 7 39 2 12 ⟶ 16 18 40 32 35 2 6 22 , 17 29 35 7 39 2 4 ⟶ 17 18 40 32 35 2 6 13 , 17 29 35 7 39 2 6 ⟶ 17 18 40 32 35 2 6 19 , 17 29 35 7 39 2 3 ⟶ 17 18 40 32 35 2 6 2 , 17 29 35 7 39 2 9 ⟶ 17 18 40 32 35 2 6 7 , 17 29 35 7 39 2 10 ⟶ 17 18 40 32 35 2 6 20 , 17 29 35 7 39 2 11 ⟶ 17 18 40 32 35 2 6 21 , 17 29 35 7 39 2 12 ⟶ 17 18 40 32 35 2 6 22 , 29 30 10 26 24 2 4 ⟶ 23 33 35 2 3 9 25 15 , 29 30 10 26 24 2 6 ⟶ 23 33 35 2 3 9 25 24 , 29 30 10 26 24 2 3 ⟶ 23 33 35 2 3 9 25 36 , 29 30 10 26 24 2 9 ⟶ 23 33 35 2 3 9 25 41 , 29 30 10 26 24 2 10 ⟶ 23 33 35 2 3 9 25 26 , 29 30 10 26 24 2 11 ⟶ 23 33 35 2 3 9 25 33 , 29 30 10 26 24 2 12 ⟶ 23 33 35 2 3 9 25 46 , 21 30 10 26 24 2 4 ⟶ 20 33 35 2 3 9 25 15 , 21 30 10 26 24 2 6 ⟶ 20 33 35 2 3 9 25 24 , 21 30 10 26 24 2 3 ⟶ 20 33 35 2 3 9 25 36 , 21 30 10 26 24 2 9 ⟶ 20 33 35 2 3 9 25 41 , 21 30 10 26 24 2 10 ⟶ 20 33 35 2 3 9 25 26 , 21 30 10 26 24 2 11 ⟶ 20 33 35 2 3 9 25 33 , 21 30 10 26 24 2 12 ⟶ 20 33 35 2 3 9 25 46 , 11 30 10 26 24 2 4 ⟶ 10 33 35 2 3 9 25 15 , 11 30 10 26 24 2 6 ⟶ 10 33 35 2 3 9 25 24 , 11 30 10 26 24 2 3 ⟶ 10 33 35 2 3 9 25 36 , 11 30 10 26 24 2 9 ⟶ 10 33 35 2 3 9 25 41 , 11 30 10 26 24 2 10 ⟶ 10 33 35 2 3 9 25 26 , 11 30 10 26 24 2 11 ⟶ 10 33 35 2 3 9 25 33 , 11 30 10 26 24 2 12 ⟶ 10 33 35 2 3 9 25 46 , 32 30 10 26 24 2 4 ⟶ 25 33 35 2 3 9 25 15 , 32 30 10 26 24 2 6 ⟶ 25 33 35 2 3 9 25 24 , 32 30 10 26 24 2 3 ⟶ 25 33 35 2 3 9 25 36 , 32 30 10 26 24 2 9 ⟶ 25 33 35 2 3 9 25 41 , 32 30 10 26 24 2 10 ⟶ 25 33 35 2 3 9 25 26 , 32 30 10 26 24 2 11 ⟶ 25 33 35 2 3 9 25 33 , 32 30 10 26 24 2 12 ⟶ 25 33 35 2 3 9 25 46 , 33 30 10 26 24 2 4 ⟶ 26 33 35 2 3 9 25 15 , 33 30 10 26 24 2 6 ⟶ 26 33 35 2 3 9 25 24 , 33 30 10 26 24 2 3 ⟶ 26 33 35 2 3 9 25 36 , 33 30 10 26 24 2 9 ⟶ 26 33 35 2 3 9 25 41 , 33 30 10 26 24 2 10 ⟶ 26 33 35 2 3 9 25 26 , 33 30 10 26 24 2 11 ⟶ 26 33 35 2 3 9 25 33 , 33 30 10 26 24 2 12 ⟶ 26 33 35 2 3 9 25 46 , 31 30 10 26 24 2 4 ⟶ 27 33 35 2 3 9 25 15 , 31 30 10 26 24 2 6 ⟶ 27 33 35 2 3 9 25 24 , 31 30 10 26 24 2 3 ⟶ 27 33 35 2 3 9 25 36 , 31 30 10 26 24 2 9 ⟶ 27 33 35 2 3 9 25 41 , 31 30 10 26 24 2 10 ⟶ 27 33 35 2 3 9 25 26 , 31 30 10 26 24 2 11 ⟶ 27 33 35 2 3 9 25 33 , 31 30 10 26 24 2 12 ⟶ 27 33 35 2 3 9 25 46 , 34 30 10 26 24 2 4 ⟶ 28 33 35 2 3 9 25 15 , 34 30 10 26 24 2 6 ⟶ 28 33 35 2 3 9 25 24 , 34 30 10 26 24 2 3 ⟶ 28 33 35 2 3 9 25 36 , 34 30 10 26 24 2 9 ⟶ 28 33 35 2 3 9 25 41 , 34 30 10 26 24 2 10 ⟶ 28 33 35 2 3 9 25 26 , 34 30 10 26 24 2 11 ⟶ 28 33 35 2 3 9 25 33 , 34 30 10 26 24 2 12 ⟶ 28 33 35 2 3 9 25 46 , 1 21 37 32 16 5 4 ⟶ 29 31 35 13 0 18 40 8 4 , 1 21 37 32 16 5 6 ⟶ 29 31 35 13 0 18 40 8 6 , 1 21 37 32 16 5 3 ⟶ 29 31 35 13 0 18 40 8 3 , 1 21 37 32 16 5 9 ⟶ 29 31 35 13 0 18 40 8 9 , 1 21 37 32 16 5 10 ⟶ 29 31 35 13 0 18 40 8 10 , 1 21 37 32 16 5 11 ⟶ 29 31 35 13 0 18 40 8 11 , 1 21 37 32 16 5 12 ⟶ 29 31 35 13 0 18 40 8 12 , 19 21 37 32 16 5 4 ⟶ 21 31 35 13 0 18 40 8 4 , 19 21 37 32 16 5 6 ⟶ 21 31 35 13 0 18 40 8 6 , 19 21 37 32 16 5 3 ⟶ 21 31 35 13 0 18 40 8 3 , 19 21 37 32 16 5 9 ⟶ 21 31 35 13 0 18 40 8 9 , 19 21 37 32 16 5 10 ⟶ 21 31 35 13 0 18 40 8 10 , 19 21 37 32 16 5 11 ⟶ 21 31 35 13 0 18 40 8 11 , 19 21 37 32 16 5 12 ⟶ 21 31 35 13 0 18 40 8 12 , 6 21 37 32 16 5 4 ⟶ 11 31 35 13 0 18 40 8 4 , 6 21 37 32 16 5 6 ⟶ 11 31 35 13 0 18 40 8 6 , 6 21 37 32 16 5 3 ⟶ 11 31 35 13 0 18 40 8 3 , 6 21 37 32 16 5 9 ⟶ 11 31 35 13 0 18 40 8 9 , 6 21 37 32 16 5 10 ⟶ 11 31 35 13 0 18 40 8 10 , 6 21 37 32 16 5 11 ⟶ 11 31 35 13 0 18 40 8 11 , 6 21 37 32 16 5 12 ⟶ 11 31 35 13 0 18 40 8 12 , 39 21 37 32 16 5 4 ⟶ 32 31 35 13 0 18 40 8 4 , 39 21 37 32 16 5 6 ⟶ 32 31 35 13 0 18 40 8 6 , 39 21 37 32 16 5 3 ⟶ 32 31 35 13 0 18 40 8 3 , 39 21 37 32 16 5 9 ⟶ 32 31 35 13 0 18 40 8 9 , 39 21 37 32 16 5 10 ⟶ 32 31 35 13 0 18 40 8 10 , 39 21 37 32 16 5 11 ⟶ 32 31 35 13 0 18 40 8 11 , 39 21 37 32 16 5 12 ⟶ 32 31 35 13 0 18 40 8 12 , 24 21 37 32 16 5 4 ⟶ 33 31 35 13 0 18 40 8 4 , 24 21 37 32 16 5 6 ⟶ 33 31 35 13 0 18 40 8 6 , 24 21 37 32 16 5 3 ⟶ 33 31 35 13 0 18 40 8 3 , 24 21 37 32 16 5 9 ⟶ 33 31 35 13 0 18 40 8 9 , 24 21 37 32 16 5 10 ⟶ 33 31 35 13 0 18 40 8 10 , 24 21 37 32 16 5 11 ⟶ 33 31 35 13 0 18 40 8 11 , 24 21 37 32 16 5 12 ⟶ 33 31 35 13 0 18 40 8 12 , 35 21 37 32 16 5 4 ⟶ 31 31 35 13 0 18 40 8 4 , 35 21 37 32 16 5 6 ⟶ 31 31 35 13 0 18 40 8 6 , 35 21 37 32 16 5 3 ⟶ 31 31 35 13 0 18 40 8 3 , 35 21 37 32 16 5 9 ⟶ 31 31 35 13 0 18 40 8 9 , 35 21 37 32 16 5 10 ⟶ 31 31 35 13 0 18 40 8 10 , 35 21 37 32 16 5 11 ⟶ 31 31 35 13 0 18 40 8 11 , 35 21 37 32 16 5 12 ⟶ 31 31 35 13 0 18 40 8 12 , 43 21 37 32 16 5 4 ⟶ 34 31 35 13 0 18 40 8 4 , 43 21 37 32 16 5 6 ⟶ 34 31 35 13 0 18 40 8 6 , 43 21 37 32 16 5 3 ⟶ 34 31 35 13 0 18 40 8 3 , 43 21 37 32 16 5 9 ⟶ 34 31 35 13 0 18 40 8 9 , 43 21 37 32 16 5 10 ⟶ 34 31 35 13 0 18 40 8 10 , 43 21 37 32 16 5 11 ⟶ 34 31 35 13 0 18 40 8 11 , 43 21 37 32 16 5 12 ⟶ 34 31 35 13 0 18 40 8 12 , 23 33 30 3 11 30 4 ⟶ 29 31 27 36 6 2 6 2 4 , 23 33 30 3 11 30 6 ⟶ 29 31 27 36 6 2 6 2 6 , 23 33 30 3 11 30 3 ⟶ 29 31 27 36 6 2 6 2 3 , 23 33 30 3 11 30 9 ⟶ 29 31 27 36 6 2 6 2 9 , 23 33 30 3 11 30 10 ⟶ 29 31 27 36 6 2 6 2 10 , 23 33 30 3 11 30 11 ⟶ 29 31 27 36 6 2 6 2 11 , 23 33 30 3 11 30 12 ⟶ 29 31 27 36 6 2 6 2 12 , 20 33 30 3 11 30 4 ⟶ 21 31 27 36 6 2 6 2 4 , 20 33 30 3 11 30 6 ⟶ 21 31 27 36 6 2 6 2 6 , 20 33 30 3 11 30 3 ⟶ 21 31 27 36 6 2 6 2 3 , 20 33 30 3 11 30 9 ⟶ 21 31 27 36 6 2 6 2 9 , 20 33 30 3 11 30 10 ⟶ 21 31 27 36 6 2 6 2 10 , 20 33 30 3 11 30 11 ⟶ 21 31 27 36 6 2 6 2 11 , 20 33 30 3 11 30 12 ⟶ 21 31 27 36 6 2 6 2 12 , 10 33 30 3 11 30 4 ⟶ 11 31 27 36 6 2 6 2 4 , 10 33 30 3 11 30 6 ⟶ 11 31 27 36 6 2 6 2 6 , 10 33 30 3 11 30 3 ⟶ 11 31 27 36 6 2 6 2 3 , 10 33 30 3 11 30 9 ⟶ 11 31 27 36 6 2 6 2 9 , 10 33 30 3 11 30 10 ⟶ 11 31 27 36 6 2 6 2 10 , 10 33 30 3 11 30 11 ⟶ 11 31 27 36 6 2 6 2 11 , 10 33 30 3 11 30 12 ⟶ 11 31 27 36 6 2 6 2 12 , 25 33 30 3 11 30 4 ⟶ 32 31 27 36 6 2 6 2 4 , 25 33 30 3 11 30 6 ⟶ 32 31 27 36 6 2 6 2 6 , 25 33 30 3 11 30 3 ⟶ 32 31 27 36 6 2 6 2 3 , 25 33 30 3 11 30 9 ⟶ 32 31 27 36 6 2 6 2 9 , 25 33 30 3 11 30 10 ⟶ 32 31 27 36 6 2 6 2 10 , 25 33 30 3 11 30 11 ⟶ 32 31 27 36 6 2 6 2 11 , 25 33 30 3 11 30 12 ⟶ 32 31 27 36 6 2 6 2 12 , 26 33 30 3 11 30 4 ⟶ 33 31 27 36 6 2 6 2 4 , 26 33 30 3 11 30 6 ⟶ 33 31 27 36 6 2 6 2 6 , 26 33 30 3 11 30 3 ⟶ 33 31 27 36 6 2 6 2 3 , 26 33 30 3 11 30 9 ⟶ 33 31 27 36 6 2 6 2 9 , 26 33 30 3 11 30 10 ⟶ 33 31 27 36 6 2 6 2 10 , 26 33 30 3 11 30 11 ⟶ 33 31 27 36 6 2 6 2 11 , 26 33 30 3 11 30 12 ⟶ 33 31 27 36 6 2 6 2 12 , 27 33 30 3 11 30 4 ⟶ 31 31 27 36 6 2 6 2 4 , 27 33 30 3 11 30 6 ⟶ 31 31 27 36 6 2 6 2 6 , 27 33 30 3 11 30 3 ⟶ 31 31 27 36 6 2 6 2 3 , 27 33 30 3 11 30 9 ⟶ 31 31 27 36 6 2 6 2 9 , 27 33 30 3 11 30 10 ⟶ 31 31 27 36 6 2 6 2 10 , 27 33 30 3 11 30 11 ⟶ 31 31 27 36 6 2 6 2 11 , 27 33 30 3 11 30 12 ⟶ 31 31 27 36 6 2 6 2 12 , 28 33 30 3 11 30 4 ⟶ 34 31 27 36 6 2 6 2 4 , 28 33 30 3 11 30 6 ⟶ 34 31 27 36 6 2 6 2 6 , 28 33 30 3 11 30 3 ⟶ 34 31 27 36 6 2 6 2 3 , 28 33 30 3 11 30 9 ⟶ 34 31 27 36 6 2 6 2 9 , 28 33 30 3 11 30 10 ⟶ 34 31 27 36 6 2 6 2 10 , 28 33 30 3 11 30 11 ⟶ 34 31 27 36 6 2 6 2 11 , 28 33 30 3 11 30 12 ⟶ 34 31 27 36 6 2 6 2 12 , 23 24 13 1 21 30 4 ⟶ 23 36 4 0 18 32 35 19 13 , 23 24 13 1 21 30 6 ⟶ 23 36 4 0 18 32 35 19 19 , 23 24 13 1 21 30 3 ⟶ 23 36 4 0 18 32 35 19 2 , 23 24 13 1 21 30 9 ⟶ 23 36 4 0 18 32 35 19 7 , 23 24 13 1 21 30 10 ⟶ 23 36 4 0 18 32 35 19 20 , 23 24 13 1 21 30 11 ⟶ 23 36 4 0 18 32 35 19 21 , 23 24 13 1 21 30 12 ⟶ 23 36 4 0 18 32 35 19 22 , 20 24 13 1 21 30 4 ⟶ 20 36 4 0 18 32 35 19 13 , 20 24 13 1 21 30 6 ⟶ 20 36 4 0 18 32 35 19 19 , 20 24 13 1 21 30 3 ⟶ 20 36 4 0 18 32 35 19 2 , 20 24 13 1 21 30 9 ⟶ 20 36 4 0 18 32 35 19 7 , 20 24 13 1 21 30 10 ⟶ 20 36 4 0 18 32 35 19 20 , 20 24 13 1 21 30 11 ⟶ 20 36 4 0 18 32 35 19 21 , 20 24 13 1 21 30 12 ⟶ 20 36 4 0 18 32 35 19 22 , 10 24 13 1 21 30 4 ⟶ 10 36 4 0 18 32 35 19 13 , 10 24 13 1 21 30 6 ⟶ 10 36 4 0 18 32 35 19 19 , 10 24 13 1 21 30 3 ⟶ 10 36 4 0 18 32 35 19 2 , 10 24 13 1 21 30 9 ⟶ 10 36 4 0 18 32 35 19 7 , 10 24 13 1 21 30 10 ⟶ 10 36 4 0 18 32 35 19 20 , 10 24 13 1 21 30 11 ⟶ 10 36 4 0 18 32 35 19 21 , 10 24 13 1 21 30 12 ⟶ 10 36 4 0 18 32 35 19 22 , 25 24 13 1 21 30 4 ⟶ 25 36 4 0 18 32 35 19 13 , 25 24 13 1 21 30 6 ⟶ 25 36 4 0 18 32 35 19 19 , 25 24 13 1 21 30 3 ⟶ 25 36 4 0 18 32 35 19 2 , 25 24 13 1 21 30 9 ⟶ 25 36 4 0 18 32 35 19 7 , 25 24 13 1 21 30 10 ⟶ 25 36 4 0 18 32 35 19 20 , 25 24 13 1 21 30 11 ⟶ 25 36 4 0 18 32 35 19 21 , 25 24 13 1 21 30 12 ⟶ 25 36 4 0 18 32 35 19 22 , 26 24 13 1 21 30 4 ⟶ 26 36 4 0 18 32 35 19 13 , 26 24 13 1 21 30 6 ⟶ 26 36 4 0 18 32 35 19 19 , 26 24 13 1 21 30 3 ⟶ 26 36 4 0 18 32 35 19 2 , 26 24 13 1 21 30 9 ⟶ 26 36 4 0 18 32 35 19 7 , 26 24 13 1 21 30 10 ⟶ 26 36 4 0 18 32 35 19 20 , 26 24 13 1 21 30 11 ⟶ 26 36 4 0 18 32 35 19 21 , 26 24 13 1 21 30 12 ⟶ 26 36 4 0 18 32 35 19 22 , 27 24 13 1 21 30 4 ⟶ 27 36 4 0 18 32 35 19 13 , 27 24 13 1 21 30 6 ⟶ 27 36 4 0 18 32 35 19 19 , 27 24 13 1 21 30 3 ⟶ 27 36 4 0 18 32 35 19 2 , 27 24 13 1 21 30 9 ⟶ 27 36 4 0 18 32 35 19 7 , 27 24 13 1 21 30 10 ⟶ 27 36 4 0 18 32 35 19 20 , 27 24 13 1 21 30 11 ⟶ 27 36 4 0 18 32 35 19 21 , 27 24 13 1 21 30 12 ⟶ 27 36 4 0 18 32 35 19 22 , 28 24 13 1 21 30 4 ⟶ 28 36 4 0 18 32 35 19 13 , 28 24 13 1 21 30 6 ⟶ 28 36 4 0 18 32 35 19 19 , 28 24 13 1 21 30 3 ⟶ 28 36 4 0 18 32 35 19 2 , 28 24 13 1 21 30 9 ⟶ 28 36 4 0 18 32 35 19 7 , 28 24 13 1 21 30 10 ⟶ 28 36 4 0 18 32 35 19 20 , 28 24 13 1 21 30 11 ⟶ 28 36 4 0 18 32 35 19 21 , 28 24 13 1 21 30 12 ⟶ 28 36 4 0 18 32 35 19 22 , 29 16 1 21 31 30 4 ⟶ 29 27 33 31 35 13 5 4 , 29 16 1 21 31 30 6 ⟶ 29 27 33 31 35 13 5 6 , 29 16 1 21 31 30 3 ⟶ 29 27 33 31 35 13 5 3 , 29 16 1 21 31 30 9 ⟶ 29 27 33 31 35 13 5 9 , 29 16 1 21 31 30 10 ⟶ 29 27 33 31 35 13 5 10 , 29 16 1 21 31 30 11 ⟶ 29 27 33 31 35 13 5 11 , 29 16 1 21 31 30 12 ⟶ 29 27 33 31 35 13 5 12 , 21 16 1 21 31 30 4 ⟶ 21 27 33 31 35 13 5 4 , 21 16 1 21 31 30 6 ⟶ 21 27 33 31 35 13 5 6 , 21 16 1 21 31 30 3 ⟶ 21 27 33 31 35 13 5 3 , 21 16 1 21 31 30 9 ⟶ 21 27 33 31 35 13 5 9 , 21 16 1 21 31 30 10 ⟶ 21 27 33 31 35 13 5 10 , 21 16 1 21 31 30 11 ⟶ 21 27 33 31 35 13 5 11 , 21 16 1 21 31 30 12 ⟶ 21 27 33 31 35 13 5 12 , 11 16 1 21 31 30 4 ⟶ 11 27 33 31 35 13 5 4 , 11 16 1 21 31 30 6 ⟶ 11 27 33 31 35 13 5 6 , 11 16 1 21 31 30 3 ⟶ 11 27 33 31 35 13 5 3 , 11 16 1 21 31 30 9 ⟶ 11 27 33 31 35 13 5 9 , 11 16 1 21 31 30 10 ⟶ 11 27 33 31 35 13 5 10 , 11 16 1 21 31 30 11 ⟶ 11 27 33 31 35 13 5 11 , 11 16 1 21 31 30 12 ⟶ 11 27 33 31 35 13 5 12 , 32 16 1 21 31 30 4 ⟶ 32 27 33 31 35 13 5 4 , 32 16 1 21 31 30 6 ⟶ 32 27 33 31 35 13 5 6 , 32 16 1 21 31 30 3 ⟶ 32 27 33 31 35 13 5 3 , 32 16 1 21 31 30 9 ⟶ 32 27 33 31 35 13 5 9 , 32 16 1 21 31 30 10 ⟶ 32 27 33 31 35 13 5 10 , 32 16 1 21 31 30 11 ⟶ 32 27 33 31 35 13 5 11 , 32 16 1 21 31 30 12 ⟶ 32 27 33 31 35 13 5 12 , 33 16 1 21 31 30 4 ⟶ 33 27 33 31 35 13 5 4 , 33 16 1 21 31 30 6 ⟶ 33 27 33 31 35 13 5 6 , 33 16 1 21 31 30 3 ⟶ 33 27 33 31 35 13 5 3 , 33 16 1 21 31 30 9 ⟶ 33 27 33 31 35 13 5 9 , 33 16 1 21 31 30 10 ⟶ 33 27 33 31 35 13 5 10 , 33 16 1 21 31 30 11 ⟶ 33 27 33 31 35 13 5 11 , 33 16 1 21 31 30 12 ⟶ 33 27 33 31 35 13 5 12 , 31 16 1 21 31 30 4 ⟶ 31 27 33 31 35 13 5 4 , 31 16 1 21 31 30 6 ⟶ 31 27 33 31 35 13 5 6 , 31 16 1 21 31 30 3 ⟶ 31 27 33 31 35 13 5 3 , 31 16 1 21 31 30 9 ⟶ 31 27 33 31 35 13 5 9 , 31 16 1 21 31 30 10 ⟶ 31 27 33 31 35 13 5 10 , 31 16 1 21 31 30 11 ⟶ 31 27 33 31 35 13 5 11 , 31 16 1 21 31 30 12 ⟶ 31 27 33 31 35 13 5 12 , 34 16 1 21 31 30 4 ⟶ 34 27 33 31 35 13 5 4 , 34 16 1 21 31 30 6 ⟶ 34 27 33 31 35 13 5 6 , 34 16 1 21 31 30 3 ⟶ 34 27 33 31 35 13 5 3 , 34 16 1 21 31 30 9 ⟶ 34 27 33 31 35 13 5 9 , 34 16 1 21 31 30 10 ⟶ 34 27 33 31 35 13 5 10 , 34 16 1 21 31 30 11 ⟶ 34 27 33 31 35 13 5 11 , 34 16 1 21 31 30 12 ⟶ 34 27 33 31 35 13 5 12 , 23 41 14 5 3 6 13 ⟶ 0 18 40 8 3 10 24 13 , 23 41 14 5 3 6 19 ⟶ 0 18 40 8 3 10 24 19 , 23 41 14 5 3 6 2 ⟶ 0 18 40 8 3 10 24 2 , 23 41 14 5 3 6 7 ⟶ 0 18 40 8 3 10 24 7 , 23 41 14 5 3 6 20 ⟶ 0 18 40 8 3 10 24 20 , 23 41 14 5 3 6 21 ⟶ 0 18 40 8 3 10 24 21 , 23 41 14 5 3 6 22 ⟶ 0 18 40 8 3 10 24 22 , 20 41 14 5 3 6 13 ⟶ 13 18 40 8 3 10 24 13 , 20 41 14 5 3 6 19 ⟶ 13 18 40 8 3 10 24 19 , 20 41 14 5 3 6 2 ⟶ 13 18 40 8 3 10 24 2 , 20 41 14 5 3 6 7 ⟶ 13 18 40 8 3 10 24 7 , 20 41 14 5 3 6 20 ⟶ 13 18 40 8 3 10 24 20 , 20 41 14 5 3 6 21 ⟶ 13 18 40 8 3 10 24 21 , 20 41 14 5 3 6 22 ⟶ 13 18 40 8 3 10 24 22 , 10 41 14 5 3 6 13 ⟶ 4 18 40 8 3 10 24 13 , 10 41 14 5 3 6 19 ⟶ 4 18 40 8 3 10 24 19 , 10 41 14 5 3 6 2 ⟶ 4 18 40 8 3 10 24 2 , 10 41 14 5 3 6 7 ⟶ 4 18 40 8 3 10 24 7 , 10 41 14 5 3 6 20 ⟶ 4 18 40 8 3 10 24 20 , 10 41 14 5 3 6 21 ⟶ 4 18 40 8 3 10 24 21 , 10 41 14 5 3 6 22 ⟶ 4 18 40 8 3 10 24 22 , 25 41 14 5 3 6 13 ⟶ 14 18 40 8 3 10 24 13 , 25 41 14 5 3 6 19 ⟶ 14 18 40 8 3 10 24 19 , 25 41 14 5 3 6 2 ⟶ 14 18 40 8 3 10 24 2 , 25 41 14 5 3 6 7 ⟶ 14 18 40 8 3 10 24 7 , 25 41 14 5 3 6 20 ⟶ 14 18 40 8 3 10 24 20 , 25 41 14 5 3 6 21 ⟶ 14 18 40 8 3 10 24 21 , 25 41 14 5 3 6 22 ⟶ 14 18 40 8 3 10 24 22 , 26 41 14 5 3 6 13 ⟶ 15 18 40 8 3 10 24 13 , 26 41 14 5 3 6 19 ⟶ 15 18 40 8 3 10 24 19 , 26 41 14 5 3 6 2 ⟶ 15 18 40 8 3 10 24 2 , 26 41 14 5 3 6 7 ⟶ 15 18 40 8 3 10 24 7 , 26 41 14 5 3 6 20 ⟶ 15 18 40 8 3 10 24 20 , 26 41 14 5 3 6 21 ⟶ 15 18 40 8 3 10 24 21 , 26 41 14 5 3 6 22 ⟶ 15 18 40 8 3 10 24 22 , 27 41 14 5 3 6 13 ⟶ 16 18 40 8 3 10 24 13 , 27 41 14 5 3 6 19 ⟶ 16 18 40 8 3 10 24 19 , 27 41 14 5 3 6 2 ⟶ 16 18 40 8 3 10 24 2 , 27 41 14 5 3 6 7 ⟶ 16 18 40 8 3 10 24 7 , 27 41 14 5 3 6 20 ⟶ 16 18 40 8 3 10 24 20 , 27 41 14 5 3 6 21 ⟶ 16 18 40 8 3 10 24 21 , 27 41 14 5 3 6 22 ⟶ 16 18 40 8 3 10 24 22 , 28 41 14 5 3 6 13 ⟶ 17 18 40 8 3 10 24 13 , 28 41 14 5 3 6 19 ⟶ 17 18 40 8 3 10 24 19 , 28 41 14 5 3 6 2 ⟶ 17 18 40 8 3 10 24 2 , 28 41 14 5 3 6 7 ⟶ 17 18 40 8 3 10 24 7 , 28 41 14 5 3 6 20 ⟶ 17 18 40 8 3 10 24 20 , 28 41 14 5 3 6 21 ⟶ 17 18 40 8 3 10 24 21 , 28 41 14 5 3 6 22 ⟶ 17 18 40 8 3 10 24 22 , 1 21 37 39 2 6 13 ⟶ 0 0 18 32 35 19 19 2 4 , 1 21 37 39 2 6 19 ⟶ 0 0 18 32 35 19 19 2 6 , 1 21 37 39 2 6 2 ⟶ 0 0 18 32 35 19 19 2 3 , 1 21 37 39 2 6 7 ⟶ 0 0 18 32 35 19 19 2 9 , 1 21 37 39 2 6 20 ⟶ 0 0 18 32 35 19 19 2 10 , 1 21 37 39 2 6 21 ⟶ 0 0 18 32 35 19 19 2 11 , 1 21 37 39 2 6 22 ⟶ 0 0 18 32 35 19 19 2 12 , 19 21 37 39 2 6 13 ⟶ 13 0 18 32 35 19 19 2 4 , 19 21 37 39 2 6 19 ⟶ 13 0 18 32 35 19 19 2 6 , 19 21 37 39 2 6 2 ⟶ 13 0 18 32 35 19 19 2 3 , 19 21 37 39 2 6 7 ⟶ 13 0 18 32 35 19 19 2 9 , 19 21 37 39 2 6 20 ⟶ 13 0 18 32 35 19 19 2 10 , 19 21 37 39 2 6 21 ⟶ 13 0 18 32 35 19 19 2 11 , 19 21 37 39 2 6 22 ⟶ 13 0 18 32 35 19 19 2 12 , 6 21 37 39 2 6 13 ⟶ 4 0 18 32 35 19 19 2 4 , 6 21 37 39 2 6 19 ⟶ 4 0 18 32 35 19 19 2 6 , 6 21 37 39 2 6 2 ⟶ 4 0 18 32 35 19 19 2 3 , 6 21 37 39 2 6 7 ⟶ 4 0 18 32 35 19 19 2 9 , 6 21 37 39 2 6 20 ⟶ 4 0 18 32 35 19 19 2 10 , 6 21 37 39 2 6 21 ⟶ 4 0 18 32 35 19 19 2 11 , 6 21 37 39 2 6 22 ⟶ 4 0 18 32 35 19 19 2 12 , 39 21 37 39 2 6 13 ⟶ 14 0 18 32 35 19 19 2 4 , 39 21 37 39 2 6 19 ⟶ 14 0 18 32 35 19 19 2 6 , 39 21 37 39 2 6 2 ⟶ 14 0 18 32 35 19 19 2 3 , 39 21 37 39 2 6 7 ⟶ 14 0 18 32 35 19 19 2 9 , 39 21 37 39 2 6 20 ⟶ 14 0 18 32 35 19 19 2 10 , 39 21 37 39 2 6 21 ⟶ 14 0 18 32 35 19 19 2 11 , 39 21 37 39 2 6 22 ⟶ 14 0 18 32 35 19 19 2 12 , 24 21 37 39 2 6 13 ⟶ 15 0 18 32 35 19 19 2 4 , 24 21 37 39 2 6 19 ⟶ 15 0 18 32 35 19 19 2 6 , 24 21 37 39 2 6 2 ⟶ 15 0 18 32 35 19 19 2 3 , 24 21 37 39 2 6 7 ⟶ 15 0 18 32 35 19 19 2 9 , 24 21 37 39 2 6 20 ⟶ 15 0 18 32 35 19 19 2 10 , 24 21 37 39 2 6 21 ⟶ 15 0 18 32 35 19 19 2 11 , 24 21 37 39 2 6 22 ⟶ 15 0 18 32 35 19 19 2 12 , 35 21 37 39 2 6 13 ⟶ 16 0 18 32 35 19 19 2 4 , 35 21 37 39 2 6 19 ⟶ 16 0 18 32 35 19 19 2 6 , 35 21 37 39 2 6 2 ⟶ 16 0 18 32 35 19 19 2 3 , 35 21 37 39 2 6 7 ⟶ 16 0 18 32 35 19 19 2 9 , 35 21 37 39 2 6 20 ⟶ 16 0 18 32 35 19 19 2 10 , 35 21 37 39 2 6 21 ⟶ 16 0 18 32 35 19 19 2 11 , 35 21 37 39 2 6 22 ⟶ 16 0 18 32 35 19 19 2 12 , 43 21 37 39 2 6 13 ⟶ 17 0 18 32 35 19 19 2 4 , 43 21 37 39 2 6 19 ⟶ 17 0 18 32 35 19 19 2 6 , 43 21 37 39 2 6 2 ⟶ 17 0 18 32 35 19 19 2 3 , 43 21 37 39 2 6 7 ⟶ 17 0 18 32 35 19 19 2 9 , 43 21 37 39 2 6 20 ⟶ 17 0 18 32 35 19 19 2 10 , 43 21 37 39 2 6 21 ⟶ 17 0 18 32 35 19 19 2 11 , 43 21 37 39 2 6 22 ⟶ 17 0 18 32 35 19 19 2 12 , 1 13 23 33 30 6 13 ⟶ 0 23 41 32 35 19 2 4 , 1 13 23 33 30 6 19 ⟶ 0 23 41 32 35 19 2 6 , 1 13 23 33 30 6 2 ⟶ 0 23 41 32 35 19 2 3 , 1 13 23 33 30 6 7 ⟶ 0 23 41 32 35 19 2 9 , 1 13 23 33 30 6 20 ⟶ 0 23 41 32 35 19 2 10 , 1 13 23 33 30 6 21 ⟶ 0 23 41 32 35 19 2 11 , 1 13 23 33 30 6 22 ⟶ 0 23 41 32 35 19 2 12 , 19 13 23 33 30 6 13 ⟶ 13 23 41 32 35 19 2 4 , 19 13 23 33 30 6 19 ⟶ 13 23 41 32 35 19 2 6 , 19 13 23 33 30 6 2 ⟶ 13 23 41 32 35 19 2 3 , 19 13 23 33 30 6 7 ⟶ 13 23 41 32 35 19 2 9 , 19 13 23 33 30 6 20 ⟶ 13 23 41 32 35 19 2 10 , 19 13 23 33 30 6 21 ⟶ 13 23 41 32 35 19 2 11 , 19 13 23 33 30 6 22 ⟶ 13 23 41 32 35 19 2 12 , 6 13 23 33 30 6 13 ⟶ 4 23 41 32 35 19 2 4 , 6 13 23 33 30 6 19 ⟶ 4 23 41 32 35 19 2 6 , 6 13 23 33 30 6 2 ⟶ 4 23 41 32 35 19 2 3 , 6 13 23 33 30 6 7 ⟶ 4 23 41 32 35 19 2 9 , 6 13 23 33 30 6 20 ⟶ 4 23 41 32 35 19 2 10 , 6 13 23 33 30 6 21 ⟶ 4 23 41 32 35 19 2 11 , 6 13 23 33 30 6 22 ⟶ 4 23 41 32 35 19 2 12 , 39 13 23 33 30 6 13 ⟶ 14 23 41 32 35 19 2 4 , 39 13 23 33 30 6 19 ⟶ 14 23 41 32 35 19 2 6 , 39 13 23 33 30 6 2 ⟶ 14 23 41 32 35 19 2 3 , 39 13 23 33 30 6 7 ⟶ 14 23 41 32 35 19 2 9 , 39 13 23 33 30 6 20 ⟶ 14 23 41 32 35 19 2 10 , 39 13 23 33 30 6 21 ⟶ 14 23 41 32 35 19 2 11 , 39 13 23 33 30 6 22 ⟶ 14 23 41 32 35 19 2 12 , 24 13 23 33 30 6 13 ⟶ 15 23 41 32 35 19 2 4 , 24 13 23 33 30 6 19 ⟶ 15 23 41 32 35 19 2 6 , 24 13 23 33 30 6 2 ⟶ 15 23 41 32 35 19 2 3 , 24 13 23 33 30 6 7 ⟶ 15 23 41 32 35 19 2 9 , 24 13 23 33 30 6 20 ⟶ 15 23 41 32 35 19 2 10 , 24 13 23 33 30 6 21 ⟶ 15 23 41 32 35 19 2 11 , 24 13 23 33 30 6 22 ⟶ 15 23 41 32 35 19 2 12 , 35 13 23 33 30 6 13 ⟶ 16 23 41 32 35 19 2 4 , 35 13 23 33 30 6 19 ⟶ 16 23 41 32 35 19 2 6 , 35 13 23 33 30 6 2 ⟶ 16 23 41 32 35 19 2 3 , 35 13 23 33 30 6 7 ⟶ 16 23 41 32 35 19 2 9 , 35 13 23 33 30 6 20 ⟶ 16 23 41 32 35 19 2 10 , 35 13 23 33 30 6 21 ⟶ 16 23 41 32 35 19 2 11 , 35 13 23 33 30 6 22 ⟶ 16 23 41 32 35 19 2 12 , 43 13 23 33 30 6 13 ⟶ 17 23 41 32 35 19 2 4 , 43 13 23 33 30 6 19 ⟶ 17 23 41 32 35 19 2 6 , 43 13 23 33 30 6 2 ⟶ 17 23 41 32 35 19 2 3 , 43 13 23 33 30 6 7 ⟶ 17 23 41 32 35 19 2 9 , 43 13 23 33 30 6 20 ⟶ 17 23 41 32 35 19 2 10 , 43 13 23 33 30 6 21 ⟶ 17 23 41 32 35 19 2 11 , 43 13 23 33 30 6 22 ⟶ 17 23 41 32 35 19 2 12 , 0 0 1 2 6 19 13 ⟶ 0 0 1 7 39 19 2 6 13 , 0 0 1 2 6 19 19 ⟶ 0 0 1 7 39 19 2 6 19 , 0 0 1 2 6 19 2 ⟶ 0 0 1 7 39 19 2 6 2 , 0 0 1 2 6 19 7 ⟶ 0 0 1 7 39 19 2 6 7 , 0 0 1 2 6 19 20 ⟶ 0 0 1 7 39 19 2 6 20 , 0 0 1 2 6 19 21 ⟶ 0 0 1 7 39 19 2 6 21 , 0 0 1 2 6 19 22 ⟶ 0 0 1 7 39 19 2 6 22 , 13 0 1 2 6 19 13 ⟶ 13 0 1 7 39 19 2 6 13 , 13 0 1 2 6 19 19 ⟶ 13 0 1 7 39 19 2 6 19 , 13 0 1 2 6 19 2 ⟶ 13 0 1 7 39 19 2 6 2 , 13 0 1 2 6 19 7 ⟶ 13 0 1 7 39 19 2 6 7 , 13 0 1 2 6 19 20 ⟶ 13 0 1 7 39 19 2 6 20 , 13 0 1 2 6 19 21 ⟶ 13 0 1 7 39 19 2 6 21 , 13 0 1 2 6 19 22 ⟶ 13 0 1 7 39 19 2 6 22 , 4 0 1 2 6 19 13 ⟶ 4 0 1 7 39 19 2 6 13 , 4 0 1 2 6 19 19 ⟶ 4 0 1 7 39 19 2 6 19 , 4 0 1 2 6 19 2 ⟶ 4 0 1 7 39 19 2 6 2 , 4 0 1 2 6 19 7 ⟶ 4 0 1 7 39 19 2 6 7 , 4 0 1 2 6 19 20 ⟶ 4 0 1 7 39 19 2 6 20 , 4 0 1 2 6 19 21 ⟶ 4 0 1 7 39 19 2 6 21 , 4 0 1 2 6 19 22 ⟶ 4 0 1 7 39 19 2 6 22 , 14 0 1 2 6 19 13 ⟶ 14 0 1 7 39 19 2 6 13 , 14 0 1 2 6 19 19 ⟶ 14 0 1 7 39 19 2 6 19 , 14 0 1 2 6 19 2 ⟶ 14 0 1 7 39 19 2 6 2 , 14 0 1 2 6 19 7 ⟶ 14 0 1 7 39 19 2 6 7 , 14 0 1 2 6 19 20 ⟶ 14 0 1 7 39 19 2 6 20 , 14 0 1 2 6 19 21 ⟶ 14 0 1 7 39 19 2 6 21 , 14 0 1 2 6 19 22 ⟶ 14 0 1 7 39 19 2 6 22 , 15 0 1 2 6 19 13 ⟶ 15 0 1 7 39 19 2 6 13 , 15 0 1 2 6 19 19 ⟶ 15 0 1 7 39 19 2 6 19 , 15 0 1 2 6 19 2 ⟶ 15 0 1 7 39 19 2 6 2 , 15 0 1 2 6 19 7 ⟶ 15 0 1 7 39 19 2 6 7 , 15 0 1 2 6 19 20 ⟶ 15 0 1 7 39 19 2 6 20 , 15 0 1 2 6 19 21 ⟶ 15 0 1 7 39 19 2 6 21 , 15 0 1 2 6 19 22 ⟶ 15 0 1 7 39 19 2 6 22 , 16 0 1 2 6 19 13 ⟶ 16 0 1 7 39 19 2 6 13 , 16 0 1 2 6 19 19 ⟶ 16 0 1 7 39 19 2 6 19 , 16 0 1 2 6 19 2 ⟶ 16 0 1 7 39 19 2 6 2 , 16 0 1 2 6 19 7 ⟶ 16 0 1 7 39 19 2 6 7 , 16 0 1 2 6 19 20 ⟶ 16 0 1 7 39 19 2 6 20 , 16 0 1 2 6 19 21 ⟶ 16 0 1 7 39 19 2 6 21 , 16 0 1 2 6 19 22 ⟶ 16 0 1 7 39 19 2 6 22 , 17 0 1 2 6 19 13 ⟶ 17 0 1 7 39 19 2 6 13 , 17 0 1 2 6 19 19 ⟶ 17 0 1 7 39 19 2 6 19 , 17 0 1 2 6 19 2 ⟶ 17 0 1 7 39 19 2 6 2 , 17 0 1 2 6 19 7 ⟶ 17 0 1 7 39 19 2 6 7 , 17 0 1 2 6 19 20 ⟶ 17 0 1 7 39 19 2 6 20 , 17 0 1 2 6 19 21 ⟶ 17 0 1 7 39 19 2 6 21 , 17 0 1 2 6 19 22 ⟶ 17 0 1 7 39 19 2 6 22 , 5 3 4 1 13 1 13 ⟶ 1 2 6 13 0 18 8 4 , 5 3 4 1 13 1 19 ⟶ 1 2 6 13 0 18 8 6 , 5 3 4 1 13 1 2 ⟶ 1 2 6 13 0 18 8 3 , 5 3 4 1 13 1 7 ⟶ 1 2 6 13 0 18 8 9 , 5 3 4 1 13 1 20 ⟶ 1 2 6 13 0 18 8 10 , 5 3 4 1 13 1 21 ⟶ 1 2 6 13 0 18 8 11 , 5 3 4 1 13 1 22 ⟶ 1 2 6 13 0 18 8 12 , 2 3 4 1 13 1 13 ⟶ 19 2 6 13 0 18 8 4 , 2 3 4 1 13 1 19 ⟶ 19 2 6 13 0 18 8 6 , 2 3 4 1 13 1 2 ⟶ 19 2 6 13 0 18 8 3 , 2 3 4 1 13 1 7 ⟶ 19 2 6 13 0 18 8 9 , 2 3 4 1 13 1 20 ⟶ 19 2 6 13 0 18 8 10 , 2 3 4 1 13 1 21 ⟶ 19 2 6 13 0 18 8 11 , 2 3 4 1 13 1 22 ⟶ 19 2 6 13 0 18 8 12 , 3 3 4 1 13 1 13 ⟶ 6 2 6 13 0 18 8 4 , 3 3 4 1 13 1 19 ⟶ 6 2 6 13 0 18 8 6 , 3 3 4 1 13 1 2 ⟶ 6 2 6 13 0 18 8 3 , 3 3 4 1 13 1 7 ⟶ 6 2 6 13 0 18 8 9 , 3 3 4 1 13 1 20 ⟶ 6 2 6 13 0 18 8 10 , 3 3 4 1 13 1 21 ⟶ 6 2 6 13 0 18 8 11 , 3 3 4 1 13 1 22 ⟶ 6 2 6 13 0 18 8 12 , 8 3 4 1 13 1 13 ⟶ 39 2 6 13 0 18 8 4 , 8 3 4 1 13 1 19 ⟶ 39 2 6 13 0 18 8 6 , 8 3 4 1 13 1 2 ⟶ 39 2 6 13 0 18 8 3 , 8 3 4 1 13 1 7 ⟶ 39 2 6 13 0 18 8 9 , 8 3 4 1 13 1 20 ⟶ 39 2 6 13 0 18 8 10 , 8 3 4 1 13 1 21 ⟶ 39 2 6 13 0 18 8 11 , 8 3 4 1 13 1 22 ⟶ 39 2 6 13 0 18 8 12 , 36 3 4 1 13 1 13 ⟶ 24 2 6 13 0 18 8 4 , 36 3 4 1 13 1 19 ⟶ 24 2 6 13 0 18 8 6 , 36 3 4 1 13 1 2 ⟶ 24 2 6 13 0 18 8 3 , 36 3 4 1 13 1 7 ⟶ 24 2 6 13 0 18 8 9 , 36 3 4 1 13 1 20 ⟶ 24 2 6 13 0 18 8 10 , 36 3 4 1 13 1 21 ⟶ 24 2 6 13 0 18 8 11 , 36 3 4 1 13 1 22 ⟶ 24 2 6 13 0 18 8 12 , 30 3 4 1 13 1 13 ⟶ 35 2 6 13 0 18 8 4 , 30 3 4 1 13 1 19 ⟶ 35 2 6 13 0 18 8 6 , 30 3 4 1 13 1 2 ⟶ 35 2 6 13 0 18 8 3 , 30 3 4 1 13 1 7 ⟶ 35 2 6 13 0 18 8 9 , 30 3 4 1 13 1 20 ⟶ 35 2 6 13 0 18 8 10 , 30 3 4 1 13 1 21 ⟶ 35 2 6 13 0 18 8 11 , 30 3 4 1 13 1 22 ⟶ 35 2 6 13 0 18 8 12 , 45 3 4 1 13 1 13 ⟶ 43 2 6 13 0 18 8 4 , 45 3 4 1 13 1 19 ⟶ 43 2 6 13 0 18 8 6 , 45 3 4 1 13 1 2 ⟶ 43 2 6 13 0 18 8 3 , 45 3 4 1 13 1 7 ⟶ 43 2 6 13 0 18 8 9 , 45 3 4 1 13 1 20 ⟶ 43 2 6 13 0 18 8 10 , 45 3 4 1 13 1 21 ⟶ 43 2 6 13 0 18 8 11 , 45 3 4 1 13 1 22 ⟶ 43 2 6 13 0 18 8 12 , 29 30 3 6 20 24 13 ⟶ 1 13 23 33 35 2 3 4 , 29 30 3 6 20 24 19 ⟶ 1 13 23 33 35 2 3 6 , 29 30 3 6 20 24 2 ⟶ 1 13 23 33 35 2 3 3 , 29 30 3 6 20 24 7 ⟶ 1 13 23 33 35 2 3 9 , 29 30 3 6 20 24 20 ⟶ 1 13 23 33 35 2 3 10 , 29 30 3 6 20 24 21 ⟶ 1 13 23 33 35 2 3 11 , 29 30 3 6 20 24 22 ⟶ 1 13 23 33 35 2 3 12 , 21 30 3 6 20 24 13 ⟶ 19 13 23 33 35 2 3 4 , 21 30 3 6 20 24 19 ⟶ 19 13 23 33 35 2 3 6 , 21 30 3 6 20 24 2 ⟶ 19 13 23 33 35 2 3 3 , 21 30 3 6 20 24 7 ⟶ 19 13 23 33 35 2 3 9 , 21 30 3 6 20 24 20 ⟶ 19 13 23 33 35 2 3 10 , 21 30 3 6 20 24 21 ⟶ 19 13 23 33 35 2 3 11 , 21 30 3 6 20 24 22 ⟶ 19 13 23 33 35 2 3 12 , 11 30 3 6 20 24 13 ⟶ 6 13 23 33 35 2 3 4 , 11 30 3 6 20 24 19 ⟶ 6 13 23 33 35 2 3 6 , 11 30 3 6 20 24 2 ⟶ 6 13 23 33 35 2 3 3 , 11 30 3 6 20 24 7 ⟶ 6 13 23 33 35 2 3 9 , 11 30 3 6 20 24 20 ⟶ 6 13 23 33 35 2 3 10 , 11 30 3 6 20 24 21 ⟶ 6 13 23 33 35 2 3 11 , 11 30 3 6 20 24 22 ⟶ 6 13 23 33 35 2 3 12 , 32 30 3 6 20 24 13 ⟶ 39 13 23 33 35 2 3 4 , 32 30 3 6 20 24 19 ⟶ 39 13 23 33 35 2 3 6 , 32 30 3 6 20 24 2 ⟶ 39 13 23 33 35 2 3 3 , 32 30 3 6 20 24 7 ⟶ 39 13 23 33 35 2 3 9 , 32 30 3 6 20 24 20 ⟶ 39 13 23 33 35 2 3 10 , 32 30 3 6 20 24 21 ⟶ 39 13 23 33 35 2 3 11 , 32 30 3 6 20 24 22 ⟶ 39 13 23 33 35 2 3 12 , 33 30 3 6 20 24 13 ⟶ 24 13 23 33 35 2 3 4 , 33 30 3 6 20 24 19 ⟶ 24 13 23 33 35 2 3 6 , 33 30 3 6 20 24 2 ⟶ 24 13 23 33 35 2 3 3 , 33 30 3 6 20 24 7 ⟶ 24 13 23 33 35 2 3 9 , 33 30 3 6 20 24 20 ⟶ 24 13 23 33 35 2 3 10 , 33 30 3 6 20 24 21 ⟶ 24 13 23 33 35 2 3 11 , 33 30 3 6 20 24 22 ⟶ 24 13 23 33 35 2 3 12 , 31 30 3 6 20 24 13 ⟶ 35 13 23 33 35 2 3 4 , 31 30 3 6 20 24 19 ⟶ 35 13 23 33 35 2 3 6 , 31 30 3 6 20 24 2 ⟶ 35 13 23 33 35 2 3 3 , 31 30 3 6 20 24 7 ⟶ 35 13 23 33 35 2 3 9 , 31 30 3 6 20 24 20 ⟶ 35 13 23 33 35 2 3 10 , 31 30 3 6 20 24 21 ⟶ 35 13 23 33 35 2 3 11 , 31 30 3 6 20 24 22 ⟶ 35 13 23 33 35 2 3 12 , 34 30 3 6 20 24 13 ⟶ 43 13 23 33 35 2 3 4 , 34 30 3 6 20 24 19 ⟶ 43 13 23 33 35 2 3 6 , 34 30 3 6 20 24 2 ⟶ 43 13 23 33 35 2 3 3 , 34 30 3 6 20 24 7 ⟶ 43 13 23 33 35 2 3 9 , 34 30 3 6 20 24 20 ⟶ 43 13 23 33 35 2 3 10 , 34 30 3 6 20 24 21 ⟶ 43 13 23 33 35 2 3 11 , 34 30 3 6 20 24 22 ⟶ 43 13 23 33 35 2 3 12 , 0 5 11 37 25 24 13 ⟶ 23 33 35 13 18 40 8 4 , 0 5 11 37 25 24 19 ⟶ 23 33 35 13 18 40 8 6 , 0 5 11 37 25 24 2 ⟶ 23 33 35 13 18 40 8 3 , 0 5 11 37 25 24 7 ⟶ 23 33 35 13 18 40 8 9 , 0 5 11 37 25 24 20 ⟶ 23 33 35 13 18 40 8 10 , 0 5 11 37 25 24 21 ⟶ 23 33 35 13 18 40 8 11 , 0 5 11 37 25 24 22 ⟶ 23 33 35 13 18 40 8 12 , 13 5 11 37 25 24 13 ⟶ 20 33 35 13 18 40 8 4 , 13 5 11 37 25 24 19 ⟶ 20 33 35 13 18 40 8 6 , 13 5 11 37 25 24 2 ⟶ 20 33 35 13 18 40 8 3 , 13 5 11 37 25 24 7 ⟶ 20 33 35 13 18 40 8 9 , 13 5 11 37 25 24 20 ⟶ 20 33 35 13 18 40 8 10 , 13 5 11 37 25 24 21 ⟶ 20 33 35 13 18 40 8 11 , 13 5 11 37 25 24 22 ⟶ 20 33 35 13 18 40 8 12 , 4 5 11 37 25 24 13 ⟶ 10 33 35 13 18 40 8 4 , 4 5 11 37 25 24 19 ⟶ 10 33 35 13 18 40 8 6 , 4 5 11 37 25 24 2 ⟶ 10 33 35 13 18 40 8 3 , 4 5 11 37 25 24 7 ⟶ 10 33 35 13 18 40 8 9 , 4 5 11 37 25 24 20 ⟶ 10 33 35 13 18 40 8 10 , 4 5 11 37 25 24 21 ⟶ 10 33 35 13 18 40 8 11 , 4 5 11 37 25 24 22 ⟶ 10 33 35 13 18 40 8 12 , 14 5 11 37 25 24 13 ⟶ 25 33 35 13 18 40 8 4 , 14 5 11 37 25 24 19 ⟶ 25 33 35 13 18 40 8 6 , 14 5 11 37 25 24 2 ⟶ 25 33 35 13 18 40 8 3 , 14 5 11 37 25 24 7 ⟶ 25 33 35 13 18 40 8 9 , 14 5 11 37 25 24 20 ⟶ 25 33 35 13 18 40 8 10 , 14 5 11 37 25 24 21 ⟶ 25 33 35 13 18 40 8 11 , 14 5 11 37 25 24 22 ⟶ 25 33 35 13 18 40 8 12 , 15 5 11 37 25 24 13 ⟶ 26 33 35 13 18 40 8 4 , 15 5 11 37 25 24 19 ⟶ 26 33 35 13 18 40 8 6 , 15 5 11 37 25 24 2 ⟶ 26 33 35 13 18 40 8 3 , 15 5 11 37 25 24 7 ⟶ 26 33 35 13 18 40 8 9 , 15 5 11 37 25 24 20 ⟶ 26 33 35 13 18 40 8 10 , 15 5 11 37 25 24 21 ⟶ 26 33 35 13 18 40 8 11 , 15 5 11 37 25 24 22 ⟶ 26 33 35 13 18 40 8 12 , 16 5 11 37 25 24 13 ⟶ 27 33 35 13 18 40 8 4 , 16 5 11 37 25 24 19 ⟶ 27 33 35 13 18 40 8 6 , 16 5 11 37 25 24 2 ⟶ 27 33 35 13 18 40 8 3 , 16 5 11 37 25 24 7 ⟶ 27 33 35 13 18 40 8 9 , 16 5 11 37 25 24 20 ⟶ 27 33 35 13 18 40 8 10 , 16 5 11 37 25 24 21 ⟶ 27 33 35 13 18 40 8 11 , 16 5 11 37 25 24 22 ⟶ 27 33 35 13 18 40 8 12 , 17 5 11 37 25 24 13 ⟶ 28 33 35 13 18 40 8 4 , 17 5 11 37 25 24 19 ⟶ 28 33 35 13 18 40 8 6 , 17 5 11 37 25 24 2 ⟶ 28 33 35 13 18 40 8 3 , 17 5 11 37 25 24 7 ⟶ 28 33 35 13 18 40 8 9 , 17 5 11 37 25 24 20 ⟶ 28 33 35 13 18 40 8 10 , 17 5 11 37 25 24 21 ⟶ 28 33 35 13 18 40 8 11 , 17 5 11 37 25 24 22 ⟶ 28 33 35 13 18 40 8 12 , 29 31 37 14 1 2 3 4 ⟶ 1 13 5 9 8 11 35 21 16 , 29 31 37 14 1 2 3 6 ⟶ 1 13 5 9 8 11 35 21 35 , 29 31 37 14 1 2 3 3 ⟶ 1 13 5 9 8 11 35 21 30 , 29 31 37 14 1 2 3 9 ⟶ 1 13 5 9 8 11 35 21 37 , 29 31 37 14 1 2 3 10 ⟶ 1 13 5 9 8 11 35 21 27 , 29 31 37 14 1 2 3 11 ⟶ 1 13 5 9 8 11 35 21 31 , 29 31 37 14 1 2 3 12 ⟶ 1 13 5 9 8 11 35 21 38 , 21 31 37 14 1 2 3 4 ⟶ 19 13 5 9 8 11 35 21 16 , 21 31 37 14 1 2 3 6 ⟶ 19 13 5 9 8 11 35 21 35 , 21 31 37 14 1 2 3 3 ⟶ 19 13 5 9 8 11 35 21 30 , 21 31 37 14 1 2 3 9 ⟶ 19 13 5 9 8 11 35 21 37 , 21 31 37 14 1 2 3 10 ⟶ 19 13 5 9 8 11 35 21 27 , 21 31 37 14 1 2 3 11 ⟶ 19 13 5 9 8 11 35 21 31 , 21 31 37 14 1 2 3 12 ⟶ 19 13 5 9 8 11 35 21 38 , 11 31 37 14 1 2 3 4 ⟶ 6 13 5 9 8 11 35 21 16 , 11 31 37 14 1 2 3 6 ⟶ 6 13 5 9 8 11 35 21 35 , 11 31 37 14 1 2 3 3 ⟶ 6 13 5 9 8 11 35 21 30 , 11 31 37 14 1 2 3 9 ⟶ 6 13 5 9 8 11 35 21 37 , 11 31 37 14 1 2 3 10 ⟶ 6 13 5 9 8 11 35 21 27 , 11 31 37 14 1 2 3 11 ⟶ 6 13 5 9 8 11 35 21 31 , 11 31 37 14 1 2 3 12 ⟶ 6 13 5 9 8 11 35 21 38 , 32 31 37 14 1 2 3 4 ⟶ 39 13 5 9 8 11 35 21 16 , 32 31 37 14 1 2 3 6 ⟶ 39 13 5 9 8 11 35 21 35 , 32 31 37 14 1 2 3 3 ⟶ 39 13 5 9 8 11 35 21 30 , 32 31 37 14 1 2 3 9 ⟶ 39 13 5 9 8 11 35 21 37 , 32 31 37 14 1 2 3 10 ⟶ 39 13 5 9 8 11 35 21 27 , 32 31 37 14 1 2 3 11 ⟶ 39 13 5 9 8 11 35 21 31 , 32 31 37 14 1 2 3 12 ⟶ 39 13 5 9 8 11 35 21 38 , 33 31 37 14 1 2 3 4 ⟶ 24 13 5 9 8 11 35 21 16 , 33 31 37 14 1 2 3 6 ⟶ 24 13 5 9 8 11 35 21 35 , 33 31 37 14 1 2 3 3 ⟶ 24 13 5 9 8 11 35 21 30 , 33 31 37 14 1 2 3 9 ⟶ 24 13 5 9 8 11 35 21 37 , 33 31 37 14 1 2 3 10 ⟶ 24 13 5 9 8 11 35 21 27 , 33 31 37 14 1 2 3 11 ⟶ 24 13 5 9 8 11 35 21 31 , 33 31 37 14 1 2 3 12 ⟶ 24 13 5 9 8 11 35 21 38 , 31 31 37 14 1 2 3 4 ⟶ 35 13 5 9 8 11 35 21 16 , 31 31 37 14 1 2 3 6 ⟶ 35 13 5 9 8 11 35 21 35 , 31 31 37 14 1 2 3 3 ⟶ 35 13 5 9 8 11 35 21 30 , 31 31 37 14 1 2 3 9 ⟶ 35 13 5 9 8 11 35 21 37 , 31 31 37 14 1 2 3 10 ⟶ 35 13 5 9 8 11 35 21 27 , 31 31 37 14 1 2 3 11 ⟶ 35 13 5 9 8 11 35 21 31 , 31 31 37 14 1 2 3 12 ⟶ 35 13 5 9 8 11 35 21 38 , 34 31 37 14 1 2 3 4 ⟶ 43 13 5 9 8 11 35 21 16 , 34 31 37 14 1 2 3 6 ⟶ 43 13 5 9 8 11 35 21 35 , 34 31 37 14 1 2 3 3 ⟶ 43 13 5 9 8 11 35 21 30 , 34 31 37 14 1 2 3 9 ⟶ 43 13 5 9 8 11 35 21 37 , 34 31 37 14 1 2 3 10 ⟶ 43 13 5 9 8 11 35 21 27 , 34 31 37 14 1 2 3 11 ⟶ 43 13 5 9 8 11 35 21 31 , 34 31 37 14 1 2 3 12 ⟶ 43 13 5 9 8 11 35 21 38 , 1 13 23 41 14 5 3 4 ⟶ 0 18 14 18 39 20 36 3 4 , 1 13 23 41 14 5 3 6 ⟶ 0 18 14 18 39 20 36 3 6 , 1 13 23 41 14 5 3 3 ⟶ 0 18 14 18 39 20 36 3 3 , 1 13 23 41 14 5 3 9 ⟶ 0 18 14 18 39 20 36 3 9 , 1 13 23 41 14 5 3 10 ⟶ 0 18 14 18 39 20 36 3 10 , 1 13 23 41 14 5 3 11 ⟶ 0 18 14 18 39 20 36 3 11 , 1 13 23 41 14 5 3 12 ⟶ 0 18 14 18 39 20 36 3 12 , 19 13 23 41 14 5 3 4 ⟶ 13 18 14 18 39 20 36 3 4 , 19 13 23 41 14 5 3 6 ⟶ 13 18 14 18 39 20 36 3 6 , 19 13 23 41 14 5 3 3 ⟶ 13 18 14 18 39 20 36 3 3 , 19 13 23 41 14 5 3 9 ⟶ 13 18 14 18 39 20 36 3 9 , 19 13 23 41 14 5 3 10 ⟶ 13 18 14 18 39 20 36 3 10 , 19 13 23 41 14 5 3 11 ⟶ 13 18 14 18 39 20 36 3 11 , 19 13 23 41 14 5 3 12 ⟶ 13 18 14 18 39 20 36 3 12 , 6 13 23 41 14 5 3 4 ⟶ 4 18 14 18 39 20 36 3 4 , 6 13 23 41 14 5 3 6 ⟶ 4 18 14 18 39 20 36 3 6 , 6 13 23 41 14 5 3 3 ⟶ 4 18 14 18 39 20 36 3 3 , 6 13 23 41 14 5 3 9 ⟶ 4 18 14 18 39 20 36 3 9 , 6 13 23 41 14 5 3 10 ⟶ 4 18 14 18 39 20 36 3 10 , 6 13 23 41 14 5 3 11 ⟶ 4 18 14 18 39 20 36 3 11 , 6 13 23 41 14 5 3 12 ⟶ 4 18 14 18 39 20 36 3 12 , 39 13 23 41 14 5 3 4 ⟶ 14 18 14 18 39 20 36 3 4 , 39 13 23 41 14 5 3 6 ⟶ 14 18 14 18 39 20 36 3 6 , 39 13 23 41 14 5 3 3 ⟶ 14 18 14 18 39 20 36 3 3 , 39 13 23 41 14 5 3 9 ⟶ 14 18 14 18 39 20 36 3 9 , 39 13 23 41 14 5 3 10 ⟶ 14 18 14 18 39 20 36 3 10 , 39 13 23 41 14 5 3 11 ⟶ 14 18 14 18 39 20 36 3 11 , 39 13 23 41 14 5 3 12 ⟶ 14 18 14 18 39 20 36 3 12 , 24 13 23 41 14 5 3 4 ⟶ 15 18 14 18 39 20 36 3 4 , 24 13 23 41 14 5 3 6 ⟶ 15 18 14 18 39 20 36 3 6 , 24 13 23 41 14 5 3 3 ⟶ 15 18 14 18 39 20 36 3 3 , 24 13 23 41 14 5 3 9 ⟶ 15 18 14 18 39 20 36 3 9 , 24 13 23 41 14 5 3 10 ⟶ 15 18 14 18 39 20 36 3 10 , 24 13 23 41 14 5 3 11 ⟶ 15 18 14 18 39 20 36 3 11 , 24 13 23 41 14 5 3 12 ⟶ 15 18 14 18 39 20 36 3 12 , 35 13 23 41 14 5 3 4 ⟶ 16 18 14 18 39 20 36 3 4 , 35 13 23 41 14 5 3 6 ⟶ 16 18 14 18 39 20 36 3 6 , 35 13 23 41 14 5 3 3 ⟶ 16 18 14 18 39 20 36 3 3 , 35 13 23 41 14 5 3 9 ⟶ 16 18 14 18 39 20 36 3 9 , 35 13 23 41 14 5 3 10 ⟶ 16 18 14 18 39 20 36 3 10 , 35 13 23 41 14 5 3 11 ⟶ 16 18 14 18 39 20 36 3 11 , 35 13 23 41 14 5 3 12 ⟶ 16 18 14 18 39 20 36 3 12 , 43 13 23 41 14 5 3 4 ⟶ 17 18 14 18 39 20 36 3 4 , 43 13 23 41 14 5 3 6 ⟶ 17 18 14 18 39 20 36 3 6 , 43 13 23 41 14 5 3 3 ⟶ 17 18 14 18 39 20 36 3 3 , 43 13 23 41 14 5 3 9 ⟶ 17 18 14 18 39 20 36 3 9 , 43 13 23 41 14 5 3 10 ⟶ 17 18 14 18 39 20 36 3 10 , 43 13 23 41 14 5 3 11 ⟶ 17 18 14 18 39 20 36 3 11 , 43 13 23 41 14 5 3 12 ⟶ 17 18 14 18 39 20 36 3 12 , 23 41 32 30 3 6 2 4 ⟶ 1 7 25 36 11 30 9 8 4 , 23 41 32 30 3 6 2 6 ⟶ 1 7 25 36 11 30 9 8 6 , 23 41 32 30 3 6 2 3 ⟶ 1 7 25 36 11 30 9 8 3 , 23 41 32 30 3 6 2 9 ⟶ 1 7 25 36 11 30 9 8 9 , 23 41 32 30 3 6 2 10 ⟶ 1 7 25 36 11 30 9 8 10 , 23 41 32 30 3 6 2 11 ⟶ 1 7 25 36 11 30 9 8 11 , 23 41 32 30 3 6 2 12 ⟶ 1 7 25 36 11 30 9 8 12 , 20 41 32 30 3 6 2 4 ⟶ 19 7 25 36 11 30 9 8 4 , 20 41 32 30 3 6 2 6 ⟶ 19 7 25 36 11 30 9 8 6 , 20 41 32 30 3 6 2 3 ⟶ 19 7 25 36 11 30 9 8 3 , 20 41 32 30 3 6 2 9 ⟶ 19 7 25 36 11 30 9 8 9 , 20 41 32 30 3 6 2 10 ⟶ 19 7 25 36 11 30 9 8 10 , 20 41 32 30 3 6 2 11 ⟶ 19 7 25 36 11 30 9 8 11 , 20 41 32 30 3 6 2 12 ⟶ 19 7 25 36 11 30 9 8 12 , 10 41 32 30 3 6 2 4 ⟶ 6 7 25 36 11 30 9 8 4 , 10 41 32 30 3 6 2 6 ⟶ 6 7 25 36 11 30 9 8 6 , 10 41 32 30 3 6 2 3 ⟶ 6 7 25 36 11 30 9 8 3 , 10 41 32 30 3 6 2 9 ⟶ 6 7 25 36 11 30 9 8 9 , 10 41 32 30 3 6 2 10 ⟶ 6 7 25 36 11 30 9 8 10 , 10 41 32 30 3 6 2 11 ⟶ 6 7 25 36 11 30 9 8 11 , 10 41 32 30 3 6 2 12 ⟶ 6 7 25 36 11 30 9 8 12 , 25 41 32 30 3 6 2 4 ⟶ 39 7 25 36 11 30 9 8 4 , 25 41 32 30 3 6 2 6 ⟶ 39 7 25 36 11 30 9 8 6 , 25 41 32 30 3 6 2 3 ⟶ 39 7 25 36 11 30 9 8 3 , 25 41 32 30 3 6 2 9 ⟶ 39 7 25 36 11 30 9 8 9 , 25 41 32 30 3 6 2 10 ⟶ 39 7 25 36 11 30 9 8 10 , 25 41 32 30 3 6 2 11 ⟶ 39 7 25 36 11 30 9 8 11 , 25 41 32 30 3 6 2 12 ⟶ 39 7 25 36 11 30 9 8 12 , 26 41 32 30 3 6 2 4 ⟶ 24 7 25 36 11 30 9 8 4 , 26 41 32 30 3 6 2 6 ⟶ 24 7 25 36 11 30 9 8 6 , 26 41 32 30 3 6 2 3 ⟶ 24 7 25 36 11 30 9 8 3 , 26 41 32 30 3 6 2 9 ⟶ 24 7 25 36 11 30 9 8 9 , 26 41 32 30 3 6 2 10 ⟶ 24 7 25 36 11 30 9 8 10 , 26 41 32 30 3 6 2 11 ⟶ 24 7 25 36 11 30 9 8 11 , 26 41 32 30 3 6 2 12 ⟶ 24 7 25 36 11 30 9 8 12 , 27 41 32 30 3 6 2 4 ⟶ 35 7 25 36 11 30 9 8 4 , 27 41 32 30 3 6 2 6 ⟶ 35 7 25 36 11 30 9 8 6 , 27 41 32 30 3 6 2 3 ⟶ 35 7 25 36 11 30 9 8 3 , 27 41 32 30 3 6 2 9 ⟶ 35 7 25 36 11 30 9 8 9 , 27 41 32 30 3 6 2 10 ⟶ 35 7 25 36 11 30 9 8 10 , 27 41 32 30 3 6 2 11 ⟶ 35 7 25 36 11 30 9 8 11 , 27 41 32 30 3 6 2 12 ⟶ 35 7 25 36 11 30 9 8 12 , 28 41 32 30 3 6 2 4 ⟶ 43 7 25 36 11 30 9 8 4 , 28 41 32 30 3 6 2 6 ⟶ 43 7 25 36 11 30 9 8 6 , 28 41 32 30 3 6 2 3 ⟶ 43 7 25 36 11 30 9 8 3 , 28 41 32 30 3 6 2 9 ⟶ 43 7 25 36 11 30 9 8 9 , 28 41 32 30 3 6 2 10 ⟶ 43 7 25 36 11 30 9 8 10 , 28 41 32 30 3 6 2 11 ⟶ 43 7 25 36 11 30 9 8 11 , 28 41 32 30 3 6 2 12 ⟶ 43 7 25 36 11 30 9 8 12 , 29 30 10 26 15 1 2 4 ⟶ 23 15 18 8 6 2 10 33 16 , 29 30 10 26 15 1 2 6 ⟶ 23 15 18 8 6 2 10 33 35 , 29 30 10 26 15 1 2 3 ⟶ 23 15 18 8 6 2 10 33 30 , 29 30 10 26 15 1 2 9 ⟶ 23 15 18 8 6 2 10 33 37 , 29 30 10 26 15 1 2 10 ⟶ 23 15 18 8 6 2 10 33 27 , 29 30 10 26 15 1 2 11 ⟶ 23 15 18 8 6 2 10 33 31 , 29 30 10 26 15 1 2 12 ⟶ 23 15 18 8 6 2 10 33 38 , 21 30 10 26 15 1 2 4 ⟶ 20 15 18 8 6 2 10 33 16 , 21 30 10 26 15 1 2 6 ⟶ 20 15 18 8 6 2 10 33 35 , 21 30 10 26 15 1 2 3 ⟶ 20 15 18 8 6 2 10 33 30 , 21 30 10 26 15 1 2 9 ⟶ 20 15 18 8 6 2 10 33 37 , 21 30 10 26 15 1 2 10 ⟶ 20 15 18 8 6 2 10 33 27 , 21 30 10 26 15 1 2 11 ⟶ 20 15 18 8 6 2 10 33 31 , 21 30 10 26 15 1 2 12 ⟶ 20 15 18 8 6 2 10 33 38 , 11 30 10 26 15 1 2 4 ⟶ 10 15 18 8 6 2 10 33 16 , 11 30 10 26 15 1 2 6 ⟶ 10 15 18 8 6 2 10 33 35 , 11 30 10 26 15 1 2 3 ⟶ 10 15 18 8 6 2 10 33 30 , 11 30 10 26 15 1 2 9 ⟶ 10 15 18 8 6 2 10 33 37 , 11 30 10 26 15 1 2 10 ⟶ 10 15 18 8 6 2 10 33 27 , 11 30 10 26 15 1 2 11 ⟶ 10 15 18 8 6 2 10 33 31 , 11 30 10 26 15 1 2 12 ⟶ 10 15 18 8 6 2 10 33 38 , 32 30 10 26 15 1 2 4 ⟶ 25 15 18 8 6 2 10 33 16 , 32 30 10 26 15 1 2 6 ⟶ 25 15 18 8 6 2 10 33 35 , 32 30 10 26 15 1 2 3 ⟶ 25 15 18 8 6 2 10 33 30 , 32 30 10 26 15 1 2 9 ⟶ 25 15 18 8 6 2 10 33 37 , 32 30 10 26 15 1 2 10 ⟶ 25 15 18 8 6 2 10 33 27 , 32 30 10 26 15 1 2 11 ⟶ 25 15 18 8 6 2 10 33 31 , 32 30 10 26 15 1 2 12 ⟶ 25 15 18 8 6 2 10 33 38 , 33 30 10 26 15 1 2 4 ⟶ 26 15 18 8 6 2 10 33 16 , 33 30 10 26 15 1 2 6 ⟶ 26 15 18 8 6 2 10 33 35 , 33 30 10 26 15 1 2 3 ⟶ 26 15 18 8 6 2 10 33 30 , 33 30 10 26 15 1 2 9 ⟶ 26 15 18 8 6 2 10 33 37 , 33 30 10 26 15 1 2 10 ⟶ 26 15 18 8 6 2 10 33 27 , 33 30 10 26 15 1 2 11 ⟶ 26 15 18 8 6 2 10 33 31 , 33 30 10 26 15 1 2 12 ⟶ 26 15 18 8 6 2 10 33 38 , 31 30 10 26 15 1 2 4 ⟶ 27 15 18 8 6 2 10 33 16 , 31 30 10 26 15 1 2 6 ⟶ 27 15 18 8 6 2 10 33 35 , 31 30 10 26 15 1 2 3 ⟶ 27 15 18 8 6 2 10 33 30 , 31 30 10 26 15 1 2 9 ⟶ 27 15 18 8 6 2 10 33 37 , 31 30 10 26 15 1 2 10 ⟶ 27 15 18 8 6 2 10 33 27 , 31 30 10 26 15 1 2 11 ⟶ 27 15 18 8 6 2 10 33 31 , 31 30 10 26 15 1 2 12 ⟶ 27 15 18 8 6 2 10 33 38 , 34 30 10 26 15 1 2 4 ⟶ 28 15 18 8 6 2 10 33 16 , 34 30 10 26 15 1 2 6 ⟶ 28 15 18 8 6 2 10 33 35 , 34 30 10 26 15 1 2 3 ⟶ 28 15 18 8 6 2 10 33 30 , 34 30 10 26 15 1 2 9 ⟶ 28 15 18 8 6 2 10 33 37 , 34 30 10 26 15 1 2 10 ⟶ 28 15 18 8 6 2 10 33 27 , 34 30 10 26 15 1 2 11 ⟶ 28 15 18 8 6 2 10 33 31 , 34 30 10 26 15 1 2 12 ⟶ 28 15 18 8 6 2 10 33 38 , 23 41 39 21 16 29 30 4 ⟶ 29 35 7 8 4 29 27 24 13 , 23 41 39 21 16 29 30 6 ⟶ 29 35 7 8 4 29 27 24 19 , 23 41 39 21 16 29 30 3 ⟶ 29 35 7 8 4 29 27 24 2 , 23 41 39 21 16 29 30 9 ⟶ 29 35 7 8 4 29 27 24 7 , 23 41 39 21 16 29 30 10 ⟶ 29 35 7 8 4 29 27 24 20 , 23 41 39 21 16 29 30 11 ⟶ 29 35 7 8 4 29 27 24 21 , 23 41 39 21 16 29 30 12 ⟶ 29 35 7 8 4 29 27 24 22 , 20 41 39 21 16 29 30 4 ⟶ 21 35 7 8 4 29 27 24 13 , 20 41 39 21 16 29 30 6 ⟶ 21 35 7 8 4 29 27 24 19 , 20 41 39 21 16 29 30 3 ⟶ 21 35 7 8 4 29 27 24 2 , 20 41 39 21 16 29 30 9 ⟶ 21 35 7 8 4 29 27 24 7 , 20 41 39 21 16 29 30 10 ⟶ 21 35 7 8 4 29 27 24 20 , 20 41 39 21 16 29 30 11 ⟶ 21 35 7 8 4 29 27 24 21 , 20 41 39 21 16 29 30 12 ⟶ 21 35 7 8 4 29 27 24 22 , 10 41 39 21 16 29 30 4 ⟶ 11 35 7 8 4 29 27 24 13 , 10 41 39 21 16 29 30 6 ⟶ 11 35 7 8 4 29 27 24 19 , 10 41 39 21 16 29 30 3 ⟶ 11 35 7 8 4 29 27 24 2 , 10 41 39 21 16 29 30 9 ⟶ 11 35 7 8 4 29 27 24 7 , 10 41 39 21 16 29 30 10 ⟶ 11 35 7 8 4 29 27 24 20 , 10 41 39 21 16 29 30 11 ⟶ 11 35 7 8 4 29 27 24 21 , 10 41 39 21 16 29 30 12 ⟶ 11 35 7 8 4 29 27 24 22 , 25 41 39 21 16 29 30 4 ⟶ 32 35 7 8 4 29 27 24 13 , 25 41 39 21 16 29 30 6 ⟶ 32 35 7 8 4 29 27 24 19 , 25 41 39 21 16 29 30 3 ⟶ 32 35 7 8 4 29 27 24 2 , 25 41 39 21 16 29 30 9 ⟶ 32 35 7 8 4 29 27 24 7 , 25 41 39 21 16 29 30 10 ⟶ 32 35 7 8 4 29 27 24 20 , 25 41 39 21 16 29 30 11 ⟶ 32 35 7 8 4 29 27 24 21 , 25 41 39 21 16 29 30 12 ⟶ 32 35 7 8 4 29 27 24 22 , 26 41 39 21 16 29 30 4 ⟶ 33 35 7 8 4 29 27 24 13 , 26 41 39 21 16 29 30 6 ⟶ 33 35 7 8 4 29 27 24 19 , 26 41 39 21 16 29 30 3 ⟶ 33 35 7 8 4 29 27 24 2 , 26 41 39 21 16 29 30 9 ⟶ 33 35 7 8 4 29 27 24 7 , 26 41 39 21 16 29 30 10 ⟶ 33 35 7 8 4 29 27 24 20 , 26 41 39 21 16 29 30 11 ⟶ 33 35 7 8 4 29 27 24 21 , 26 41 39 21 16 29 30 12 ⟶ 33 35 7 8 4 29 27 24 22 , 27 41 39 21 16 29 30 4 ⟶ 31 35 7 8 4 29 27 24 13 , 27 41 39 21 16 29 30 6 ⟶ 31 35 7 8 4 29 27 24 19 , 27 41 39 21 16 29 30 3 ⟶ 31 35 7 8 4 29 27 24 2 , 27 41 39 21 16 29 30 9 ⟶ 31 35 7 8 4 29 27 24 7 , 27 41 39 21 16 29 30 10 ⟶ 31 35 7 8 4 29 27 24 20 , 27 41 39 21 16 29 30 11 ⟶ 31 35 7 8 4 29 27 24 21 , 27 41 39 21 16 29 30 12 ⟶ 31 35 7 8 4 29 27 24 22 , 28 41 39 21 16 29 30 4 ⟶ 34 35 7 8 4 29 27 24 13 , 28 41 39 21 16 29 30 6 ⟶ 34 35 7 8 4 29 27 24 19 , 28 41 39 21 16 29 30 3 ⟶ 34 35 7 8 4 29 27 24 2 , 28 41 39 21 16 29 30 9 ⟶ 34 35 7 8 4 29 27 24 7 , 28 41 39 21 16 29 30 10 ⟶ 34 35 7 8 4 29 27 24 20 , 28 41 39 21 16 29 30 11 ⟶ 34 35 7 8 4 29 27 24 21 , 28 41 39 21 16 29 30 12 ⟶ 34 35 7 8 4 29 27 24 22 , 1 21 16 5 11 31 30 4 ⟶ 29 16 29 35 2 3 9 32 16 , 1 21 16 5 11 31 30 6 ⟶ 29 16 29 35 2 3 9 32 35 , 1 21 16 5 11 31 30 3 ⟶ 29 16 29 35 2 3 9 32 30 , 1 21 16 5 11 31 30 9 ⟶ 29 16 29 35 2 3 9 32 37 , 1 21 16 5 11 31 30 10 ⟶ 29 16 29 35 2 3 9 32 27 , 1 21 16 5 11 31 30 11 ⟶ 29 16 29 35 2 3 9 32 31 , 1 21 16 5 11 31 30 12 ⟶ 29 16 29 35 2 3 9 32 38 , 19 21 16 5 11 31 30 4 ⟶ 21 16 29 35 2 3 9 32 16 , 19 21 16 5 11 31 30 6 ⟶ 21 16 29 35 2 3 9 32 35 , 19 21 16 5 11 31 30 3 ⟶ 21 16 29 35 2 3 9 32 30 , 19 21 16 5 11 31 30 9 ⟶ 21 16 29 35 2 3 9 32 37 , 19 21 16 5 11 31 30 10 ⟶ 21 16 29 35 2 3 9 32 27 , 19 21 16 5 11 31 30 11 ⟶ 21 16 29 35 2 3 9 32 31 , 19 21 16 5 11 31 30 12 ⟶ 21 16 29 35 2 3 9 32 38 , 6 21 16 5 11 31 30 4 ⟶ 11 16 29 35 2 3 9 32 16 , 6 21 16 5 11 31 30 6 ⟶ 11 16 29 35 2 3 9 32 35 , 6 21 16 5 11 31 30 3 ⟶ 11 16 29 35 2 3 9 32 30 , 6 21 16 5 11 31 30 9 ⟶ 11 16 29 35 2 3 9 32 37 , 6 21 16 5 11 31 30 10 ⟶ 11 16 29 35 2 3 9 32 27 , 6 21 16 5 11 31 30 11 ⟶ 11 16 29 35 2 3 9 32 31 , 6 21 16 5 11 31 30 12 ⟶ 11 16 29 35 2 3 9 32 38 , 39 21 16 5 11 31 30 4 ⟶ 32 16 29 35 2 3 9 32 16 , 39 21 16 5 11 31 30 6 ⟶ 32 16 29 35 2 3 9 32 35 , 39 21 16 5 11 31 30 3 ⟶ 32 16 29 35 2 3 9 32 30 , 39 21 16 5 11 31 30 9 ⟶ 32 16 29 35 2 3 9 32 37 , 39 21 16 5 11 31 30 10 ⟶ 32 16 29 35 2 3 9 32 27 , 39 21 16 5 11 31 30 11 ⟶ 32 16 29 35 2 3 9 32 31 , 39 21 16 5 11 31 30 12 ⟶ 32 16 29 35 2 3 9 32 38 , 24 21 16 5 11 31 30 4 ⟶ 33 16 29 35 2 3 9 32 16 , 24 21 16 5 11 31 30 6 ⟶ 33 16 29 35 2 3 9 32 35 , 24 21 16 5 11 31 30 3 ⟶ 33 16 29 35 2 3 9 32 30 , 24 21 16 5 11 31 30 9 ⟶ 33 16 29 35 2 3 9 32 37 , 24 21 16 5 11 31 30 10 ⟶ 33 16 29 35 2 3 9 32 27 , 24 21 16 5 11 31 30 11 ⟶ 33 16 29 35 2 3 9 32 31 , 24 21 16 5 11 31 30 12 ⟶ 33 16 29 35 2 3 9 32 38 , 35 21 16 5 11 31 30 4 ⟶ 31 16 29 35 2 3 9 32 16 , 35 21 16 5 11 31 30 6 ⟶ 31 16 29 35 2 3 9 32 35 , 35 21 16 5 11 31 30 3 ⟶ 31 16 29 35 2 3 9 32 30 , 35 21 16 5 11 31 30 9 ⟶ 31 16 29 35 2 3 9 32 37 , 35 21 16 5 11 31 30 10 ⟶ 31 16 29 35 2 3 9 32 27 , 35 21 16 5 11 31 30 11 ⟶ 31 16 29 35 2 3 9 32 31 , 35 21 16 5 11 31 30 12 ⟶ 31 16 29 35 2 3 9 32 38 , 43 21 16 5 11 31 30 4 ⟶ 34 16 29 35 2 3 9 32 16 , 43 21 16 5 11 31 30 6 ⟶ 34 16 29 35 2 3 9 32 35 , 43 21 16 5 11 31 30 3 ⟶ 34 16 29 35 2 3 9 32 30 , 43 21 16 5 11 31 30 9 ⟶ 34 16 29 35 2 3 9 32 37 , 43 21 16 5 11 31 30 10 ⟶ 34 16 29 35 2 3 9 32 27 , 43 21 16 5 11 31 30 11 ⟶ 34 16 29 35 2 3 9 32 31 , 43 21 16 5 11 31 30 12 ⟶ 34 16 29 35 2 3 9 32 38 , 23 41 32 16 29 31 30 4 ⟶ 29 31 31 27 24 13 18 8 4 , 23 41 32 16 29 31 30 6 ⟶ 29 31 31 27 24 13 18 8 6 , 23 41 32 16 29 31 30 3 ⟶ 29 31 31 27 24 13 18 8 3 , 23 41 32 16 29 31 30 9 ⟶ 29 31 31 27 24 13 18 8 9 , 23 41 32 16 29 31 30 10 ⟶ 29 31 31 27 24 13 18 8 10 , 23 41 32 16 29 31 30 11 ⟶ 29 31 31 27 24 13 18 8 11 , 23 41 32 16 29 31 30 12 ⟶ 29 31 31 27 24 13 18 8 12 , 20 41 32 16 29 31 30 4 ⟶ 21 31 31 27 24 13 18 8 4 , 20 41 32 16 29 31 30 6 ⟶ 21 31 31 27 24 13 18 8 6 , 20 41 32 16 29 31 30 3 ⟶ 21 31 31 27 24 13 18 8 3 , 20 41 32 16 29 31 30 9 ⟶ 21 31 31 27 24 13 18 8 9 , 20 41 32 16 29 31 30 10 ⟶ 21 31 31 27 24 13 18 8 10 , 20 41 32 16 29 31 30 11 ⟶ 21 31 31 27 24 13 18 8 11 , 20 41 32 16 29 31 30 12 ⟶ 21 31 31 27 24 13 18 8 12 , 10 41 32 16 29 31 30 4 ⟶ 11 31 31 27 24 13 18 8 4 , 10 41 32 16 29 31 30 6 ⟶ 11 31 31 27 24 13 18 8 6 , 10 41 32 16 29 31 30 3 ⟶ 11 31 31 27 24 13 18 8 3 , 10 41 32 16 29 31 30 9 ⟶ 11 31 31 27 24 13 18 8 9 , 10 41 32 16 29 31 30 10 ⟶ 11 31 31 27 24 13 18 8 10 , 10 41 32 16 29 31 30 11 ⟶ 11 31 31 27 24 13 18 8 11 , 10 41 32 16 29 31 30 12 ⟶ 11 31 31 27 24 13 18 8 12 , 25 41 32 16 29 31 30 4 ⟶ 32 31 31 27 24 13 18 8 4 , 25 41 32 16 29 31 30 6 ⟶ 32 31 31 27 24 13 18 8 6 , 25 41 32 16 29 31 30 3 ⟶ 32 31 31 27 24 13 18 8 3 , 25 41 32 16 29 31 30 9 ⟶ 32 31 31 27 24 13 18 8 9 , 25 41 32 16 29 31 30 10 ⟶ 32 31 31 27 24 13 18 8 10 , 25 41 32 16 29 31 30 11 ⟶ 32 31 31 27 24 13 18 8 11 , 25 41 32 16 29 31 30 12 ⟶ 32 31 31 27 24 13 18 8 12 , 26 41 32 16 29 31 30 4 ⟶ 33 31 31 27 24 13 18 8 4 , 26 41 32 16 29 31 30 6 ⟶ 33 31 31 27 24 13 18 8 6 , 26 41 32 16 29 31 30 3 ⟶ 33 31 31 27 24 13 18 8 3 , 26 41 32 16 29 31 30 9 ⟶ 33 31 31 27 24 13 18 8 9 , 26 41 32 16 29 31 30 10 ⟶ 33 31 31 27 24 13 18 8 10 , 26 41 32 16 29 31 30 11 ⟶ 33 31 31 27 24 13 18 8 11 , 26 41 32 16 29 31 30 12 ⟶ 33 31 31 27 24 13 18 8 12 , 27 41 32 16 29 31 30 4 ⟶ 31 31 31 27 24 13 18 8 4 , 27 41 32 16 29 31 30 6 ⟶ 31 31 31 27 24 13 18 8 6 , 27 41 32 16 29 31 30 3 ⟶ 31 31 31 27 24 13 18 8 3 , 27 41 32 16 29 31 30 9 ⟶ 31 31 31 27 24 13 18 8 9 , 27 41 32 16 29 31 30 10 ⟶ 31 31 31 27 24 13 18 8 10 , 27 41 32 16 29 31 30 11 ⟶ 31 31 31 27 24 13 18 8 11 , 27 41 32 16 29 31 30 12 ⟶ 31 31 31 27 24 13 18 8 12 , 28 41 32 16 29 31 30 4 ⟶ 34 31 31 27 24 13 18 8 4 , 28 41 32 16 29 31 30 6 ⟶ 34 31 31 27 24 13 18 8 6 , 28 41 32 16 29 31 30 3 ⟶ 34 31 31 27 24 13 18 8 3 , 28 41 32 16 29 31 30 9 ⟶ 34 31 31 27 24 13 18 8 9 , 28 41 32 16 29 31 30 10 ⟶ 34 31 31 27 24 13 18 8 10 , 28 41 32 16 29 31 30 11 ⟶ 34 31 31 27 24 13 18 8 11 , 28 41 32 16 29 31 30 12 ⟶ 34 31 31 27 24 13 18 8 12 , 29 27 41 14 1 2 6 13 ⟶ 23 41 39 21 35 13 5 9 14 , 29 27 41 14 1 2 6 19 ⟶ 23 41 39 21 35 13 5 9 39 , 29 27 41 14 1 2 6 2 ⟶ 23 41 39 21 35 13 5 9 8 , 29 27 41 14 1 2 6 7 ⟶ 23 41 39 21 35 13 5 9 40 , 29 27 41 14 1 2 6 20 ⟶ 23 41 39 21 35 13 5 9 25 , 29 27 41 14 1 2 6 21 ⟶ 23 41 39 21 35 13 5 9 32 , 29 27 41 14 1 2 6 22 ⟶ 23 41 39 21 35 13 5 9 44 , 21 27 41 14 1 2 6 13 ⟶ 20 41 39 21 35 13 5 9 14 , 21 27 41 14 1 2 6 19 ⟶ 20 41 39 21 35 13 5 9 39 , 21 27 41 14 1 2 6 2 ⟶ 20 41 39 21 35 13 5 9 8 , 21 27 41 14 1 2 6 7 ⟶ 20 41 39 21 35 13 5 9 40 , 21 27 41 14 1 2 6 20 ⟶ 20 41 39 21 35 13 5 9 25 , 21 27 41 14 1 2 6 21 ⟶ 20 41 39 21 35 13 5 9 32 , 21 27 41 14 1 2 6 22 ⟶ 20 41 39 21 35 13 5 9 44 , 11 27 41 14 1 2 6 13 ⟶ 10 41 39 21 35 13 5 9 14 , 11 27 41 14 1 2 6 19 ⟶ 10 41 39 21 35 13 5 9 39 , 11 27 41 14 1 2 6 2 ⟶ 10 41 39 21 35 13 5 9 8 , 11 27 41 14 1 2 6 7 ⟶ 10 41 39 21 35 13 5 9 40 , 11 27 41 14 1 2 6 20 ⟶ 10 41 39 21 35 13 5 9 25 , 11 27 41 14 1 2 6 21 ⟶ 10 41 39 21 35 13 5 9 32 , 11 27 41 14 1 2 6 22 ⟶ 10 41 39 21 35 13 5 9 44 , 32 27 41 14 1 2 6 13 ⟶ 25 41 39 21 35 13 5 9 14 , 32 27 41 14 1 2 6 19 ⟶ 25 41 39 21 35 13 5 9 39 , 32 27 41 14 1 2 6 2 ⟶ 25 41 39 21 35 13 5 9 8 , 32 27 41 14 1 2 6 7 ⟶ 25 41 39 21 35 13 5 9 40 , 32 27 41 14 1 2 6 20 ⟶ 25 41 39 21 35 13 5 9 25 , 32 27 41 14 1 2 6 21 ⟶ 25 41 39 21 35 13 5 9 32 , 32 27 41 14 1 2 6 22 ⟶ 25 41 39 21 35 13 5 9 44 , 33 27 41 14 1 2 6 13 ⟶ 26 41 39 21 35 13 5 9 14 , 33 27 41 14 1 2 6 19 ⟶ 26 41 39 21 35 13 5 9 39 , 33 27 41 14 1 2 6 2 ⟶ 26 41 39 21 35 13 5 9 8 , 33 27 41 14 1 2 6 7 ⟶ 26 41 39 21 35 13 5 9 40 , 33 27 41 14 1 2 6 20 ⟶ 26 41 39 21 35 13 5 9 25 , 33 27 41 14 1 2 6 21 ⟶ 26 41 39 21 35 13 5 9 32 , 33 27 41 14 1 2 6 22 ⟶ 26 41 39 21 35 13 5 9 44 , 31 27 41 14 1 2 6 13 ⟶ 27 41 39 21 35 13 5 9 14 , 31 27 41 14 1 2 6 19 ⟶ 27 41 39 21 35 13 5 9 39 , 31 27 41 14 1 2 6 2 ⟶ 27 41 39 21 35 13 5 9 8 , 31 27 41 14 1 2 6 7 ⟶ 27 41 39 21 35 13 5 9 40 , 31 27 41 14 1 2 6 20 ⟶ 27 41 39 21 35 13 5 9 25 , 31 27 41 14 1 2 6 21 ⟶ 27 41 39 21 35 13 5 9 32 , 31 27 41 14 1 2 6 22 ⟶ 27 41 39 21 35 13 5 9 44 , 34 27 41 14 1 2 6 13 ⟶ 28 41 39 21 35 13 5 9 14 , 34 27 41 14 1 2 6 19 ⟶ 28 41 39 21 35 13 5 9 39 , 34 27 41 14 1 2 6 2 ⟶ 28 41 39 21 35 13 5 9 8 , 34 27 41 14 1 2 6 7 ⟶ 28 41 39 21 35 13 5 9 40 , 34 27 41 14 1 2 6 20 ⟶ 28 41 39 21 35 13 5 9 25 , 34 27 41 14 1 2 6 21 ⟶ 28 41 39 21 35 13 5 9 32 , 34 27 41 14 1 2 6 22 ⟶ 28 41 39 21 35 13 5 9 44 , 0 0 5 4 5 6 19 13 ⟶ 0 0 18 8 4 5 6 19 13 , 0 0 5 4 5 6 19 19 ⟶ 0 0 18 8 4 5 6 19 19 , 0 0 5 4 5 6 19 2 ⟶ 0 0 18 8 4 5 6 19 2 , 0 0 5 4 5 6 19 7 ⟶ 0 0 18 8 4 5 6 19 7 , 0 0 5 4 5 6 19 20 ⟶ 0 0 18 8 4 5 6 19 20 , 0 0 5 4 5 6 19 21 ⟶ 0 0 18 8 4 5 6 19 21 , 0 0 5 4 5 6 19 22 ⟶ 0 0 18 8 4 5 6 19 22 , 13 0 5 4 5 6 19 13 ⟶ 13 0 18 8 4 5 6 19 13 , 13 0 5 4 5 6 19 19 ⟶ 13 0 18 8 4 5 6 19 19 , 13 0 5 4 5 6 19 2 ⟶ 13 0 18 8 4 5 6 19 2 , 13 0 5 4 5 6 19 7 ⟶ 13 0 18 8 4 5 6 19 7 , 13 0 5 4 5 6 19 20 ⟶ 13 0 18 8 4 5 6 19 20 , 13 0 5 4 5 6 19 21 ⟶ 13 0 18 8 4 5 6 19 21 , 13 0 5 4 5 6 19 22 ⟶ 13 0 18 8 4 5 6 19 22 , 4 0 5 4 5 6 19 13 ⟶ 4 0 18 8 4 5 6 19 13 , 4 0 5 4 5 6 19 19 ⟶ 4 0 18 8 4 5 6 19 19 , 4 0 5 4 5 6 19 2 ⟶ 4 0 18 8 4 5 6 19 2 , 4 0 5 4 5 6 19 7 ⟶ 4 0 18 8 4 5 6 19 7 , 4 0 5 4 5 6 19 20 ⟶ 4 0 18 8 4 5 6 19 20 , 4 0 5 4 5 6 19 21 ⟶ 4 0 18 8 4 5 6 19 21 , 4 0 5 4 5 6 19 22 ⟶ 4 0 18 8 4 5 6 19 22 , 14 0 5 4 5 6 19 13 ⟶ 14 0 18 8 4 5 6 19 13 , 14 0 5 4 5 6 19 19 ⟶ 14 0 18 8 4 5 6 19 19 , 14 0 5 4 5 6 19 2 ⟶ 14 0 18 8 4 5 6 19 2 , 14 0 5 4 5 6 19 7 ⟶ 14 0 18 8 4 5 6 19 7 , 14 0 5 4 5 6 19 20 ⟶ 14 0 18 8 4 5 6 19 20 , 14 0 5 4 5 6 19 21 ⟶ 14 0 18 8 4 5 6 19 21 , 14 0 5 4 5 6 19 22 ⟶ 14 0 18 8 4 5 6 19 22 , 15 0 5 4 5 6 19 13 ⟶ 15 0 18 8 4 5 6 19 13 , 15 0 5 4 5 6 19 19 ⟶ 15 0 18 8 4 5 6 19 19 , 15 0 5 4 5 6 19 2 ⟶ 15 0 18 8 4 5 6 19 2 , 15 0 5 4 5 6 19 7 ⟶ 15 0 18 8 4 5 6 19 7 , 15 0 5 4 5 6 19 20 ⟶ 15 0 18 8 4 5 6 19 20 , 15 0 5 4 5 6 19 21 ⟶ 15 0 18 8 4 5 6 19 21 , 15 0 5 4 5 6 19 22 ⟶ 15 0 18 8 4 5 6 19 22 , 16 0 5 4 5 6 19 13 ⟶ 16 0 18 8 4 5 6 19 13 , 16 0 5 4 5 6 19 19 ⟶ 16 0 18 8 4 5 6 19 19 , 16 0 5 4 5 6 19 2 ⟶ 16 0 18 8 4 5 6 19 2 , 16 0 5 4 5 6 19 7 ⟶ 16 0 18 8 4 5 6 19 7 , 16 0 5 4 5 6 19 20 ⟶ 16 0 18 8 4 5 6 19 20 , 16 0 5 4 5 6 19 21 ⟶ 16 0 18 8 4 5 6 19 21 , 16 0 5 4 5 6 19 22 ⟶ 16 0 18 8 4 5 6 19 22 , 17 0 5 4 5 6 19 13 ⟶ 17 0 18 8 4 5 6 19 13 , 17 0 5 4 5 6 19 19 ⟶ 17 0 18 8 4 5 6 19 19 , 17 0 5 4 5 6 19 2 ⟶ 17 0 18 8 4 5 6 19 2 , 17 0 5 4 5 6 19 7 ⟶ 17 0 18 8 4 5 6 19 7 , 17 0 5 4 5 6 19 20 ⟶ 17 0 18 8 4 5 6 19 20 , 17 0 5 4 5 6 19 21 ⟶ 17 0 18 8 4 5 6 19 21 , 17 0 5 4 5 6 19 22 ⟶ 17 0 18 8 4 5 6 19 22 , 29 37 32 37 25 15 1 13 ⟶ 29 37 25 15 0 18 39 21 16 , 29 37 32 37 25 15 1 19 ⟶ 29 37 25 15 0 18 39 21 35 , 29 37 32 37 25 15 1 2 ⟶ 29 37 25 15 0 18 39 21 30 , 29 37 32 37 25 15 1 7 ⟶ 29 37 25 15 0 18 39 21 37 , 29 37 32 37 25 15 1 20 ⟶ 29 37 25 15 0 18 39 21 27 , 29 37 32 37 25 15 1 21 ⟶ 29 37 25 15 0 18 39 21 31 , 29 37 32 37 25 15 1 22 ⟶ 29 37 25 15 0 18 39 21 38 , 21 37 32 37 25 15 1 13 ⟶ 21 37 25 15 0 18 39 21 16 , 21 37 32 37 25 15 1 19 ⟶ 21 37 25 15 0 18 39 21 35 , 21 37 32 37 25 15 1 2 ⟶ 21 37 25 15 0 18 39 21 30 , 21 37 32 37 25 15 1 7 ⟶ 21 37 25 15 0 18 39 21 37 , 21 37 32 37 25 15 1 20 ⟶ 21 37 25 15 0 18 39 21 27 , 21 37 32 37 25 15 1 21 ⟶ 21 37 25 15 0 18 39 21 31 , 21 37 32 37 25 15 1 22 ⟶ 21 37 25 15 0 18 39 21 38 , 11 37 32 37 25 15 1 13 ⟶ 11 37 25 15 0 18 39 21 16 , 11 37 32 37 25 15 1 19 ⟶ 11 37 25 15 0 18 39 21 35 , 11 37 32 37 25 15 1 2 ⟶ 11 37 25 15 0 18 39 21 30 , 11 37 32 37 25 15 1 7 ⟶ 11 37 25 15 0 18 39 21 37 , 11 37 32 37 25 15 1 20 ⟶ 11 37 25 15 0 18 39 21 27 , 11 37 32 37 25 15 1 21 ⟶ 11 37 25 15 0 18 39 21 31 , 11 37 32 37 25 15 1 22 ⟶ 11 37 25 15 0 18 39 21 38 , 32 37 32 37 25 15 1 13 ⟶ 32 37 25 15 0 18 39 21 16 , 32 37 32 37 25 15 1 19 ⟶ 32 37 25 15 0 18 39 21 35 , 32 37 32 37 25 15 1 2 ⟶ 32 37 25 15 0 18 39 21 30 , 32 37 32 37 25 15 1 7 ⟶ 32 37 25 15 0 18 39 21 37 , 32 37 32 37 25 15 1 20 ⟶ 32 37 25 15 0 18 39 21 27 , 32 37 32 37 25 15 1 21 ⟶ 32 37 25 15 0 18 39 21 31 , 32 37 32 37 25 15 1 22 ⟶ 32 37 25 15 0 18 39 21 38 , 33 37 32 37 25 15 1 13 ⟶ 33 37 25 15 0 18 39 21 16 , 33 37 32 37 25 15 1 19 ⟶ 33 37 25 15 0 18 39 21 35 , 33 37 32 37 25 15 1 2 ⟶ 33 37 25 15 0 18 39 21 30 , 33 37 32 37 25 15 1 7 ⟶ 33 37 25 15 0 18 39 21 37 , 33 37 32 37 25 15 1 20 ⟶ 33 37 25 15 0 18 39 21 27 , 33 37 32 37 25 15 1 21 ⟶ 33 37 25 15 0 18 39 21 31 , 33 37 32 37 25 15 1 22 ⟶ 33 37 25 15 0 18 39 21 38 , 31 37 32 37 25 15 1 13 ⟶ 31 37 25 15 0 18 39 21 16 , 31 37 32 37 25 15 1 19 ⟶ 31 37 25 15 0 18 39 21 35 , 31 37 32 37 25 15 1 2 ⟶ 31 37 25 15 0 18 39 21 30 , 31 37 32 37 25 15 1 7 ⟶ 31 37 25 15 0 18 39 21 37 , 31 37 32 37 25 15 1 20 ⟶ 31 37 25 15 0 18 39 21 27 , 31 37 32 37 25 15 1 21 ⟶ 31 37 25 15 0 18 39 21 31 , 31 37 32 37 25 15 1 22 ⟶ 31 37 25 15 0 18 39 21 38 , 34 37 32 37 25 15 1 13 ⟶ 34 37 25 15 0 18 39 21 16 , 34 37 32 37 25 15 1 19 ⟶ 34 37 25 15 0 18 39 21 35 , 34 37 32 37 25 15 1 2 ⟶ 34 37 25 15 0 18 39 21 30 , 34 37 32 37 25 15 1 7 ⟶ 34 37 25 15 0 18 39 21 37 , 34 37 32 37 25 15 1 20 ⟶ 34 37 25 15 0 18 39 21 27 , 34 37 32 37 25 15 1 21 ⟶ 34 37 25 15 0 18 39 21 31 , 34 37 32 37 25 15 1 22 ⟶ 34 37 25 15 0 18 39 21 38 , 0 29 16 29 37 25 24 13 ⟶ 23 33 35 13 0 18 39 21 16 , 0 29 16 29 37 25 24 19 ⟶ 23 33 35 13 0 18 39 21 35 , 0 29 16 29 37 25 24 2 ⟶ 23 33 35 13 0 18 39 21 30 , 0 29 16 29 37 25 24 7 ⟶ 23 33 35 13 0 18 39 21 37 , 0 29 16 29 37 25 24 20 ⟶ 23 33 35 13 0 18 39 21 27 , 0 29 16 29 37 25 24 21 ⟶ 23 33 35 13 0 18 39 21 31 , 0 29 16 29 37 25 24 22 ⟶ 23 33 35 13 0 18 39 21 38 , 13 29 16 29 37 25 24 13 ⟶ 20 33 35 13 0 18 39 21 16 , 13 29 16 29 37 25 24 19 ⟶ 20 33 35 13 0 18 39 21 35 , 13 29 16 29 37 25 24 2 ⟶ 20 33 35 13 0 18 39 21 30 , 13 29 16 29 37 25 24 7 ⟶ 20 33 35 13 0 18 39 21 37 , 13 29 16 29 37 25 24 20 ⟶ 20 33 35 13 0 18 39 21 27 , 13 29 16 29 37 25 24 21 ⟶ 20 33 35 13 0 18 39 21 31 , 13 29 16 29 37 25 24 22 ⟶ 20 33 35 13 0 18 39 21 38 , 4 29 16 29 37 25 24 13 ⟶ 10 33 35 13 0 18 39 21 16 , 4 29 16 29 37 25 24 19 ⟶ 10 33 35 13 0 18 39 21 35 , 4 29 16 29 37 25 24 2 ⟶ 10 33 35 13 0 18 39 21 30 , 4 29 16 29 37 25 24 7 ⟶ 10 33 35 13 0 18 39 21 37 , 4 29 16 29 37 25 24 20 ⟶ 10 33 35 13 0 18 39 21 27 , 4 29 16 29 37 25 24 21 ⟶ 10 33 35 13 0 18 39 21 31 , 4 29 16 29 37 25 24 22 ⟶ 10 33 35 13 0 18 39 21 38 , 14 29 16 29 37 25 24 13 ⟶ 25 33 35 13 0 18 39 21 16 , 14 29 16 29 37 25 24 19 ⟶ 25 33 35 13 0 18 39 21 35 , 14 29 16 29 37 25 24 2 ⟶ 25 33 35 13 0 18 39 21 30 , 14 29 16 29 37 25 24 7 ⟶ 25 33 35 13 0 18 39 21 37 , 14 29 16 29 37 25 24 20 ⟶ 25 33 35 13 0 18 39 21 27 , 14 29 16 29 37 25 24 21 ⟶ 25 33 35 13 0 18 39 21 31 , 14 29 16 29 37 25 24 22 ⟶ 25 33 35 13 0 18 39 21 38 , 15 29 16 29 37 25 24 13 ⟶ 26 33 35 13 0 18 39 21 16 , 15 29 16 29 37 25 24 19 ⟶ 26 33 35 13 0 18 39 21 35 , 15 29 16 29 37 25 24 2 ⟶ 26 33 35 13 0 18 39 21 30 , 15 29 16 29 37 25 24 7 ⟶ 26 33 35 13 0 18 39 21 37 , 15 29 16 29 37 25 24 20 ⟶ 26 33 35 13 0 18 39 21 27 , 15 29 16 29 37 25 24 21 ⟶ 26 33 35 13 0 18 39 21 31 , 15 29 16 29 37 25 24 22 ⟶ 26 33 35 13 0 18 39 21 38 , 16 29 16 29 37 25 24 13 ⟶ 27 33 35 13 0 18 39 21 16 , 16 29 16 29 37 25 24 19 ⟶ 27 33 35 13 0 18 39 21 35 , 16 29 16 29 37 25 24 2 ⟶ 27 33 35 13 0 18 39 21 30 , 16 29 16 29 37 25 24 7 ⟶ 27 33 35 13 0 18 39 21 37 , 16 29 16 29 37 25 24 20 ⟶ 27 33 35 13 0 18 39 21 27 , 16 29 16 29 37 25 24 21 ⟶ 27 33 35 13 0 18 39 21 31 , 16 29 16 29 37 25 24 22 ⟶ 27 33 35 13 0 18 39 21 38 , 17 29 16 29 37 25 24 13 ⟶ 28 33 35 13 0 18 39 21 16 , 17 29 16 29 37 25 24 19 ⟶ 28 33 35 13 0 18 39 21 35 , 17 29 16 29 37 25 24 2 ⟶ 28 33 35 13 0 18 39 21 30 , 17 29 16 29 37 25 24 7 ⟶ 28 33 35 13 0 18 39 21 37 , 17 29 16 29 37 25 24 20 ⟶ 28 33 35 13 0 18 39 21 27 , 17 29 16 29 37 25 24 21 ⟶ 28 33 35 13 0 18 39 21 31 , 17 29 16 29 37 25 24 22 ⟶ 28 33 35 13 0 18 39 21 38 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 2 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 13 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 7 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 8 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 4 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 8 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 2 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 2 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 8 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 7 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 15 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 5 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 7 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 40 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 41 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 42 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 43 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 44 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 45 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 46 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 6 ↦ 3, 19 ↦ 4, 13 ↦ 5, 7 ↦ 6, 39 ↦ 7, 20 ↦ 8, 21 ↦ 9, 22 ↦ 10, 4 ↦ 11, 14 ↦ 12, 15 ↦ 13, 16 ↦ 14, 17 ↦ 15 }, it remains to prove termination of the 49-rule system { 0 0 1 2 3 4 5 ⟶ 0 0 1 6 7 4 2 3 5 , 0 0 1 2 3 4 4 ⟶ 0 0 1 6 7 4 2 3 4 , 0 0 1 2 3 4 2 ⟶ 0 0 1 6 7 4 2 3 2 , 0 0 1 2 3 4 6 ⟶ 0 0 1 6 7 4 2 3 6 , 0 0 1 2 3 4 8 ⟶ 0 0 1 6 7 4 2 3 8 , 0 0 1 2 3 4 9 ⟶ 0 0 1 6 7 4 2 3 9 , 0 0 1 2 3 4 10 ⟶ 0 0 1 6 7 4 2 3 10 , 5 0 1 2 3 4 5 ⟶ 5 0 1 6 7 4 2 3 5 , 5 0 1 2 3 4 4 ⟶ 5 0 1 6 7 4 2 3 4 , 5 0 1 2 3 4 2 ⟶ 5 0 1 6 7 4 2 3 2 , 5 0 1 2 3 4 6 ⟶ 5 0 1 6 7 4 2 3 6 , 5 0 1 2 3 4 8 ⟶ 5 0 1 6 7 4 2 3 8 , 5 0 1 2 3 4 9 ⟶ 5 0 1 6 7 4 2 3 9 , 5 0 1 2 3 4 10 ⟶ 5 0 1 6 7 4 2 3 10 , 11 0 1 2 3 4 5 ⟶ 11 0 1 6 7 4 2 3 5 , 11 0 1 2 3 4 4 ⟶ 11 0 1 6 7 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 6 7 4 2 3 2 , 11 0 1 2 3 4 6 ⟶ 11 0 1 6 7 4 2 3 6 , 11 0 1 2 3 4 8 ⟶ 11 0 1 6 7 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 6 7 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 6 7 4 2 3 10 , 12 0 1 2 3 4 5 ⟶ 12 0 1 6 7 4 2 3 5 , 12 0 1 2 3 4 4 ⟶ 12 0 1 6 7 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 6 7 4 2 3 2 , 12 0 1 2 3 4 6 ⟶ 12 0 1 6 7 4 2 3 6 , 12 0 1 2 3 4 8 ⟶ 12 0 1 6 7 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 6 7 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 6 7 4 2 3 10 , 13 0 1 2 3 4 5 ⟶ 13 0 1 6 7 4 2 3 5 , 13 0 1 2 3 4 4 ⟶ 13 0 1 6 7 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 6 7 4 2 3 2 , 13 0 1 2 3 4 6 ⟶ 13 0 1 6 7 4 2 3 6 , 13 0 1 2 3 4 8 ⟶ 13 0 1 6 7 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 6 7 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 6 7 4 2 3 10 , 14 0 1 2 3 4 5 ⟶ 14 0 1 6 7 4 2 3 5 , 14 0 1 2 3 4 4 ⟶ 14 0 1 6 7 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 6 7 4 2 3 2 , 14 0 1 2 3 4 6 ⟶ 14 0 1 6 7 4 2 3 6 , 14 0 1 2 3 4 8 ⟶ 14 0 1 6 7 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 6 7 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 6 7 4 2 3 10 , 15 0 1 2 3 4 5 ⟶ 15 0 1 6 7 4 2 3 5 , 15 0 1 2 3 4 4 ⟶ 15 0 1 6 7 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 6 7 4 2 3 2 , 15 0 1 2 3 4 6 ⟶ 15 0 1 6 7 4 2 3 6 , 15 0 1 2 3 4 8 ⟶ 15 0 1 6 7 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 6 7 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 6 7 4 2 3 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 6 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 5 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 48-rule system { 0 0 1 2 3 4 4 ⟶ 0 0 1 5 6 4 2 3 4 , 0 0 1 2 3 4 2 ⟶ 0 0 1 5 6 4 2 3 2 , 0 0 1 2 3 4 5 ⟶ 0 0 1 5 6 4 2 3 5 , 0 0 1 2 3 4 7 ⟶ 0 0 1 5 6 4 2 3 7 , 0 0 1 2 3 4 8 ⟶ 0 0 1 5 6 4 2 3 8 , 0 0 1 2 3 4 9 ⟶ 0 0 1 5 6 4 2 3 9 , 10 0 1 2 3 4 10 ⟶ 10 0 1 5 6 4 2 3 10 , 10 0 1 2 3 4 4 ⟶ 10 0 1 5 6 4 2 3 4 , 10 0 1 2 3 4 2 ⟶ 10 0 1 5 6 4 2 3 2 , 10 0 1 2 3 4 5 ⟶ 10 0 1 5 6 4 2 3 5 , 10 0 1 2 3 4 7 ⟶ 10 0 1 5 6 4 2 3 7 , 10 0 1 2 3 4 8 ⟶ 10 0 1 5 6 4 2 3 8 , 10 0 1 2 3 4 9 ⟶ 10 0 1 5 6 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 5 6 4 2 3 10 , 11 0 1 2 3 4 4 ⟶ 11 0 1 5 6 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 5 6 4 2 3 2 , 11 0 1 2 3 4 5 ⟶ 11 0 1 5 6 4 2 3 5 , 11 0 1 2 3 4 7 ⟶ 11 0 1 5 6 4 2 3 7 , 11 0 1 2 3 4 8 ⟶ 11 0 1 5 6 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 5 6 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 5 6 4 2 3 10 , 12 0 1 2 3 4 4 ⟶ 12 0 1 5 6 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 5 6 4 2 3 2 , 12 0 1 2 3 4 5 ⟶ 12 0 1 5 6 4 2 3 5 , 12 0 1 2 3 4 7 ⟶ 12 0 1 5 6 4 2 3 7 , 12 0 1 2 3 4 8 ⟶ 12 0 1 5 6 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 5 6 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 5 6 4 2 3 10 , 13 0 1 2 3 4 4 ⟶ 13 0 1 5 6 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 5 6 4 2 3 2 , 13 0 1 2 3 4 5 ⟶ 13 0 1 5 6 4 2 3 5 , 13 0 1 2 3 4 7 ⟶ 13 0 1 5 6 4 2 3 7 , 13 0 1 2 3 4 8 ⟶ 13 0 1 5 6 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 5 6 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 5 6 4 2 3 10 , 14 0 1 2 3 4 4 ⟶ 14 0 1 5 6 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 5 6 4 2 3 2 , 14 0 1 2 3 4 5 ⟶ 14 0 1 5 6 4 2 3 5 , 14 0 1 2 3 4 7 ⟶ 14 0 1 5 6 4 2 3 7 , 14 0 1 2 3 4 8 ⟶ 14 0 1 5 6 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 5 6 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 5 6 4 2 3 10 , 15 0 1 2 3 4 4 ⟶ 15 0 1 5 6 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 5 6 4 2 3 2 , 15 0 1 2 3 4 5 ⟶ 15 0 1 5 6 4 2 3 5 , 15 0 1 2 3 4 7 ⟶ 15 0 1 5 6 4 2 3 7 , 15 0 1 2 3 4 8 ⟶ 15 0 1 5 6 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 5 6 4 2 3 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 47-rule system { 0 0 1 2 3 4 2 ⟶ 0 0 1 5 6 4 2 3 2 , 0 0 1 2 3 4 5 ⟶ 0 0 1 5 6 4 2 3 5 , 0 0 1 2 3 4 7 ⟶ 0 0 1 5 6 4 2 3 7 , 0 0 1 2 3 4 8 ⟶ 0 0 1 5 6 4 2 3 8 , 0 0 1 2 3 4 9 ⟶ 0 0 1 5 6 4 2 3 9 , 10 0 1 2 3 4 10 ⟶ 10 0 1 5 6 4 2 3 10 , 10 0 1 2 3 4 4 ⟶ 10 0 1 5 6 4 2 3 4 , 10 0 1 2 3 4 2 ⟶ 10 0 1 5 6 4 2 3 2 , 10 0 1 2 3 4 5 ⟶ 10 0 1 5 6 4 2 3 5 , 10 0 1 2 3 4 7 ⟶ 10 0 1 5 6 4 2 3 7 , 10 0 1 2 3 4 8 ⟶ 10 0 1 5 6 4 2 3 8 , 10 0 1 2 3 4 9 ⟶ 10 0 1 5 6 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 5 6 4 2 3 10 , 11 0 1 2 3 4 4 ⟶ 11 0 1 5 6 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 5 6 4 2 3 2 , 11 0 1 2 3 4 5 ⟶ 11 0 1 5 6 4 2 3 5 , 11 0 1 2 3 4 7 ⟶ 11 0 1 5 6 4 2 3 7 , 11 0 1 2 3 4 8 ⟶ 11 0 1 5 6 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 5 6 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 5 6 4 2 3 10 , 12 0 1 2 3 4 4 ⟶ 12 0 1 5 6 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 5 6 4 2 3 2 , 12 0 1 2 3 4 5 ⟶ 12 0 1 5 6 4 2 3 5 , 12 0 1 2 3 4 7 ⟶ 12 0 1 5 6 4 2 3 7 , 12 0 1 2 3 4 8 ⟶ 12 0 1 5 6 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 5 6 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 5 6 4 2 3 10 , 13 0 1 2 3 4 4 ⟶ 13 0 1 5 6 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 5 6 4 2 3 2 , 13 0 1 2 3 4 5 ⟶ 13 0 1 5 6 4 2 3 5 , 13 0 1 2 3 4 7 ⟶ 13 0 1 5 6 4 2 3 7 , 13 0 1 2 3 4 8 ⟶ 13 0 1 5 6 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 5 6 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 5 6 4 2 3 10 , 14 0 1 2 3 4 4 ⟶ 14 0 1 5 6 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 5 6 4 2 3 2 , 14 0 1 2 3 4 5 ⟶ 14 0 1 5 6 4 2 3 5 , 14 0 1 2 3 4 7 ⟶ 14 0 1 5 6 4 2 3 7 , 14 0 1 2 3 4 8 ⟶ 14 0 1 5 6 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 5 6 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 5 6 4 2 3 10 , 15 0 1 2 3 4 4 ⟶ 15 0 1 5 6 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 5 6 4 2 3 2 , 15 0 1 2 3 4 5 ⟶ 15 0 1 5 6 4 2 3 5 , 15 0 1 2 3 4 7 ⟶ 15 0 1 5 6 4 2 3 7 , 15 0 1 2 3 4 8 ⟶ 15 0 1 5 6 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 5 6 4 2 3 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 46-rule system { 0 0 1 2 3 4 5 ⟶ 0 0 1 5 6 4 2 3 5 , 0 0 1 2 3 4 7 ⟶ 0 0 1 5 6 4 2 3 7 , 0 0 1 2 3 4 8 ⟶ 0 0 1 5 6 4 2 3 8 , 0 0 1 2 3 4 9 ⟶ 0 0 1 5 6 4 2 3 9 , 10 0 1 2 3 4 10 ⟶ 10 0 1 5 6 4 2 3 10 , 10 0 1 2 3 4 4 ⟶ 10 0 1 5 6 4 2 3 4 , 10 0 1 2 3 4 2 ⟶ 10 0 1 5 6 4 2 3 2 , 10 0 1 2 3 4 5 ⟶ 10 0 1 5 6 4 2 3 5 , 10 0 1 2 3 4 7 ⟶ 10 0 1 5 6 4 2 3 7 , 10 0 1 2 3 4 8 ⟶ 10 0 1 5 6 4 2 3 8 , 10 0 1 2 3 4 9 ⟶ 10 0 1 5 6 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 5 6 4 2 3 10 , 11 0 1 2 3 4 4 ⟶ 11 0 1 5 6 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 5 6 4 2 3 2 , 11 0 1 2 3 4 5 ⟶ 11 0 1 5 6 4 2 3 5 , 11 0 1 2 3 4 7 ⟶ 11 0 1 5 6 4 2 3 7 , 11 0 1 2 3 4 8 ⟶ 11 0 1 5 6 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 5 6 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 5 6 4 2 3 10 , 12 0 1 2 3 4 4 ⟶ 12 0 1 5 6 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 5 6 4 2 3 2 , 12 0 1 2 3 4 5 ⟶ 12 0 1 5 6 4 2 3 5 , 12 0 1 2 3 4 7 ⟶ 12 0 1 5 6 4 2 3 7 , 12 0 1 2 3 4 8 ⟶ 12 0 1 5 6 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 5 6 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 5 6 4 2 3 10 , 13 0 1 2 3 4 4 ⟶ 13 0 1 5 6 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 5 6 4 2 3 2 , 13 0 1 2 3 4 5 ⟶ 13 0 1 5 6 4 2 3 5 , 13 0 1 2 3 4 7 ⟶ 13 0 1 5 6 4 2 3 7 , 13 0 1 2 3 4 8 ⟶ 13 0 1 5 6 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 5 6 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 5 6 4 2 3 10 , 14 0 1 2 3 4 4 ⟶ 14 0 1 5 6 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 5 6 4 2 3 2 , 14 0 1 2 3 4 5 ⟶ 14 0 1 5 6 4 2 3 5 , 14 0 1 2 3 4 7 ⟶ 14 0 1 5 6 4 2 3 7 , 14 0 1 2 3 4 8 ⟶ 14 0 1 5 6 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 5 6 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 5 6 4 2 3 10 , 15 0 1 2 3 4 4 ⟶ 15 0 1 5 6 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 5 6 4 2 3 2 , 15 0 1 2 3 4 5 ⟶ 15 0 1 5 6 4 2 3 5 , 15 0 1 2 3 4 7 ⟶ 15 0 1 5 6 4 2 3 7 , 15 0 1 2 3 4 8 ⟶ 15 0 1 5 6 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 5 6 4 2 3 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 7 ↦ 5, 5 ↦ 6, 6 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 45-rule system { 0 0 1 2 3 4 5 ⟶ 0 0 1 6 7 4 2 3 5 , 0 0 1 2 3 4 8 ⟶ 0 0 1 6 7 4 2 3 8 , 0 0 1 2 3 4 9 ⟶ 0 0 1 6 7 4 2 3 9 , 10 0 1 2 3 4 10 ⟶ 10 0 1 6 7 4 2 3 10 , 10 0 1 2 3 4 4 ⟶ 10 0 1 6 7 4 2 3 4 , 10 0 1 2 3 4 2 ⟶ 10 0 1 6 7 4 2 3 2 , 10 0 1 2 3 4 6 ⟶ 10 0 1 6 7 4 2 3 6 , 10 0 1 2 3 4 5 ⟶ 10 0 1 6 7 4 2 3 5 , 10 0 1 2 3 4 8 ⟶ 10 0 1 6 7 4 2 3 8 , 10 0 1 2 3 4 9 ⟶ 10 0 1 6 7 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 6 7 4 2 3 10 , 11 0 1 2 3 4 4 ⟶ 11 0 1 6 7 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 6 7 4 2 3 2 , 11 0 1 2 3 4 6 ⟶ 11 0 1 6 7 4 2 3 6 , 11 0 1 2 3 4 5 ⟶ 11 0 1 6 7 4 2 3 5 , 11 0 1 2 3 4 8 ⟶ 11 0 1 6 7 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 6 7 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 6 7 4 2 3 10 , 12 0 1 2 3 4 4 ⟶ 12 0 1 6 7 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 6 7 4 2 3 2 , 12 0 1 2 3 4 6 ⟶ 12 0 1 6 7 4 2 3 6 , 12 0 1 2 3 4 5 ⟶ 12 0 1 6 7 4 2 3 5 , 12 0 1 2 3 4 8 ⟶ 12 0 1 6 7 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 6 7 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 6 7 4 2 3 10 , 13 0 1 2 3 4 4 ⟶ 13 0 1 6 7 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 6 7 4 2 3 2 , 13 0 1 2 3 4 6 ⟶ 13 0 1 6 7 4 2 3 6 , 13 0 1 2 3 4 5 ⟶ 13 0 1 6 7 4 2 3 5 , 13 0 1 2 3 4 8 ⟶ 13 0 1 6 7 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 6 7 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 6 7 4 2 3 10 , 14 0 1 2 3 4 4 ⟶ 14 0 1 6 7 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 6 7 4 2 3 2 , 14 0 1 2 3 4 6 ⟶ 14 0 1 6 7 4 2 3 6 , 14 0 1 2 3 4 5 ⟶ 14 0 1 6 7 4 2 3 5 , 14 0 1 2 3 4 8 ⟶ 14 0 1 6 7 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 6 7 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 6 7 4 2 3 10 , 15 0 1 2 3 4 4 ⟶ 15 0 1 6 7 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 6 7 4 2 3 2 , 15 0 1 2 3 4 6 ⟶ 15 0 1 6 7 4 2 3 6 , 15 0 1 2 3 4 5 ⟶ 15 0 1 6 7 4 2 3 5 , 15 0 1 2 3 4 8 ⟶ 15 0 1 6 7 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 6 7 4 2 3 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 8 ↦ 5, 6 ↦ 6, 7 ↦ 7, 9 ↦ 8, 10 ↦ 9, 5 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 44-rule system { 0 0 1 2 3 4 5 ⟶ 0 0 1 6 7 4 2 3 5 , 0 0 1 2 3 4 8 ⟶ 0 0 1 6 7 4 2 3 8 , 9 0 1 2 3 4 9 ⟶ 9 0 1 6 7 4 2 3 9 , 9 0 1 2 3 4 4 ⟶ 9 0 1 6 7 4 2 3 4 , 9 0 1 2 3 4 2 ⟶ 9 0 1 6 7 4 2 3 2 , 9 0 1 2 3 4 6 ⟶ 9 0 1 6 7 4 2 3 6 , 9 0 1 2 3 4 10 ⟶ 9 0 1 6 7 4 2 3 10 , 9 0 1 2 3 4 5 ⟶ 9 0 1 6 7 4 2 3 5 , 9 0 1 2 3 4 8 ⟶ 9 0 1 6 7 4 2 3 8 , 11 0 1 2 3 4 9 ⟶ 11 0 1 6 7 4 2 3 9 , 11 0 1 2 3 4 4 ⟶ 11 0 1 6 7 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 6 7 4 2 3 2 , 11 0 1 2 3 4 6 ⟶ 11 0 1 6 7 4 2 3 6 , 11 0 1 2 3 4 10 ⟶ 11 0 1 6 7 4 2 3 10 , 11 0 1 2 3 4 5 ⟶ 11 0 1 6 7 4 2 3 5 , 11 0 1 2 3 4 8 ⟶ 11 0 1 6 7 4 2 3 8 , 12 0 1 2 3 4 9 ⟶ 12 0 1 6 7 4 2 3 9 , 12 0 1 2 3 4 4 ⟶ 12 0 1 6 7 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 6 7 4 2 3 2 , 12 0 1 2 3 4 6 ⟶ 12 0 1 6 7 4 2 3 6 , 12 0 1 2 3 4 10 ⟶ 12 0 1 6 7 4 2 3 10 , 12 0 1 2 3 4 5 ⟶ 12 0 1 6 7 4 2 3 5 , 12 0 1 2 3 4 8 ⟶ 12 0 1 6 7 4 2 3 8 , 13 0 1 2 3 4 9 ⟶ 13 0 1 6 7 4 2 3 9 , 13 0 1 2 3 4 4 ⟶ 13 0 1 6 7 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 6 7 4 2 3 2 , 13 0 1 2 3 4 6 ⟶ 13 0 1 6 7 4 2 3 6 , 13 0 1 2 3 4 10 ⟶ 13 0 1 6 7 4 2 3 10 , 13 0 1 2 3 4 5 ⟶ 13 0 1 6 7 4 2 3 5 , 13 0 1 2 3 4 8 ⟶ 13 0 1 6 7 4 2 3 8 , 14 0 1 2 3 4 9 ⟶ 14 0 1 6 7 4 2 3 9 , 14 0 1 2 3 4 4 ⟶ 14 0 1 6 7 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 6 7 4 2 3 2 , 14 0 1 2 3 4 6 ⟶ 14 0 1 6 7 4 2 3 6 , 14 0 1 2 3 4 10 ⟶ 14 0 1 6 7 4 2 3 10 , 14 0 1 2 3 4 5 ⟶ 14 0 1 6 7 4 2 3 5 , 14 0 1 2 3 4 8 ⟶ 14 0 1 6 7 4 2 3 8 , 15 0 1 2 3 4 9 ⟶ 15 0 1 6 7 4 2 3 9 , 15 0 1 2 3 4 4 ⟶ 15 0 1 6 7 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 6 7 4 2 3 2 , 15 0 1 2 3 4 6 ⟶ 15 0 1 6 7 4 2 3 6 , 15 0 1 2 3 4 10 ⟶ 15 0 1 6 7 4 2 3 10 , 15 0 1 2 3 4 5 ⟶ 15 0 1 6 7 4 2 3 5 , 15 0 1 2 3 4 8 ⟶ 15 0 1 6 7 4 2 3 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 8 ↦ 5, 6 ↦ 6, 7 ↦ 7, 9 ↦ 8, 10 ↦ 9, 5 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 43-rule system { 0 0 1 2 3 4 5 ⟶ 0 0 1 6 7 4 2 3 5 , 8 0 1 2 3 4 8 ⟶ 8 0 1 6 7 4 2 3 8 , 8 0 1 2 3 4 4 ⟶ 8 0 1 6 7 4 2 3 4 , 8 0 1 2 3 4 2 ⟶ 8 0 1 6 7 4 2 3 2 , 8 0 1 2 3 4 6 ⟶ 8 0 1 6 7 4 2 3 6 , 8 0 1 2 3 4 9 ⟶ 8 0 1 6 7 4 2 3 9 , 8 0 1 2 3 4 10 ⟶ 8 0 1 6 7 4 2 3 10 , 8 0 1 2 3 4 5 ⟶ 8 0 1 6 7 4 2 3 5 , 11 0 1 2 3 4 8 ⟶ 11 0 1 6 7 4 2 3 8 , 11 0 1 2 3 4 4 ⟶ 11 0 1 6 7 4 2 3 4 , 11 0 1 2 3 4 2 ⟶ 11 0 1 6 7 4 2 3 2 , 11 0 1 2 3 4 6 ⟶ 11 0 1 6 7 4 2 3 6 , 11 0 1 2 3 4 9 ⟶ 11 0 1 6 7 4 2 3 9 , 11 0 1 2 3 4 10 ⟶ 11 0 1 6 7 4 2 3 10 , 11 0 1 2 3 4 5 ⟶ 11 0 1 6 7 4 2 3 5 , 12 0 1 2 3 4 8 ⟶ 12 0 1 6 7 4 2 3 8 , 12 0 1 2 3 4 4 ⟶ 12 0 1 6 7 4 2 3 4 , 12 0 1 2 3 4 2 ⟶ 12 0 1 6 7 4 2 3 2 , 12 0 1 2 3 4 6 ⟶ 12 0 1 6 7 4 2 3 6 , 12 0 1 2 3 4 9 ⟶ 12 0 1 6 7 4 2 3 9 , 12 0 1 2 3 4 10 ⟶ 12 0 1 6 7 4 2 3 10 , 12 0 1 2 3 4 5 ⟶ 12 0 1 6 7 4 2 3 5 , 13 0 1 2 3 4 8 ⟶ 13 0 1 6 7 4 2 3 8 , 13 0 1 2 3 4 4 ⟶ 13 0 1 6 7 4 2 3 4 , 13 0 1 2 3 4 2 ⟶ 13 0 1 6 7 4 2 3 2 , 13 0 1 2 3 4 6 ⟶ 13 0 1 6 7 4 2 3 6 , 13 0 1 2 3 4 9 ⟶ 13 0 1 6 7 4 2 3 9 , 13 0 1 2 3 4 10 ⟶ 13 0 1 6 7 4 2 3 10 , 13 0 1 2 3 4 5 ⟶ 13 0 1 6 7 4 2 3 5 , 14 0 1 2 3 4 8 ⟶ 14 0 1 6 7 4 2 3 8 , 14 0 1 2 3 4 4 ⟶ 14 0 1 6 7 4 2 3 4 , 14 0 1 2 3 4 2 ⟶ 14 0 1 6 7 4 2 3 2 , 14 0 1 2 3 4 6 ⟶ 14 0 1 6 7 4 2 3 6 , 14 0 1 2 3 4 9 ⟶ 14 0 1 6 7 4 2 3 9 , 14 0 1 2 3 4 10 ⟶ 14 0 1 6 7 4 2 3 10 , 14 0 1 2 3 4 5 ⟶ 14 0 1 6 7 4 2 3 5 , 15 0 1 2 3 4 8 ⟶ 15 0 1 6 7 4 2 3 8 , 15 0 1 2 3 4 4 ⟶ 15 0 1 6 7 4 2 3 4 , 15 0 1 2 3 4 2 ⟶ 15 0 1 6 7 4 2 3 2 , 15 0 1 2 3 4 6 ⟶ 15 0 1 6 7 4 2 3 6 , 15 0 1 2 3 4 9 ⟶ 15 0 1 6 7 4 2 3 9 , 15 0 1 2 3 4 10 ⟶ 15 0 1 6 7 4 2 3 10 , 15 0 1 2 3 4 5 ⟶ 15 0 1 6 7 4 2 3 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 8 ↦ 0, 0 ↦ 1, 1 ↦ 2, 2 ↦ 3, 3 ↦ 4, 4 ↦ 5, 6 ↦ 6, 7 ↦ 7, 9 ↦ 8, 10 ↦ 9, 5 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 42-rule system { 0 1 2 3 4 5 0 ⟶ 0 1 2 6 7 5 3 4 0 , 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 0 ⟶ 11 1 2 6 7 5 3 4 0 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 12 1 2 3 4 5 0 ⟶ 12 1 2 6 7 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 6 7 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 6 7 5 3 4 3 , 12 1 2 3 4 5 6 ⟶ 12 1 2 6 7 5 3 4 6 , 12 1 2 3 4 5 8 ⟶ 12 1 2 6 7 5 3 4 8 , 12 1 2 3 4 5 9 ⟶ 12 1 2 6 7 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 0 ⟶ 13 1 2 6 7 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 0 ⟶ 14 1 2 6 7 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 0 ⟶ 15 1 2 6 7 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 41-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 0 ⟶ 11 1 2 6 7 5 3 4 0 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 12 1 2 3 4 5 0 ⟶ 12 1 2 6 7 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 6 7 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 6 7 5 3 4 3 , 12 1 2 3 4 5 6 ⟶ 12 1 2 6 7 5 3 4 6 , 12 1 2 3 4 5 8 ⟶ 12 1 2 6 7 5 3 4 8 , 12 1 2 3 4 5 9 ⟶ 12 1 2 6 7 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 0 ⟶ 13 1 2 6 7 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 0 ⟶ 14 1 2 6 7 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 0 ⟶ 15 1 2 6 7 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 40-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 0 ⟶ 11 1 2 6 7 5 3 4 0 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 12 1 2 3 4 5 0 ⟶ 12 1 2 6 7 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 6 7 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 6 7 5 3 4 3 , 12 1 2 3 4 5 6 ⟶ 12 1 2 6 7 5 3 4 6 , 12 1 2 3 4 5 8 ⟶ 12 1 2 6 7 5 3 4 8 , 12 1 2 3 4 5 9 ⟶ 12 1 2 6 7 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 0 ⟶ 13 1 2 6 7 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 0 ⟶ 14 1 2 6 7 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 0 ⟶ 15 1 2 6 7 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 39-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 0 ⟶ 11 1 2 6 7 5 3 4 0 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 12 1 2 3 4 5 0 ⟶ 12 1 2 6 7 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 6 7 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 6 7 5 3 4 3 , 12 1 2 3 4 5 6 ⟶ 12 1 2 6 7 5 3 4 6 , 12 1 2 3 4 5 8 ⟶ 12 1 2 6 7 5 3 4 8 , 12 1 2 3 4 5 9 ⟶ 12 1 2 6 7 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 0 ⟶ 13 1 2 6 7 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 0 ⟶ 14 1 2 6 7 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 0 ⟶ 15 1 2 6 7 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 38-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 11 1 2 3 4 5 0 ⟶ 11 1 2 7 8 5 3 4 0 , 11 1 2 3 4 5 5 ⟶ 11 1 2 7 8 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 7 8 5 3 4 3 , 11 1 2 3 4 5 7 ⟶ 11 1 2 7 8 5 3 4 7 , 11 1 2 3 4 5 6 ⟶ 11 1 2 7 8 5 3 4 6 , 11 1 2 3 4 5 9 ⟶ 11 1 2 7 8 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 0 ⟶ 12 1 2 7 8 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 0 ⟶ 13 1 2 7 8 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 0 ⟶ 14 1 2 7 8 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 15 1 2 3 4 5 0 ⟶ 15 1 2 7 8 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 9 ⟶ 15 1 2 7 8 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 6 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 37-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 10 1 2 3 4 5 0 ⟶ 10 1 2 7 8 5 3 4 0 , 10 1 2 3 4 5 5 ⟶ 10 1 2 7 8 5 3 4 5 , 10 1 2 3 4 5 3 ⟶ 10 1 2 7 8 5 3 4 3 , 10 1 2 3 4 5 7 ⟶ 10 1 2 7 8 5 3 4 7 , 10 1 2 3 4 5 11 ⟶ 10 1 2 7 8 5 3 4 11 , 10 1 2 3 4 5 6 ⟶ 10 1 2 7 8 5 3 4 6 , 10 1 2 3 4 5 9 ⟶ 10 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 0 ⟶ 12 1 2 7 8 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 0 ⟶ 13 1 2 7 8 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 0 ⟶ 14 1 2 7 8 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 15 1 2 3 4 5 0 ⟶ 15 1 2 7 8 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 11 ⟶ 15 1 2 7 8 5 3 4 11 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 9 ⟶ 15 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 6 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 36-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 9 1 2 3 4 5 0 ⟶ 9 1 2 7 8 5 3 4 0 , 9 1 2 3 4 5 5 ⟶ 9 1 2 7 8 5 3 4 5 , 9 1 2 3 4 5 3 ⟶ 9 1 2 7 8 5 3 4 3 , 9 1 2 3 4 5 7 ⟶ 9 1 2 7 8 5 3 4 7 , 9 1 2 3 4 5 10 ⟶ 9 1 2 7 8 5 3 4 10 , 9 1 2 3 4 5 11 ⟶ 9 1 2 7 8 5 3 4 11 , 9 1 2 3 4 5 6 ⟶ 9 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 0 ⟶ 12 1 2 7 8 5 3 4 0 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 0 ⟶ 13 1 2 7 8 5 3 4 0 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 0 ⟶ 14 1 2 7 8 5 3 4 0 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 0 ⟶ 15 1 2 7 8 5 3 4 0 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 10 ⟶ 15 1 2 7 8 5 3 4 10 , 15 1 2 3 4 5 11 ⟶ 15 1 2 7 8 5 3 4 11 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 9 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 0 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 6 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 35-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 5 ⟶ 0 1 2 7 8 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 7 8 5 3 4 3 , 0 1 2 3 4 5 7 ⟶ 0 1 2 7 8 5 3 4 7 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 0 1 2 3 4 5 11 ⟶ 0 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 9 ⟶ 15 1 2 7 8 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 7 8 5 3 4 10 , 15 1 2 3 4 5 11 ⟶ 15 1 2 7 8 5 3 4 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 34-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 12 ⟶ 15 1 2 6 7 5 3 4 12 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 33-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 12 ⟶ 15 1 2 6 7 5 3 4 12 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 32-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 , 15 1 2 3 4 5 12 ⟶ 15 1 2 6 7 5 3 4 12 , 15 1 2 3 4 5 5 ⟶ 15 1 2 6 7 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 6 7 5 3 4 3 , 15 1 2 3 4 5 6 ⟶ 15 1 2 6 7 5 3 4 6 , 15 1 2 3 4 5 8 ⟶ 15 1 2 6 7 5 3 4 8 , 15 1 2 3 4 5 9 ⟶ 15 1 2 6 7 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 31-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 7 8 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 7 8 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 7 8 5 3 4 3 , 11 1 2 3 4 5 7 ⟶ 11 1 2 7 8 5 3 4 7 , 11 1 2 3 4 5 6 ⟶ 11 1 2 7 8 5 3 4 6 , 11 1 2 3 4 5 9 ⟶ 11 1 2 7 8 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 15 1 2 3 4 5 12 ⟶ 15 1 2 7 8 5 3 4 12 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 9 ⟶ 15 1 2 7 8 5 3 4 9 , 15 1 2 3 4 5 10 ⟶ 15 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 30-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 10 1 2 3 4 5 11 ⟶ 10 1 2 7 8 5 3 4 11 , 10 1 2 3 4 5 5 ⟶ 10 1 2 7 8 5 3 4 5 , 10 1 2 3 4 5 3 ⟶ 10 1 2 7 8 5 3 4 3 , 10 1 2 3 4 5 7 ⟶ 10 1 2 7 8 5 3 4 7 , 10 1 2 3 4 5 12 ⟶ 10 1 2 7 8 5 3 4 12 , 10 1 2 3 4 5 6 ⟶ 10 1 2 7 8 5 3 4 6 , 10 1 2 3 4 5 9 ⟶ 10 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 15 1 2 3 4 5 11 ⟶ 15 1 2 7 8 5 3 4 11 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 12 ⟶ 15 1 2 7 8 5 3 4 12 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 9 ⟶ 15 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15 }, it remains to prove termination of the 29-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 9 1 2 3 4 5 10 ⟶ 9 1 2 7 8 5 3 4 10 , 9 1 2 3 4 5 5 ⟶ 9 1 2 7 8 5 3 4 5 , 9 1 2 3 4 5 3 ⟶ 9 1 2 7 8 5 3 4 3 , 9 1 2 3 4 5 7 ⟶ 9 1 2 7 8 5 3 4 7 , 9 1 2 3 4 5 11 ⟶ 9 1 2 7 8 5 3 4 11 , 9 1 2 3 4 5 12 ⟶ 9 1 2 7 8 5 3 4 12 , 9 1 2 3 4 5 6 ⟶ 9 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 15 1 2 3 4 5 10 ⟶ 15 1 2 7 8 5 3 4 10 , 15 1 2 3 4 5 5 ⟶ 15 1 2 7 8 5 3 4 5 , 15 1 2 3 4 5 3 ⟶ 15 1 2 7 8 5 3 4 3 , 15 1 2 3 4 5 7 ⟶ 15 1 2 7 8 5 3 4 7 , 15 1 2 3 4 5 11 ⟶ 15 1 2 7 8 5 3 4 11 , 15 1 2 3 4 5 12 ⟶ 15 1 2 7 8 5 3 4 12 , 15 1 2 3 4 5 6 ⟶ 15 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 9 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 10 ↦ 6, 7 ↦ 7, 8 ↦ 8, 11 ↦ 9, 12 ↦ 10, 6 ↦ 11, 13 ↦ 12, 14 ↦ 13, 15 ↦ 14 }, it remains to prove termination of the 28-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 5 ⟶ 0 1 2 7 8 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 7 8 5 3 4 3 , 0 1 2 3 4 5 7 ⟶ 0 1 2 7 8 5 3 4 7 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 0 1 2 3 4 5 11 ⟶ 0 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14 }, it remains to prove termination of the 27-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 26-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 25-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 6 7 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 6 7 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 6 7 5 3 4 3 , 14 1 2 3 4 5 6 ⟶ 14 1 2 6 7 5 3 4 6 , 14 1 2 3 4 5 8 ⟶ 14 1 2 6 7 5 3 4 8 , 14 1 2 3 4 5 9 ⟶ 14 1 2 6 7 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14 }, it remains to prove termination of the 24-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 7 8 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 7 8 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 7 8 5 3 4 3 , 11 1 2 3 4 5 7 ⟶ 11 1 2 7 8 5 3 4 7 , 11 1 2 3 4 5 6 ⟶ 11 1 2 7 8 5 3 4 6 , 11 1 2 3 4 5 9 ⟶ 11 1 2 7 8 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14 }, it remains to prove termination of the 23-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 10 1 2 3 4 5 11 ⟶ 10 1 2 7 8 5 3 4 11 , 10 1 2 3 4 5 5 ⟶ 10 1 2 7 8 5 3 4 5 , 10 1 2 3 4 5 3 ⟶ 10 1 2 7 8 5 3 4 3 , 10 1 2 3 4 5 7 ⟶ 10 1 2 7 8 5 3 4 7 , 10 1 2 3 4 5 12 ⟶ 10 1 2 7 8 5 3 4 12 , 10 1 2 3 4 5 6 ⟶ 10 1 2 7 8 5 3 4 6 , 10 1 2 3 4 5 9 ⟶ 10 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 9 ⟶ 14 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13, 14 ↦ 14 }, it remains to prove termination of the 22-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 9 1 2 3 4 5 10 ⟶ 9 1 2 7 8 5 3 4 10 , 9 1 2 3 4 5 5 ⟶ 9 1 2 7 8 5 3 4 5 , 9 1 2 3 4 5 3 ⟶ 9 1 2 7 8 5 3 4 3 , 9 1 2 3 4 5 7 ⟶ 9 1 2 7 8 5 3 4 7 , 9 1 2 3 4 5 11 ⟶ 9 1 2 7 8 5 3 4 11 , 9 1 2 3 4 5 12 ⟶ 9 1 2 7 8 5 3 4 12 , 9 1 2 3 4 5 6 ⟶ 9 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 14 1 2 3 4 5 10 ⟶ 14 1 2 7 8 5 3 4 10 , 14 1 2 3 4 5 5 ⟶ 14 1 2 7 8 5 3 4 5 , 14 1 2 3 4 5 3 ⟶ 14 1 2 7 8 5 3 4 3 , 14 1 2 3 4 5 7 ⟶ 14 1 2 7 8 5 3 4 7 , 14 1 2 3 4 5 11 ⟶ 14 1 2 7 8 5 3 4 11 , 14 1 2 3 4 5 12 ⟶ 14 1 2 7 8 5 3 4 12 , 14 1 2 3 4 5 6 ⟶ 14 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 9 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 10 ↦ 6, 7 ↦ 7, 8 ↦ 8, 11 ↦ 9, 12 ↦ 10, 6 ↦ 11, 13 ↦ 12, 14 ↦ 13 }, it remains to prove termination of the 21-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 5 ⟶ 0 1 2 7 8 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 7 8 5 3 4 3 , 0 1 2 3 4 5 7 ⟶ 0 1 2 7 8 5 3 4 7 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 0 1 2 3 4 5 11 ⟶ 0 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13 }, it remains to prove termination of the 20-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 19-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 18-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 6 7 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 6 7 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 6 7 5 3 4 3 , 13 1 2 3 4 5 6 ⟶ 13 1 2 6 7 5 3 4 6 , 13 1 2 3 4 5 8 ⟶ 13 1 2 6 7 5 3 4 8 , 13 1 2 3 4 5 9 ⟶ 13 1 2 6 7 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13 }, it remains to prove termination of the 17-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 7 8 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 7 8 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 7 8 5 3 4 3 , 11 1 2 3 4 5 7 ⟶ 11 1 2 7 8 5 3 4 7 , 11 1 2 3 4 5 6 ⟶ 11 1 2 7 8 5 3 4 6 , 11 1 2 3 4 5 9 ⟶ 11 1 2 7 8 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13 }, it remains to prove termination of the 16-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 10 1 2 3 4 5 11 ⟶ 10 1 2 7 8 5 3 4 11 , 10 1 2 3 4 5 5 ⟶ 10 1 2 7 8 5 3 4 5 , 10 1 2 3 4 5 3 ⟶ 10 1 2 7 8 5 3 4 3 , 10 1 2 3 4 5 7 ⟶ 10 1 2 7 8 5 3 4 7 , 10 1 2 3 4 5 12 ⟶ 10 1 2 7 8 5 3 4 12 , 10 1 2 3 4 5 6 ⟶ 10 1 2 7 8 5 3 4 6 , 10 1 2 3 4 5 9 ⟶ 10 1 2 7 8 5 3 4 9 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 9 ⟶ 13 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12, 13 ↦ 13 }, it remains to prove termination of the 15-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 9 1 2 3 4 5 10 ⟶ 9 1 2 7 8 5 3 4 10 , 9 1 2 3 4 5 5 ⟶ 9 1 2 7 8 5 3 4 5 , 9 1 2 3 4 5 3 ⟶ 9 1 2 7 8 5 3 4 3 , 9 1 2 3 4 5 7 ⟶ 9 1 2 7 8 5 3 4 7 , 9 1 2 3 4 5 11 ⟶ 9 1 2 7 8 5 3 4 11 , 9 1 2 3 4 5 12 ⟶ 9 1 2 7 8 5 3 4 12 , 9 1 2 3 4 5 6 ⟶ 9 1 2 7 8 5 3 4 6 , 13 1 2 3 4 5 10 ⟶ 13 1 2 7 8 5 3 4 10 , 13 1 2 3 4 5 5 ⟶ 13 1 2 7 8 5 3 4 5 , 13 1 2 3 4 5 3 ⟶ 13 1 2 7 8 5 3 4 3 , 13 1 2 3 4 5 7 ⟶ 13 1 2 7 8 5 3 4 7 , 13 1 2 3 4 5 11 ⟶ 13 1 2 7 8 5 3 4 11 , 13 1 2 3 4 5 12 ⟶ 13 1 2 7 8 5 3 4 12 , 13 1 2 3 4 5 6 ⟶ 13 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 9 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 10 ↦ 6, 7 ↦ 7, 8 ↦ 8, 11 ↦ 9, 12 ↦ 10, 6 ↦ 11, 13 ↦ 12 }, it remains to prove termination of the 14-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 5 ⟶ 0 1 2 7 8 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 7 8 5 3 4 3 , 0 1 2 3 4 5 7 ⟶ 0 1 2 7 8 5 3 4 7 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 0 1 2 3 4 5 11 ⟶ 0 1 2 7 8 5 3 4 11 , 12 1 2 3 4 5 6 ⟶ 12 1 2 7 8 5 3 4 6 , 12 1 2 3 4 5 5 ⟶ 12 1 2 7 8 5 3 4 5 , 12 1 2 3 4 5 3 ⟶ 12 1 2 7 8 5 3 4 3 , 12 1 2 3 4 5 7 ⟶ 12 1 2 7 8 5 3 4 7 , 12 1 2 3 4 5 9 ⟶ 12 1 2 7 8 5 3 4 9 , 12 1 2 3 4 5 10 ⟶ 12 1 2 7 8 5 3 4 10 , 12 1 2 3 4 5 11 ⟶ 12 1 2 7 8 5 3 4 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12 }, it remains to prove termination of the 13-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 12-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 }, it remains to prove termination of the 11-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 6 7 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 6 7 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 6 7 5 3 4 3 , 11 1 2 3 4 5 6 ⟶ 11 1 2 6 7 5 3 4 6 , 11 1 2 3 4 5 8 ⟶ 11 1 2 6 7 5 3 4 8 , 11 1 2 3 4 5 9 ⟶ 11 1 2 6 7 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 }, it remains to prove termination of the 10-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 11 1 2 3 4 5 12 ⟶ 11 1 2 7 8 5 3 4 12 , 11 1 2 3 4 5 5 ⟶ 11 1 2 7 8 5 3 4 5 , 11 1 2 3 4 5 3 ⟶ 11 1 2 7 8 5 3 4 3 , 11 1 2 3 4 5 7 ⟶ 11 1 2 7 8 5 3 4 7 , 11 1 2 3 4 5 6 ⟶ 11 1 2 7 8 5 3 4 6 , 11 1 2 3 4 5 9 ⟶ 11 1 2 7 8 5 3 4 9 , 11 1 2 3 4 5 10 ⟶ 11 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12 }, it remains to prove termination of the 9-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 10 1 2 3 4 5 11 ⟶ 10 1 2 7 8 5 3 4 11 , 10 1 2 3 4 5 5 ⟶ 10 1 2 7 8 5 3 4 5 , 10 1 2 3 4 5 3 ⟶ 10 1 2 7 8 5 3 4 3 , 10 1 2 3 4 5 7 ⟶ 10 1 2 7 8 5 3 4 7 , 10 1 2 3 4 5 12 ⟶ 10 1 2 7 8 5 3 4 12 , 10 1 2 3 4 5 6 ⟶ 10 1 2 7 8 5 3 4 6 , 10 1 2 3 4 5 9 ⟶ 10 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 6 ↦ 12 }, it remains to prove termination of the 8-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 9 1 2 3 4 5 10 ⟶ 9 1 2 7 8 5 3 4 10 , 9 1 2 3 4 5 5 ⟶ 9 1 2 7 8 5 3 4 5 , 9 1 2 3 4 5 3 ⟶ 9 1 2 7 8 5 3 4 3 , 9 1 2 3 4 5 7 ⟶ 9 1 2 7 8 5 3 4 7 , 9 1 2 3 4 5 11 ⟶ 9 1 2 7 8 5 3 4 11 , 9 1 2 3 4 5 12 ⟶ 9 1 2 7 8 5 3 4 12 , 9 1 2 3 4 5 6 ⟶ 9 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 9 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 10 ↦ 6, 7 ↦ 7, 8 ↦ 8, 11 ↦ 9, 12 ↦ 10, 6 ↦ 11 }, it remains to prove termination of the 7-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 5 ⟶ 0 1 2 7 8 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 7 8 5 3 4 3 , 0 1 2 3 4 5 7 ⟶ 0 1 2 7 8 5 3 4 7 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 , 0 1 2 3 4 5 11 ⟶ 0 1 2 7 8 5 3 4 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10 }, it remains to prove termination of the 6-rule system { 0 1 2 3 4 5 5 ⟶ 0 1 2 6 7 5 3 4 5 , 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 5-rule system { 0 1 2 3 4 5 3 ⟶ 0 1 2 6 7 5 3 4 3 , 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 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 4-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 6 7 5 3 4 6 , 0 1 2 3 4 5 8 ⟶ 0 1 2 6 7 5 3 4 8 , 0 1 2 3 4 5 9 ⟶ 0 1 2 6 7 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 6 7 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 8 ↦ 6, 6 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10 }, it remains to prove termination of the 3-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 , 0 1 2 3 4 5 10 ⟶ 0 1 2 7 8 5 3 4 10 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9 }, it remains to prove termination of the 2-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 , 0 1 2 3 4 5 9 ⟶ 0 1 2 7 8 5 3 4 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 9 ↦ 6, 7 ↦ 7, 8 ↦ 8 }, it remains to prove termination of the 1-rule system { 0 1 2 3 4 5 6 ⟶ 0 1 2 7 8 5 3 4 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 the bijection { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.