/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo the bijection { 0 ↦ 0, 2 ↦ 1, 3 ↦ 2, 1 ↦ 3 }, it remains to prove termination of the 80-rule system { 0 0 0 1 2 0 1 1 0 2 0 3 1 2 2 0 1 0 ⟶ 0 3 2 1 2 1 1 1 0 0 2 2 1 0 0 0 0 0 , 0 0 0 2 0 3 2 0 1 0 2 0 2 0 2 3 0 2 ⟶ 0 0 3 0 0 3 0 2 2 0 0 2 1 0 2 0 2 2 , 0 0 1 0 2 0 2 3 3 0 0 3 2 0 2 0 0 1 ⟶ 0 0 3 3 3 0 2 0 2 2 0 0 1 0 2 0 0 1 , 0 0 1 0 2 3 2 1 3 3 1 2 2 0 1 1 1 1 ⟶ 2 1 2 3 1 0 3 2 1 0 1 0 1 2 0 3 1 1 , 0 0 1 2 0 1 3 1 1 2 0 2 2 3 3 0 1 0 ⟶ 0 0 3 1 1 2 2 1 0 2 3 0 1 3 0 2 1 0 , 0 0 2 3 1 2 3 0 1 2 2 0 1 3 2 0 1 1 ⟶ 0 2 1 0 2 2 3 1 1 0 3 2 0 0 1 3 2 1 , 0 3 0 0 1 1 3 3 2 0 0 3 1 0 3 1 1 0 ⟶ 0 3 3 0 0 0 1 1 3 1 0 3 3 0 2 1 1 0 , 0 3 0 1 2 0 1 3 1 1 3 3 2 2 1 0 2 2 ⟶ 0 3 1 0 1 1 2 2 1 0 3 2 1 2 0 3 3 2 , 0 3 3 2 0 1 0 2 0 3 1 2 0 1 0 2 0 2 ⟶ 0 0 0 1 2 2 3 0 3 1 0 0 0 3 2 2 1 2 , 0 3 1 2 1 0 1 2 3 0 2 0 1 1 3 3 2 2 ⟶ 0 3 1 1 2 1 2 3 3 1 2 2 1 0 0 3 0 2 , 0 3 1 2 1 1 3 2 0 1 3 2 2 3 0 0 1 3 ⟶ 0 2 1 3 0 3 0 1 2 0 3 2 1 3 2 1 1 3 , 0 1 3 2 0 2 2 2 2 3 3 3 2 2 2 1 3 1 ⟶ 3 2 1 2 2 2 3 0 3 2 3 2 2 2 1 0 3 1 , 0 1 1 0 2 3 2 2 0 3 0 2 2 3 3 0 3 1 ⟶ 0 2 3 1 0 2 1 2 3 0 0 2 3 0 3 2 3 1 , 0 2 0 0 3 2 0 0 3 2 0 2 2 3 3 3 3 0 ⟶ 0 2 0 2 0 0 2 3 0 3 2 3 3 0 2 3 3 0 , 0 2 0 0 2 3 0 2 0 0 0 3 1 3 1 0 1 0 ⟶ 0 2 0 0 3 3 0 1 1 2 0 0 3 0 0 2 1 0 , 0 2 0 1 0 0 0 0 1 1 0 1 3 0 1 1 1 0 ⟶ 0 1 1 1 3 1 0 0 2 1 1 0 0 1 0 0 0 0 , 0 2 0 2 0 2 0 3 2 0 0 2 1 0 1 3 0 2 ⟶ 3 2 1 2 0 0 3 0 0 2 1 0 2 0 0 2 0 2 , 0 2 0 2 3 2 0 3 2 0 1 1 2 3 1 0 2 3 ⟶ 3 0 2 0 2 0 0 2 1 2 0 3 1 2 3 1 2 3 , 0 2 0 2 1 1 0 0 1 2 1 3 2 2 0 1 0 1 ⟶ 0 2 2 3 0 0 1 1 0 0 0 1 2 1 2 1 2 1 , 0 2 3 1 2 1 3 1 2 2 1 3 1 2 2 1 1 1 ⟶ 3 1 2 1 2 3 1 0 2 2 3 2 1 1 2 1 1 1 , 0 2 1 0 3 0 3 3 3 0 0 1 3 3 1 1 3 3 ⟶ 0 2 1 3 0 3 1 3 1 0 0 3 3 0 3 1 3 3 , 3 0 3 3 3 1 1 2 0 1 0 2 1 2 0 2 0 0 ⟶ 3 2 1 0 2 3 3 0 2 1 0 2 1 0 1 3 0 0 , 3 0 3 1 1 1 0 2 2 1 3 1 0 1 0 3 1 1 ⟶ 3 0 1 1 3 1 0 1 1 3 3 0 0 1 2 1 2 1 , 3 0 2 0 2 2 0 1 3 1 2 2 3 0 1 1 2 2 ⟶ 3 0 2 3 1 2 2 3 0 1 1 2 0 0 2 1 2 2 , 3 3 0 3 2 0 2 3 2 3 3 2 2 3 1 1 2 2 ⟶ 3 2 3 2 3 0 2 3 2 3 2 3 2 1 2 1 3 0 , 3 3 3 0 1 3 2 1 1 1 3 2 2 3 0 0 1 0 ⟶ 3 0 3 2 1 3 1 3 3 2 1 1 2 0 0 3 1 0 , 3 3 3 3 3 3 1 3 1 1 1 1 1 0 2 2 3 0 ⟶ 3 3 2 1 1 2 3 1 3 3 1 0 3 0 1 3 3 1 , 3 3 3 1 0 3 1 3 2 3 0 2 2 0 0 1 3 2 ⟶ 3 3 3 3 1 1 0 2 3 0 2 1 0 0 3 2 3 2 , 3 3 3 1 2 0 2 0 1 1 3 0 3 2 2 2 2 3 ⟶ 3 1 2 0 3 1 2 3 2 2 1 0 3 2 3 2 0 3 , 3 3 3 2 0 3 0 3 2 3 3 0 1 2 3 3 3 2 ⟶ 3 3 2 3 2 0 3 3 0 3 0 3 2 3 1 3 3 2 , 3 3 3 2 0 1 0 2 2 2 0 0 0 3 1 0 1 3 ⟶ 3 1 2 1 0 3 0 2 0 0 3 2 0 3 0 2 1 3 , 3 3 1 1 1 1 2 0 1 3 2 0 0 0 1 1 1 3 ⟶ 3 1 1 2 0 3 1 0 0 1 2 3 0 1 1 1 1 3 , 3 3 2 0 1 3 1 3 0 2 3 0 2 1 2 0 1 3 ⟶ 3 3 0 1 2 2 2 2 0 3 3 0 3 1 1 0 1 3 , 3 3 2 3 3 1 0 1 3 2 0 1 2 2 2 1 3 2 ⟶ 3 0 2 1 3 2 2 3 1 3 3 2 1 1 2 0 3 2 , 3 2 0 1 0 3 3 3 3 2 0 0 3 3 1 2 3 3 ⟶ 3 0 3 3 1 3 2 1 2 3 2 0 3 3 0 0 3 3 , 3 2 0 1 3 3 2 3 3 0 2 1 2 2 3 3 1 1 ⟶ 3 1 2 0 2 2 2 1 3 3 0 3 3 3 2 3 1 1 , 3 2 0 1 3 2 0 3 1 1 3 3 0 1 2 2 2 1 ⟶ 2 1 3 3 2 1 3 2 1 2 3 0 0 3 0 1 2 1 , 3 2 0 1 3 2 3 1 3 3 0 1 3 3 3 3 3 3 ⟶ 3 2 3 3 3 3 0 3 1 3 3 0 3 1 2 1 3 3 , 3 2 0 1 3 2 1 0 0 2 0 3 1 2 2 1 1 1 ⟶ 3 2 3 0 0 1 0 3 2 2 1 1 2 1 0 1 2 1 , 3 2 3 2 0 3 2 0 0 0 2 2 0 3 1 1 1 2 ⟶ 3 0 0 1 2 3 0 2 3 2 1 2 1 0 3 2 0 2 , 3 2 3 2 0 1 3 0 3 2 0 1 3 1 3 3 2 3 ⟶ 3 0 3 0 3 2 1 1 0 2 3 1 3 3 3 2 2 3 , 3 2 2 3 2 2 3 0 1 3 3 2 3 1 1 2 1 2 ⟶ 3 2 3 1 3 3 0 2 3 1 2 2 3 1 2 2 1 2 , 1 0 0 2 0 2 1 0 1 0 3 1 0 3 2 3 0 2 ⟶ 1 0 0 2 0 2 1 1 2 0 3 1 0 0 3 3 0 2 , 1 0 3 2 3 2 0 1 3 2 0 1 3 3 0 1 2 1 ⟶ 2 0 3 3 1 3 2 1 2 3 1 0 0 3 1 0 2 1 , 1 0 1 3 2 0 0 0 2 3 0 1 1 2 0 1 0 0 ⟶ 1 0 2 1 0 1 3 1 0 2 0 0 2 0 3 1 0 0 , 1 0 1 1 3 0 1 0 1 1 1 3 2 0 1 0 0 0 ⟶ 1 0 0 3 0 0 0 1 2 0 3 1 1 1 1 1 1 0 , 1 0 1 1 1 1 3 2 3 1 2 0 2 0 2 2 2 2 ⟶ 1 0 2 0 1 3 2 2 0 3 2 1 1 1 1 2 2 2 , 1 3 3 2 0 0 2 1 3 1 3 1 2 2 0 2 3 0 ⟶ 1 3 3 2 1 2 0 3 3 1 0 0 2 2 0 2 3 1 , 1 3 1 1 3 0 1 3 1 1 3 2 0 1 1 3 3 3 ⟶ 1 0 1 3 1 1 2 1 1 3 0 1 3 3 3 1 3 3 , 1 3 1 1 1 0 1 0 1 3 2 2 1 1 2 3 2 2 ⟶ 1 3 2 1 2 1 2 2 1 0 1 1 0 3 3 2 1 1 , 1 3 1 1 1 1 0 2 0 2 1 0 3 0 0 1 0 1 ⟶ 1 1 2 1 1 0 0 3 0 1 0 1 1 3 0 2 0 1 , 1 3 2 1 2 1 3 1 1 3 2 0 0 0 2 3 3 1 ⟶ 1 2 1 0 0 3 3 2 1 1 3 2 3 1 0 3 2 1 , 1 1 0 3 0 1 2 2 1 0 3 2 1 3 1 1 2 1 ⟶ 1 1 3 2 1 1 1 2 1 2 3 1 0 0 0 3 2 1 , 1 1 3 0 3 2 0 1 3 0 1 3 0 1 3 3 0 3 ⟶ 1 1 0 3 3 0 3 2 0 3 3 1 3 1 0 1 0 3 , 1 1 3 1 3 2 0 3 0 1 1 0 3 2 2 0 1 3 ⟶ 1 1 1 3 2 1 1 3 3 1 2 0 0 3 2 0 0 3 , 1 1 2 0 0 2 3 2 0 1 2 0 2 2 3 1 2 1 ⟶ 3 0 1 2 1 2 0 0 2 0 2 2 3 2 1 1 2 1 , 1 2 0 3 3 0 1 3 1 0 2 3 0 2 1 3 2 3 ⟶ 1 0 3 3 3 2 2 3 1 2 1 0 0 3 1 0 2 3 , 1 2 0 1 3 1 0 0 2 0 0 1 0 1 2 3 1 0 ⟶ 2 1 0 3 0 1 1 0 0 0 2 3 0 1 2 1 1 0 , 1 2 3 3 3 3 1 0 0 1 0 1 1 3 2 2 3 1 ⟶ 1 2 1 2 0 1 3 2 3 1 3 1 3 0 0 3 3 1 , 2 0 0 0 0 3 1 1 2 0 2 0 2 3 2 2 2 2 ⟶ 2 1 2 0 0 0 2 1 2 0 0 0 3 3 2 2 2 2 , 2 0 3 3 1 2 0 0 2 0 2 3 1 3 2 3 3 0 ⟶ 2 0 3 1 2 2 3 0 2 0 3 0 2 1 3 3 3 0 , 2 0 1 3 3 3 2 3 2 1 3 2 0 0 2 1 2 1 ⟶ 2 2 0 3 1 1 0 3 3 3 2 1 2 2 0 3 2 1 , 2 0 1 1 0 0 1 3 1 0 1 3 0 3 1 0 3 0 ⟶ 0 3 0 1 0 1 0 0 3 1 3 1 2 1 1 0 3 0 , 2 0 1 2 3 1 2 2 0 0 0 2 1 1 1 3 1 3 ⟶ 2 0 2 2 1 2 1 2 0 1 0 1 0 3 1 3 1 3 , 2 0 1 2 1 3 0 3 2 2 1 1 2 0 2 1 0 0 ⟶ 2 0 2 1 2 2 3 1 2 1 1 0 3 1 0 0 2 0 , 2 0 2 0 2 2 3 0 2 0 2 2 3 2 3 3 0 2 ⟶ 0 3 2 3 2 2 2 2 3 0 0 3 2 2 2 0 0 2 , 2 0 2 3 0 0 2 3 2 0 1 0 1 2 0 0 0 0 ⟶ 0 0 0 1 2 3 3 0 0 0 0 0 2 2 1 2 2 0 , 2 3 0 3 1 1 3 2 2 2 0 1 2 3 0 3 1 2 ⟶ 2 3 0 3 3 1 1 2 1 1 0 0 2 3 2 2 3 2 , 2 3 1 1 2 2 3 0 1 3 2 2 1 3 3 1 0 0 ⟶ 2 3 2 0 1 1 1 3 3 2 3 2 1 2 3 1 0 0 , 2 3 2 0 1 0 1 1 1 1 1 3 2 0 0 2 0 0 ⟶ 1 3 2 1 0 2 3 2 0 0 2 1 1 0 1 1 0 0 , 2 3 2 0 1 3 1 2 1 1 2 1 2 1 2 0 0 2 ⟶ 0 3 3 2 1 2 2 1 2 1 2 1 1 0 2 0 1 2 , 2 3 2 0 1 2 2 0 3 2 1 1 1 2 1 3 0 1 ⟶ 2 1 3 2 1 2 1 2 0 3 2 2 3 1 0 1 0 1 , 2 1 3 2 2 3 2 0 2 0 1 1 1 1 3 3 0 1 ⟶ 2 2 1 1 3 0 0 2 0 1 3 3 1 3 1 2 2 1 , 2 2 0 1 0 1 0 2 3 2 0 1 0 0 1 1 0 2 ⟶ 0 1 2 0 0 1 0 2 2 1 3 0 1 0 2 1 0 2 , 2 2 0 1 3 0 2 1 1 1 2 2 0 3 2 2 0 1 ⟶ 2 2 1 1 2 2 2 2 0 2 3 1 3 0 1 0 0 1 , 2 2 3 0 0 0 2 2 0 2 0 0 2 1 3 1 2 2 ⟶ 2 0 0 3 0 3 2 1 2 2 2 1 2 0 2 0 0 2 , 2 2 3 3 2 2 0 0 1 0 2 3 1 3 1 2 0 0 ⟶ 2 0 3 3 2 2 0 2 0 3 2 0 3 1 2 1 1 0 , 2 2 1 0 0 0 2 0 3 0 2 3 1 3 1 3 1 1 ⟶ 0 1 1 0 3 3 0 2 3 2 1 0 3 0 2 1 2 1 , 2 2 1 0 1 3 2 3 1 1 1 1 3 1 3 0 2 1 ⟶ 2 0 1 1 2 3 3 1 3 2 1 1 3 1 0 1 2 1 , 2 2 2 0 3 1 3 2 3 3 3 2 0 2 0 0 2 0 ⟶ 2 2 2 3 2 1 3 2 3 3 0 0 2 3 2 0 0 0 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,0) ↦ 3, (1,1) ↦ 4, (1,0) ↦ 5, (0,2) ↦ 6, (0,3) ↦ 7, (3,1) ↦ 8, (2,2) ↦ 9, (3,2) ↦ 10, (2,1) ↦ 11, (0,5) ↦ 12, (3,0) ↦ 13, (4,0) ↦ 14, (2,3) ↦ 15, (2,5) ↦ 16, (3,3) ↦ 17, (1,3) ↦ 18, (1,5) ↦ 19, (4,2) ↦ 20, (3,5) ↦ 21, (4,3) ↦ 22, (4,1) ↦ 23 }, it remains to prove termination of the 2000-rule system { 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 0 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 0 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 1 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 1 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 6 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 6 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 7 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 7 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 12 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 12 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 0 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 0 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 1 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 1 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 6 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 6 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 7 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 7 , 5 0 1 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15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 2 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 2 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 2 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 9 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 5 ⟶ 9 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 5 , 9 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 4 ⟶ 9 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 4 , 9 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 2 ⟶ 9 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 2 , 9 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 9 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 9 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 9 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 5 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 5 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 4 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 4 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 2 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 2 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 5 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 5 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 4 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 4 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 2 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 2 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23 }, it remains to prove termination of the 1985-rule system { 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 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11 5 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 5 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 4 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 4 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 2 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 2 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 10 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 10 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 5 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 5 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 4 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 4 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 2 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 2 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 18 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 18 , 20 9 11 5 1 18 10 15 8 4 4 4 18 8 18 13 6 11 19 ⟶ 20 3 1 4 2 15 17 8 18 10 11 4 18 8 5 1 2 11 19 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 6 9 9 15 10 11 18 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9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23 }, it remains to prove termination of the 1980-rule system { 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 0 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 0 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 5 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 5 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 3 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 3 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 13 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 13 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 0 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 0 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 1 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 1 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 6 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 6 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 7 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 7 , 14 0 0 1 2 3 1 4 5 6 3 7 8 2 9 3 1 5 12 ⟶ 14 7 10 11 2 11 4 4 5 0 6 9 11 5 0 0 0 0 12 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 0 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 0 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 5 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 5 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 3 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 3 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 13 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 13 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 3 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 3 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 11 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 11 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 9 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 9 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 15 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 15 , 14 0 0 6 3 7 10 3 1 5 6 3 6 3 6 15 13 6 16 ⟶ 14 0 7 13 0 7 13 6 9 3 0 6 11 5 6 3 6 9 16 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 0 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 0 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 5 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 5 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 3 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 3 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 13 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 13 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 5 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 5 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 4 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 4 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 2 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 2 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 18 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 18 , 14 0 1 5 6 3 6 15 17 13 0 7 10 3 6 3 0 1 19 ⟶ 14 0 7 17 17 13 6 3 6 9 3 0 1 5 6 3 0 1 19 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 0 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 6 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 5 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 2 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 3 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 9 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 13 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 10 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 5 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 5 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 4 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 4 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 2 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 2 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 18 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 18 , 14 0 1 5 6 15 10 11 18 17 8 2 9 3 1 4 4 4 19 ⟶ 20 11 2 15 8 5 7 10 11 5 1 5 1 2 3 7 8 4 19 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 0 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 0 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 1 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 1 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 6 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 6 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 7 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 7 , 0 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 12 ⟶ 0 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 12 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 0 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 0 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 1 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 1 , 5 0 1 2 3 1 18 8 4 2 3 6 9 15 17 13 1 5 6 ⟶ 5 0 7 8 4 2 9 11 5 6 15 13 1 18 13 6 11 5 6 , 5 0 1 2 3 1 18 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0 0 6 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 6 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 6 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 2 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 2 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 9 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 9 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 10 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 10 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 0 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 0 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 1 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 1 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 6 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 6 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 7 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 7 , 20 9 9 3 7 8 18 10 15 17 17 10 3 6 3 0 6 3 12 ⟶ 20 9 9 15 10 11 18 10 15 17 13 0 6 15 10 3 0 0 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 18 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 12 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 5 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 12 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 6 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 3 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 6 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 5 ↦ 2, 6 ↦ 3, 3 ↦ 4, 15 ↦ 5, 17 ↦ 6, 13 ↦ 7, 7 ↦ 8, 10 ↦ 9, 9 ↦ 10, 4 ↦ 11, 2 ↦ 12, 18 ↦ 13, 19 ↦ 14, 14 ↦ 15, 8 ↦ 16, 11 ↦ 17, 22 ↦ 18, 16 ↦ 19, 23 ↦ 20, 12 ↦ 21, 20 ↦ 22 }, it remains to prove termination of the 130-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 0 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 2 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 11 ⟶ 0 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 11 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 0 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 12 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 0 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 13 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 0 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 14 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 2 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 2 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 11 ⟶ 2 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 11 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 11 ⟶ 4 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 11 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 11 ⟶ 7 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 11 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 11 ⟶ 15 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 11 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 10 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 10 5 16 11 12 10 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 10 5 16 11 12 10 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 10 5 16 11 12 10 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 10 5 16 11 12 10 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 10 5 16 11 12 10 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 10 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 10 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 10 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 10 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 10 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 10 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 10 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 10 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 10 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 10 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 2 , 1 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 11 ⟶ 1 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 11 , 1 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 12 , 1 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 13 , 1 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 14 , 11 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 11 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 2 , 11 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 11 ⟶ 11 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 11 , 11 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 11 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 12 , 11 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 11 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 13 , 11 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 11 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 14 , 17 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 2 , 17 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 11 ⟶ 17 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 11 , 17 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 12 , 17 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 13 , 17 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 14 , 16 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 2 , 16 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 11 ⟶ 16 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 11 , 16 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 12 , 16 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 13 , 16 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 14 , 20 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 2 , 20 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 11 ⟶ 20 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 11 , 20 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 12 , 20 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 13 , 20 13 16 11 11 11 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 11 12 17 11 2 0 8 7 1 2 1 11 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 21 , 10 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 0 ⟶ 10 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 0 , 10 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 1 ⟶ 10 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 1 , 10 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 3 ⟶ 10 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 3 , 10 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 8 ⟶ 10 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 8 , 10 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 21 ⟶ 10 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 10 17 11 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 10 5 16 12 17 11 2 8 16 2 0 3 4 21 , 3 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 21 , 10 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 0 ⟶ 10 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 0 , 10 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 1 ⟶ 10 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 1 , 10 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 3 ⟶ 10 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 3 , 10 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 8 ⟶ 10 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 8 , 10 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 21 ⟶ 10 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 11 12 10 5 7 1 13 9 10 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 11 11 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 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0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 11 ↦ 10, 10 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 129-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 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0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 128-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 12 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 12 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 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0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 127-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 14 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 14 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 126-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 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0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 125-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 124-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 12 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 12 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 14 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 14 17 12 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 12 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 12 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 14 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 12 6 9 19 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 1 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 10 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 17 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 16 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 2 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 10 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 14 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 12 , 20 12 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 14 17 10 2 0 8 7 1 2 1 10 12 7 3 4 1 13 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 3 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 3 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 14 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 14 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 11 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 11 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 9 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 9 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 0 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 0 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 1 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 1 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 3 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 3 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 8 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 8 , 22 4 1 14 17 12 7 8 9 11 17 10 14 4 3 17 2 0 21 ⟶ 22 4 3 17 14 11 5 16 14 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 3 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 14 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 14 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 11 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 9 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 0 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 1 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 3 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 8 , 22 5 16 10 14 11 5 7 1 12 9 11 17 12 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 12 6 9 5 9 17 14 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 123-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 14 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 14 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 13 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 13 17 14 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 14 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 14 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 13 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 14 6 9 19 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 1 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 10 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 17 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 16 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 2 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 10 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 13 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 14 , 20 14 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 13 17 10 2 0 8 7 1 2 1 10 14 7 3 4 1 12 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 3 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 3 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 13 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 13 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 11 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 11 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 9 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 9 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 0 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 0 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 1 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 1 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 3 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 3 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 8 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 8 , 22 4 1 13 17 14 7 8 9 11 17 10 13 4 3 17 2 0 21 ⟶ 22 4 3 17 13 11 5 16 13 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 3 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 13 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 13 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 11 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 9 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 0 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 1 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 3 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 8 , 22 5 16 10 13 11 5 7 1 14 9 11 17 14 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 14 6 9 5 9 17 13 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 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⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 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, 13 ↦ 12, 14 ↦ 13, 12 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 122-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 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⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 121-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 120-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 119-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 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0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 118-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 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0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 117-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 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0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 116-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 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0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 115-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 114-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 8 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 8 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 113-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 13 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 13 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 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0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 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⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 112-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 5 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 5 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 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0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 111-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 6 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 6 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 18 6 7 8 9 4 3 5 9 5 6 9 11 5 16 10 12 11 17 ⟶ 18 9 5 9 5 7 3 5 9 5 9 5 9 17 12 17 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 18 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 18 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 19 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 18 ↦ 16, 16 ↦ 17, 17 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 110-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 16 6 7 8 9 4 3 5 9 5 6 9 11 5 17 10 12 11 18 ⟶ 16 9 5 9 5 7 3 5 9 5 9 5 9 18 12 18 13 7 1 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 18 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 19 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 18 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 19 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 18 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 19 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 18 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 19 , 16 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 16 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 4 , 16 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 16 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 18 , 16 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 16 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 11 , 16 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 16 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 5 , 16 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 19 ⟶ 16 6 9 5 9 4 8 6 7 8 7 8 9 5 17 13 6 9 19 , 1 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 2 ⟶ 1 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 10 ⟶ 1 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 12 ⟶ 1 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 13 ⟶ 1 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 14 ⟶ 1 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 2 ⟶ 10 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 10 ⟶ 10 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 12 ⟶ 10 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 13 ⟶ 10 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 14 ⟶ 10 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 18 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 2 ⟶ 18 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 18 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 10 ⟶ 18 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 18 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 12 ⟶ 18 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 18 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 13 ⟶ 18 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 18 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 14 ⟶ 18 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 2 ⟶ 17 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 10 ⟶ 17 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 12 ⟶ 17 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 13 ⟶ 17 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 14 ⟶ 17 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 2 ⟶ 20 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 10 ⟶ 20 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 12 ⟶ 20 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 13 ⟶ 20 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 17 10 10 10 2 3 4 3 18 2 8 7 0 1 2 1 14 ⟶ 20 10 12 18 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 0 ⟶ 3 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 0 , 3 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 1 ⟶ 3 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 1 , 3 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 3 ⟶ 3 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 3 , 3 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 8 ⟶ 3 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 8 , 3 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 21 ⟶ 3 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 21 , 12 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 0 ⟶ 12 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 0 , 12 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 1 ⟶ 12 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 1 , 12 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 3 ⟶ 12 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 3 , 12 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 8 ⟶ 12 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 8 , 12 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 21 ⟶ 12 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 21 , 11 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 0 ⟶ 11 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 0 , 11 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 1 ⟶ 11 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 1 , 11 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 3 ⟶ 11 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 3 , 11 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 8 ⟶ 11 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 8 , 11 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 21 ⟶ 11 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 21 , 9 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 0 ⟶ 9 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 0 , 9 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 1 ⟶ 9 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 1 , 9 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 3 ⟶ 9 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 3 , 9 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 8 ⟶ 9 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 8 , 9 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 21 ⟶ 9 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 21 , 22 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 0 ⟶ 22 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 0 , 22 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 1 ⟶ 22 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 1 , 22 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 3 ⟶ 22 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 3 , 22 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 8 ⟶ 22 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 8 , 22 4 1 12 18 13 7 8 9 11 18 10 12 4 3 18 2 0 21 ⟶ 22 4 3 18 12 11 5 17 12 18 10 2 8 17 2 0 3 4 21 , 3 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 0 , 3 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 1 , 3 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 3 , 3 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 8 , 3 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 21 , 12 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 0 , 12 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 1 , 12 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 3 , 12 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 8 , 12 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 21 , 11 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 0 , 11 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 1 , 11 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 3 , 11 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 8 , 11 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 21 , 9 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 0 , 9 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 1 , 9 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 3 , 9 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 8 , 9 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 21 , 22 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 0 , 22 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 1 , 22 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 3 , 22 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 8 , 22 5 17 10 12 11 5 7 1 13 9 11 18 13 6 17 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 18 12 5 17 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 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0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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, 17 ↦ 16, 18 ↦ 17, 19 ↦ 18, 16 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22 }, it remains to prove termination of the 109-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 8 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 8 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 18 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 13 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 13 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 18 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 5 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 5 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 18 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 6 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 6 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 18 , 19 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 4 ⟶ 19 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 4 , 19 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 17 ⟶ 19 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 17 , 19 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 11 ⟶ 19 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 11 , 19 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 5 ⟶ 19 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 5 , 19 6 6 9 4 8 7 8 9 5 6 7 1 12 5 6 6 9 18 ⟶ 19 6 9 5 9 4 8 6 7 8 7 8 9 5 16 13 6 9 18 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 20 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 20 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 22 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 21 ⟶ 22 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 21 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 3 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 3 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 12 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 12 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 11 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 11 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 9 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 9 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 0 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 0 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 1 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 1 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 3 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 3 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 8 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 8 , 22 5 16 10 12 11 5 7 1 13 9 11 17 13 6 16 2 0 21 ⟶ 22 5 9 4 1 10 10 13 6 9 5 9 17 12 5 16 2 0 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 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, 16 ↦ 16, 17 ↦ 17, 20 ↦ 18, 21 ↦ 19, 22 ↦ 20 }, it remains to prove termination of the 59-rule system { 0 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 0 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 2 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 2 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 2 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 2 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 12 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 12 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 13 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 13 , 4 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 14 ⟶ 4 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 14 , 7 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 7 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 15 0 1 2 3 4 3 5 6 7 0 8 9 4 3 4 0 1 10 ⟶ 15 0 8 6 6 7 3 4 3 11 4 0 1 2 3 4 0 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 1 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 1 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 10 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 10 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 17 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 17 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 16 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 16 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 18 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 2 ⟶ 18 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 2 , 18 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 10 ⟶ 18 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 10 , 18 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 12 ⟶ 18 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 12 , 18 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 13 ⟶ 18 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 13 , 18 13 16 10 10 10 2 3 4 3 17 2 8 7 0 1 2 1 14 ⟶ 18 10 12 17 10 2 0 8 7 1 2 1 10 13 7 3 4 1 14 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 3 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 19 ⟶ 3 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 19 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 12 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 19 ⟶ 12 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 19 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 11 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 19 ⟶ 11 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 19 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 9 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 19 ⟶ 9 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 19 , 20 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 0 ⟶ 20 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 0 , 20 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 1 ⟶ 20 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 1 , 20 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 3 ⟶ 20 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 3 , 20 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 8 ⟶ 20 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 8 , 20 4 1 12 17 13 7 8 9 11 17 10 12 4 3 17 2 0 19 ⟶ 20 4 3 17 12 11 5 16 12 17 10 2 8 16 2 0 3 4 19 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 3 ↦ 0, 4 ↦ 1, 1 ↦ 2, 12 ↦ 3, 17 ↦ 4, 13 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 11 ↦ 9, 10 ↦ 10, 2 ↦ 11, 0 ↦ 12, 5 ↦ 13, 16 ↦ 14, 19 ↦ 15, 20 ↦ 16 }, it remains to prove termination of the 25-rule system { 0 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 12 ⟶ 0 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 12 , 0 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 2 ⟶ 0 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 2 , 0 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 0 ⟶ 0 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 0 , 0 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 7 ⟶ 0 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 7 , 0 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 15 ⟶ 0 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 15 , 3 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 12 ⟶ 3 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 12 , 3 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 2 ⟶ 3 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 2 , 3 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 0 ⟶ 3 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 0 , 3 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 7 ⟶ 3 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 7 , 3 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 15 ⟶ 3 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 15 , 9 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 12 ⟶ 9 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 12 , 9 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 2 ⟶ 9 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 2 , 9 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 0 ⟶ 9 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 0 , 9 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 7 ⟶ 9 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 7 , 9 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 15 ⟶ 9 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 15 , 8 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 12 ⟶ 8 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 12 , 8 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 2 ⟶ 8 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 2 , 8 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 0 ⟶ 8 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 0 , 8 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 7 ⟶ 8 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 7 , 8 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 15 ⟶ 8 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 15 , 16 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 12 ⟶ 16 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 12 , 16 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 2 ⟶ 16 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 2 , 16 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 0 ⟶ 16 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 0 , 16 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 7 ⟶ 16 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 7 , 16 1 2 3 4 5 6 7 8 9 4 10 3 1 0 4 11 12 15 ⟶ 16 1 0 4 3 9 13 14 3 4 10 11 7 14 11 12 0 1 15 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.