/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 },
it remains to prove termination of the 50-rule system
{ 0 1 0 ⟶ 0 2 1 0 ,
  0 1 0 ⟶ 0 0 2 1 0 ,
  0 1 0 ⟶ 0 0 2 1 2 ,
  0 1 0 ⟶ 0 2 1 0 2 ,
  0 1 0 ⟶ 0 3 2 1 0 ,
  0 1 0 ⟶ 1 0 0 0 2 ,
  0 1 0 ⟶ 1 0 0 2 0 ,
  0 1 0 ⟶ 1 0 4 2 0 ,
  0 1 0 ⟶ 1 4 0 4 0 ,
  0 1 0 ⟶ 4 0 0 2 1 ,
  0 1 0 ⟶ 5 0 0 4 1 ,
  0 1 0 ⟶ 5 1 0 4 0 ,
  0 1 0 ⟶ 0 2 1 0 3 2 ,
  0 1 0 ⟶ 0 4 0 4 1 3 ,
  0 1 0 ⟶ 0 4 2 2 1 0 ,
  0 1 0 ⟶ 0 5 2 1 2 0 ,
  0 1 0 ⟶ 0 5 2 5 1 0 ,
  0 1 0 ⟶ 1 0 0 5 4 4 ,
  0 1 0 ⟶ 1 0 4 4 4 0 ,
  0 1 0 ⟶ 1 5 0 0 4 2 ,
  0 1 0 ⟶ 3 0 0 4 1 4 ,
  0 1 0 ⟶ 4 5 1 0 2 0 ,
  0 1 0 ⟶ 5 5 1 0 0 2 ,
  0 0 1 0 ⟶ 1 0 0 2 0 ,
  0 0 1 0 ⟶ 0 1 5 0 0 2 ,
  0 1 0 3 ⟶ 1 0 3 3 0 2 ,
  0 1 0 3 ⟶ 1 0 5 3 2 0 ,
  0 1 1 0 ⟶ 0 4 4 1 1 0 ,
  0 1 1 3 ⟶ 3 4 5 1 1 0 ,
  0 1 2 0 ⟶ 1 1 0 2 0 ,
  0 1 2 0 ⟶ 3 0 2 1 0 ,
  0 1 2 0 ⟶ 4 1 0 0 2 ,
  0 1 2 0 ⟶ 0 0 4 2 5 1 ,
  0 1 2 0 ⟶ 1 1 2 0 4 0 ,
  0 1 2 0 ⟶ 3 0 2 1 0 4 ,
  0 1 3 0 ⟶ 1 0 3 0 2 ,
  0 1 4 0 ⟶ 0 3 4 2 1 0 ,
  0 1 5 0 ⟶ 0 5 1 4 0 ,
  0 1 5 0 ⟶ 1 5 3 0 2 0 ,
  0 3 1 0 ⟶ 1 2 3 0 5 0 ,
  5 0 1 0 ⟶ 1 4 0 0 5 1 ,
  5 0 1 0 ⟶ 2 1 0 0 4 5 ,
  0 1 0 0 0 ⟶ 0 0 5 1 0 0 ,
  0 1 2 4 0 ⟶ 0 0 5 4 2 1 ,
  0 1 2 5 0 ⟶ 1 0 2 0 5 4 ,
  0 1 4 0 0 ⟶ 0 0 0 4 1 0 ,
  0 1 4 5 0 ⟶ 1 5 0 0 4 2 ,
  0 3 0 1 0 ⟶ 0 3 0 0 2 1 ,
  3 0 3 1 0 ⟶ 0 1 3 2 3 0 ,
  5 0 1 2 0 ⟶ 0 0 5 2 1 0 }

Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,0) ↦ 2, (0,2) ↦ 3, (2,1) ↦ 4, (0,3) ↦ 5, (0,4) ↦ 6, (0,5) ↦ 7, (0,7) ↦ 8, (2,0) ↦ 9, (3,0) ↦ 10, (4,0) ↦ 11, (5,0) ↦ 12, (6,0) ↦ 13, (1,2) ↦ 14, (2,2) ↦ 15, (2,3) ↦ 16, (2,4) ↦ 17, (2,5) ↦ 18, (2,7) ↦ 19, (3,2) ↦ 20, (1,1) ↦ 21, (3,1) ↦ 22, (4,1) ↦ 23, (5,1) ↦ 24, (6,1) ↦ 25, (4,2) ↦ 26, (1,4) ↦ 27, (1,3) ↦ 28, (1,5) ↦ 29, (1,7) ↦ 30, (3,4) ↦ 31, (4,4) ↦ 32, (5,4) ↦ 33, (6,4) ↦ 34, (3,5) ↦ 35, (4,5) ↦ 36, (5,5) ↦ 37, (6,5) ↦ 38, (3,3) ↦ 39, (3,7) ↦ 40, (5,2) ↦ 41, (4,3) ↦ 42, (4,7) ↦ 43, (5,3) ↦ 44, (6,3) ↦ 45, (5,7) ↦ 46, (6,2) ↦ 47 },
it remains to prove termination of the 2450-rule system
{ 0 1 2 0 ⟶ 0 3 4 2 0 ,
  0 1 2 1 ⟶ 0 3 4 2 1 ,
  0 1 2 3 ⟶ 0 3 4 2 3 ,
  0 1 2 5 ⟶ 0 3 4 2 5 ,
  0 1 2 6 ⟶ 0 3 4 2 6 ,
  0 1 2 7 ⟶ 0 3 4 2 7 ,
  0 1 2 8 ⟶ 0 3 4 2 8 ,
  2 1 2 0 ⟶ 2 3 4 2 0 ,
  2 1 2 1 ⟶ 2 3 4 2 1 ,
  2 1 2 3 ⟶ 2 3 4 2 3 ,
  2 1 2 5 ⟶ 2 3 4 2 5 ,
  2 1 2 6 ⟶ 2 3 4 2 6 ,
  2 1 2 7 ⟶ 2 3 4 2 7 ,
  2 1 2 8 ⟶ 2 3 4 2 8 ,
  9 1 2 0 ⟶ 9 3 4 2 0 ,
  9 1 2 1 ⟶ 9 3 4 2 1 ,
  9 1 2 3 ⟶ 9 3 4 2 3 ,
  9 1 2 5 ⟶ 9 3 4 2 5 ,
  9 1 2 6 ⟶ 9 3 4 2 6 ,
  9 1 2 7 ⟶ 9 3 4 2 7 ,
  9 1 2 8 ⟶ 9 3 4 2 8 ,
  10 1 2 0 ⟶ 10 3 4 2 0 ,
  10 1 2 1 ⟶ 10 3 4 2 1 ,
  10 1 2 3 ⟶ 10 3 4 2 3 ,
  10 1 2 5 ⟶ 10 3 4 2 5 ,
  10 1 2 6 ⟶ 10 3 4 2 6 ,
  10 1 2 7 ⟶ 10 3 4 2 7 ,
  10 1 2 8 ⟶ 10 3 4 2 8 ,
  11 1 2 0 ⟶ 11 3 4 2 0 ,
  11 1 2 1 ⟶ 11 3 4 2 1 ,
  11 1 2 3 ⟶ 11 3 4 2 3 ,
  11 1 2 5 ⟶ 11 3 4 2 5 ,
  11 1 2 6 ⟶ 11 3 4 2 6 ,
  11 1 2 7 ⟶ 11 3 4 2 7 ,
  11 1 2 8 ⟶ 11 3 4 2 8 ,
  12 1 2 0 ⟶ 12 3 4 2 0 ,
  12 1 2 1 ⟶ 12 3 4 2 1 ,
  12 1 2 3 ⟶ 12 3 4 2 3 ,
  12 1 2 5 ⟶ 12 3 4 2 5 ,
  12 1 2 6 ⟶ 12 3 4 2 6 ,
  12 1 2 7 ⟶ 12 3 4 2 7 ,
  12 1 2 8 ⟶ 12 3 4 2 8 ,
  13 1 2 0 ⟶ 13 3 4 2 0 ,
  13 1 2 1 ⟶ 13 3 4 2 1 ,
  13 1 2 3 ⟶ 13 3 4 2 3 ,
  13 1 2 5 ⟶ 13 3 4 2 5 ,
  13 1 2 6 ⟶ 13 3 4 2 6 ,
  13 1 2 7 ⟶ 13 3 4 2 7 ,
  13 1 2 8 ⟶ 13 3 4 2 8 ,
  0 1 2 0 ⟶ 0 0 3 4 2 0 ,
  0 1 2 1 ⟶ 0 0 3 4 2 1 ,
  0 1 2 3 ⟶ 0 0 3 4 2 3 ,
  0 1 2 5 ⟶ 0 0 3 4 2 5 ,
  0 1 2 6 ⟶ 0 0 3 4 2 6 ,
  0 1 2 7 ⟶ 0 0 3 4 2 7 ,
  0 1 2 8 ⟶ 0 0 3 4 2 8 ,
  2 1 2 0 ⟶ 2 0 3 4 2 0 ,
  2 1 2 1 ⟶ 2 0 3 4 2 1 ,
  2 1 2 3 ⟶ 2 0 3 4 2 3 ,
  2 1 2 5 ⟶ 2 0 3 4 2 5 ,
  2 1 2 6 ⟶ 2 0 3 4 2 6 ,
  2 1 2 7 ⟶ 2 0 3 4 2 7 ,
  2 1 2 8 ⟶ 2 0 3 4 2 8 ,
  9 1 2 0 ⟶ 9 0 3 4 2 0 ,
  9 1 2 1 ⟶ 9 0 3 4 2 1 ,
  9 1 2 3 ⟶ 9 0 3 4 2 3 ,
  9 1 2 5 ⟶ 9 0 3 4 2 5 ,
  9 1 2 6 ⟶ 9 0 3 4 2 6 ,
  9 1 2 7 ⟶ 9 0 3 4 2 7 ,
  9 1 2 8 ⟶ 9 0 3 4 2 8 ,
  10 1 2 0 ⟶ 10 0 3 4 2 0 ,
  10 1 2 1 ⟶ 10 0 3 4 2 1 ,
  10 1 2 3 ⟶ 10 0 3 4 2 3 ,
  10 1 2 5 ⟶ 10 0 3 4 2 5 ,
  10 1 2 6 ⟶ 10 0 3 4 2 6 ,
  10 1 2 7 ⟶ 10 0 3 4 2 7 ,
  10 1 2 8 ⟶ 10 0 3 4 2 8 ,
  11 1 2 0 ⟶ 11 0 3 4 2 0 ,
  11 1 2 1 ⟶ 11 0 3 4 2 1 ,
  11 1 2 3 ⟶ 11 0 3 4 2 3 ,
  11 1 2 5 ⟶ 11 0 3 4 2 5 ,
  11 1 2 6 ⟶ 11 0 3 4 2 6 ,
  11 1 2 7 ⟶ 11 0 3 4 2 7 ,
  11 1 2 8 ⟶ 11 0 3 4 2 8 ,
  12 1 2 0 ⟶ 12 0 3 4 2 0 ,
  12 1 2 1 ⟶ 12 0 3 4 2 1 ,
  12 1 2 3 ⟶ 12 0 3 4 2 3 ,
  12 1 2 5 ⟶ 12 0 3 4 2 5 ,
  12 1 2 6 ⟶ 12 0 3 4 2 6 ,
  12 1 2 7 ⟶ 12 0 3 4 2 7 ,
  12 1 2 8 ⟶ 12 0 3 4 2 8 ,
  13 1 2 0 ⟶ 13 0 3 4 2 0 ,
  13 1 2 1 ⟶ 13 0 3 4 2 1 ,
  13 1 2 3 ⟶ 13 0 3 4 2 3 ,
  13 1 2 5 ⟶ 13 0 3 4 2 5 ,
  13 1 2 6 ⟶ 13 0 3 4 2 6 ,
  13 1 2 7 ⟶ 13 0 3 4 2 7 ,
  13 1 2 8 ⟶ 13 0 3 4 2 8 ,
  0 1 2 0 ⟶ 0 0 3 4 14 9 ,
  0 1 2 1 ⟶ 0 0 3 4 14 4 ,
  0 1 2 3 ⟶ 0 0 3 4 14 15 ,
  0 1 2 5 ⟶ 0 0 3 4 14 16 ,
  0 1 2 6 ⟶ 0 0 3 4 14 17 ,
  0 1 2 7 ⟶ 0 0 3 4 14 18 ,
  0 1 2 8 ⟶ 0 0 3 4 14 19 ,
  2 1 2 0 ⟶ 2 0 3 4 14 9 ,
  2 1 2 1 ⟶ 2 0 3 4 14 4 ,
  2 1 2 3 ⟶ 2 0 3 4 14 15 ,
  2 1 2 5 ⟶ 2 0 3 4 14 16 ,
  2 1 2 6 ⟶ 2 0 3 4 14 17 ,
  2 1 2 7 ⟶ 2 0 3 4 14 18 ,
  2 1 2 8 ⟶ 2 0 3 4 14 19 ,
  9 1 2 0 ⟶ 9 0 3 4 14 9 ,
  9 1 2 1 ⟶ 9 0 3 4 14 4 ,
  9 1 2 3 ⟶ 9 0 3 4 14 15 ,
  9 1 2 5 ⟶ 9 0 3 4 14 16 ,
  9 1 2 6 ⟶ 9 0 3 4 14 17 ,
  9 1 2 7 ⟶ 9 0 3 4 14 18 ,
  9 1 2 8 ⟶ 9 0 3 4 14 19 ,
  10 1 2 0 ⟶ 10 0 3 4 14 9 ,
  10 1 2 1 ⟶ 10 0 3 4 14 4 ,
  10 1 2 3 ⟶ 10 0 3 4 14 15 ,
  10 1 2 5 ⟶ 10 0 3 4 14 16 ,
  10 1 2 6 ⟶ 10 0 3 4 14 17 ,
  10 1 2 7 ⟶ 10 0 3 4 14 18 ,
  10 1 2 8 ⟶ 10 0 3 4 14 19 ,
  11 1 2 0 ⟶ 11 0 3 4 14 9 ,
  11 1 2 1 ⟶ 11 0 3 4 14 4 ,
  11 1 2 3 ⟶ 11 0 3 4 14 15 ,
  11 1 2 5 ⟶ 11 0 3 4 14 16 ,
  11 1 2 6 ⟶ 11 0 3 4 14 17 ,
  11 1 2 7 ⟶ 11 0 3 4 14 18 ,
  11 1 2 8 ⟶ 11 0 3 4 14 19 ,
  12 1 2 0 ⟶ 12 0 3 4 14 9 ,
  12 1 2 1 ⟶ 12 0 3 4 14 4 ,
  12 1 2 3 ⟶ 12 0 3 4 14 15 ,
  12 1 2 5 ⟶ 12 0 3 4 14 16 ,
  12 1 2 6 ⟶ 12 0 3 4 14 17 ,
  12 1 2 7 ⟶ 12 0 3 4 14 18 ,
  12 1 2 8 ⟶ 12 0 3 4 14 19 ,
  13 1 2 0 ⟶ 13 0 3 4 14 9 ,
  13 1 2 1 ⟶ 13 0 3 4 14 4 ,
  13 1 2 3 ⟶ 13 0 3 4 14 15 ,
  13 1 2 5 ⟶ 13 0 3 4 14 16 ,
  13 1 2 6 ⟶ 13 0 3 4 14 17 ,
  13 1 2 7 ⟶ 13 0 3 4 14 18 ,
  13 1 2 8 ⟶ 13 0 3 4 14 19 ,
  0 1 2 0 ⟶ 0 3 4 2 3 9 ,
  0 1 2 1 ⟶ 0 3 4 2 3 4 ,
  0 1 2 3 ⟶ 0 3 4 2 3 15 ,
  0 1 2 5 ⟶ 0 3 4 2 3 16 ,
  0 1 2 6 ⟶ 0 3 4 2 3 17 ,
  0 1 2 7 ⟶ 0 3 4 2 3 18 ,
  0 1 2 8 ⟶ 0 3 4 2 3 19 ,
  2 1 2 0 ⟶ 2 3 4 2 3 9 ,
  2 1 2 1 ⟶ 2 3 4 2 3 4 ,
  2 1 2 3 ⟶ 2 3 4 2 3 15 ,
  2 1 2 5 ⟶ 2 3 4 2 3 16 ,
  2 1 2 6 ⟶ 2 3 4 2 3 17 ,
  2 1 2 7 ⟶ 2 3 4 2 3 18 ,
  2 1 2 8 ⟶ 2 3 4 2 3 19 ,
  9 1 2 0 ⟶ 9 3 4 2 3 9 ,
  9 1 2 1 ⟶ 9 3 4 2 3 4 ,
  9 1 2 3 ⟶ 9 3 4 2 3 15 ,
  9 1 2 5 ⟶ 9 3 4 2 3 16 ,
  9 1 2 6 ⟶ 9 3 4 2 3 17 ,
  9 1 2 7 ⟶ 9 3 4 2 3 18 ,
  9 1 2 8 ⟶ 9 3 4 2 3 19 ,
  10 1 2 0 ⟶ 10 3 4 2 3 9 ,
  10 1 2 1 ⟶ 10 3 4 2 3 4 ,
  10 1 2 3 ⟶ 10 3 4 2 3 15 ,
  10 1 2 5 ⟶ 10 3 4 2 3 16 ,
  10 1 2 6 ⟶ 10 3 4 2 3 17 ,
  10 1 2 7 ⟶ 10 3 4 2 3 18 ,
  10 1 2 8 ⟶ 10 3 4 2 3 19 ,
  11 1 2 0 ⟶ 11 3 4 2 3 9 ,
  11 1 2 1 ⟶ 11 3 4 2 3 4 ,
  11 1 2 3 ⟶ 11 3 4 2 3 15 ,
  11 1 2 5 ⟶ 11 3 4 2 3 16 ,
  11 1 2 6 ⟶ 11 3 4 2 3 17 ,
  11 1 2 7 ⟶ 11 3 4 2 3 18 ,
  11 1 2 8 ⟶ 11 3 4 2 3 19 ,
  12 1 2 0 ⟶ 12 3 4 2 3 9 ,
  12 1 2 1 ⟶ 12 3 4 2 3 4 ,
  12 1 2 3 ⟶ 12 3 4 2 3 15 ,
  12 1 2 5 ⟶ 12 3 4 2 3 16 ,
  12 1 2 6 ⟶ 12 3 4 2 3 17 ,
  12 1 2 7 ⟶ 12 3 4 2 3 18 ,
  12 1 2 8 ⟶ 12 3 4 2 3 19 ,
  13 1 2 0 ⟶ 13 3 4 2 3 9 ,
  13 1 2 1 ⟶ 13 3 4 2 3 4 ,
  13 1 2 3 ⟶ 13 3 4 2 3 15 ,
  13 1 2 5 ⟶ 13 3 4 2 3 16 ,
  13 1 2 6 ⟶ 13 3 4 2 3 17 ,
  13 1 2 7 ⟶ 13 3 4 2 3 18 ,
  13 1 2 8 ⟶ 13 3 4 2 3 19 ,
  0 1 2 0 ⟶ 0 5 20 4 2 0 ,
  0 1 2 1 ⟶ 0 5 20 4 2 1 ,
  0 1 2 3 ⟶ 0 5 20 4 2 3 ,
  0 1 2 5 ⟶ 0 5 20 4 2 5 ,
  0 1 2 6 ⟶ 0 5 20 4 2 6 ,
  0 1 2 7 ⟶ 0 5 20 4 2 7 ,
  0 1 2 8 ⟶ 0 5 20 4 2 8 ,
  2 1 2 0 ⟶ 2 5 20 4 2 0 ,
  2 1 2 1 ⟶ 2 5 20 4 2 1 ,
  2 1 2 3 ⟶ 2 5 20 4 2 3 ,
  2 1 2 5 ⟶ 2 5 20 4 2 5 ,
  2 1 2 6 ⟶ 2 5 20 4 2 6 ,
  2 1 2 7 ⟶ 2 5 20 4 2 7 ,
  2 1 2 8 ⟶ 2 5 20 4 2 8 ,
  9 1 2 0 ⟶ 9 5 20 4 2 0 ,
  9 1 2 1 ⟶ 9 5 20 4 2 1 ,
  9 1 2 3 ⟶ 9 5 20 4 2 3 ,
  9 1 2 5 ⟶ 9 5 20 4 2 5 ,
  9 1 2 6 ⟶ 9 5 20 4 2 6 ,
  9 1 2 7 ⟶ 9 5 20 4 2 7 ,
  9 1 2 8 ⟶ 9 5 20 4 2 8 ,
  10 1 2 0 ⟶ 10 5 20 4 2 0 ,
  10 1 2 1 ⟶ 10 5 20 4 2 1 ,
  10 1 2 3 ⟶ 10 5 20 4 2 3 ,
  10 1 2 5 ⟶ 10 5 20 4 2 5 ,
  10 1 2 6 ⟶ 10 5 20 4 2 6 ,
  10 1 2 7 ⟶ 10 5 20 4 2 7 ,
  10 1 2 8 ⟶ 10 5 20 4 2 8 ,
  11 1 2 0 ⟶ 11 5 20 4 2 0 ,
  11 1 2 1 ⟶ 11 5 20 4 2 1 ,
  11 1 2 3 ⟶ 11 5 20 4 2 3 ,
  11 1 2 5 ⟶ 11 5 20 4 2 5 ,
  11 1 2 6 ⟶ 11 5 20 4 2 6 ,
  11 1 2 7 ⟶ 11 5 20 4 2 7 ,
  11 1 2 8 ⟶ 11 5 20 4 2 8 ,
  12 1 2 0 ⟶ 12 5 20 4 2 0 ,
  12 1 2 1 ⟶ 12 5 20 4 2 1 ,
  12 1 2 3 ⟶ 12 5 20 4 2 3 ,
  12 1 2 5 ⟶ 12 5 20 4 2 5 ,
  12 1 2 6 ⟶ 12 5 20 4 2 6 ,
  12 1 2 7 ⟶ 12 5 20 4 2 7 ,
  12 1 2 8 ⟶ 12 5 20 4 2 8 ,
  13 1 2 0 ⟶ 13 5 20 4 2 0 ,
  13 1 2 1 ⟶ 13 5 20 4 2 1 ,
  13 1 2 3 ⟶ 13 5 20 4 2 3 ,
  13 1 2 5 ⟶ 13 5 20 4 2 5 ,
  13 1 2 6 ⟶ 13 5 20 4 2 6 ,
  13 1 2 7 ⟶ 13 5 20 4 2 7 ,
  13 1 2 8 ⟶ 13 5 20 4 2 8 ,
  0 1 2 0 ⟶ 1 2 0 0 3 9 ,
  0 1 2 1 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 15 ,
  0 1 2 5 ⟶ 1 2 0 0 3 16 ,
  0 1 2 6 ⟶ 1 2 0 0 3 17 ,
  0 1 2 7 ⟶ 1 2 0 0 3 18 ,
  0 1 2 8 ⟶ 1 2 0 0 3 19 ,
  2 1 2 0 ⟶ 21 2 0 0 3 9 ,
  2 1 2 1 ⟶ 21 2 0 0 3 4 ,
  2 1 2 3 ⟶ 21 2 0 0 3 15 ,
  2 1 2 5 ⟶ 21 2 0 0 3 16 ,
  2 1 2 6 ⟶ 21 2 0 0 3 17 ,
  2 1 2 7 ⟶ 21 2 0 0 3 18 ,
  2 1 2 8 ⟶ 21 2 0 0 3 19 ,
  9 1 2 0 ⟶ 4 2 0 0 3 9 ,
  9 1 2 1 ⟶ 4 2 0 0 3 4 ,
  9 1 2 3 ⟶ 4 2 0 0 3 15 ,
  9 1 2 5 ⟶ 4 2 0 0 3 16 ,
  9 1 2 6 ⟶ 4 2 0 0 3 17 ,
  9 1 2 7 ⟶ 4 2 0 0 3 18 ,
  9 1 2 8 ⟶ 4 2 0 0 3 19 ,
  10 1 2 0 ⟶ 22 2 0 0 3 9 ,
  10 1 2 1 ⟶ 22 2 0 0 3 4 ,
  10 1 2 3 ⟶ 22 2 0 0 3 15 ,
  10 1 2 5 ⟶ 22 2 0 0 3 16 ,
  10 1 2 6 ⟶ 22 2 0 0 3 17 ,
  10 1 2 7 ⟶ 22 2 0 0 3 18 ,
  10 1 2 8 ⟶ 22 2 0 0 3 19 ,
  11 1 2 0 ⟶ 23 2 0 0 3 9 ,
  11 1 2 1 ⟶ 23 2 0 0 3 4 ,
  11 1 2 3 ⟶ 23 2 0 0 3 15 ,
  11 1 2 5 ⟶ 23 2 0 0 3 16 ,
  11 1 2 6 ⟶ 23 2 0 0 3 17 ,
  11 1 2 7 ⟶ 23 2 0 0 3 18 ,
  11 1 2 8 ⟶ 23 2 0 0 3 19 ,
  12 1 2 0 ⟶ 24 2 0 0 3 9 ,
  12 1 2 1 ⟶ 24 2 0 0 3 4 ,
  12 1 2 3 ⟶ 24 2 0 0 3 15 ,
  12 1 2 5 ⟶ 24 2 0 0 3 16 ,
  12 1 2 6 ⟶ 24 2 0 0 3 17 ,
  12 1 2 7 ⟶ 24 2 0 0 3 18 ,
  12 1 2 8 ⟶ 24 2 0 0 3 19 ,
  13 1 2 0 ⟶ 25 2 0 0 3 9 ,
  13 1 2 1 ⟶ 25 2 0 0 3 4 ,
  13 1 2 3 ⟶ 25 2 0 0 3 15 ,
  13 1 2 5 ⟶ 25 2 0 0 3 16 ,
  13 1 2 6 ⟶ 25 2 0 0 3 17 ,
  13 1 2 7 ⟶ 25 2 0 0 3 18 ,
  13 1 2 8 ⟶ 25 2 0 0 3 19 ,
  0 1 2 0 ⟶ 1 2 0 3 9 0 ,
  0 1 2 1 ⟶ 1 2 0 3 9 1 ,
  0 1 2 3 ⟶ 1 2 0 3 9 3 ,
  0 1 2 5 ⟶ 1 2 0 3 9 5 ,
  0 1 2 6 ⟶ 1 2 0 3 9 6 ,
  0 1 2 7 ⟶ 1 2 0 3 9 7 ,
  0 1 2 8 ⟶ 1 2 0 3 9 8 ,
  2 1 2 0 ⟶ 21 2 0 3 9 0 ,
  2 1 2 1 ⟶ 21 2 0 3 9 1 ,
  2 1 2 3 ⟶ 21 2 0 3 9 3 ,
  2 1 2 5 ⟶ 21 2 0 3 9 5 ,
  2 1 2 6 ⟶ 21 2 0 3 9 6 ,
  2 1 2 7 ⟶ 21 2 0 3 9 7 ,
  2 1 2 8 ⟶ 21 2 0 3 9 8 ,
  9 1 2 0 ⟶ 4 2 0 3 9 0 ,
  9 1 2 1 ⟶ 4 2 0 3 9 1 ,
  9 1 2 3 ⟶ 4 2 0 3 9 3 ,
  9 1 2 5 ⟶ 4 2 0 3 9 5 ,
  9 1 2 6 ⟶ 4 2 0 3 9 6 ,
  9 1 2 7 ⟶ 4 2 0 3 9 7 ,
  9 1 2 8 ⟶ 4 2 0 3 9 8 ,
  10 1 2 0 ⟶ 22 2 0 3 9 0 ,
  10 1 2 1 ⟶ 22 2 0 3 9 1 ,
  10 1 2 3 ⟶ 22 2 0 3 9 3 ,
  10 1 2 5 ⟶ 22 2 0 3 9 5 ,
  10 1 2 6 ⟶ 22 2 0 3 9 6 ,
  10 1 2 7 ⟶ 22 2 0 3 9 7 ,
  10 1 2 8 ⟶ 22 2 0 3 9 8 ,
  11 1 2 0 ⟶ 23 2 0 3 9 0 ,
  11 1 2 1 ⟶ 23 2 0 3 9 1 ,
  11 1 2 3 ⟶ 23 2 0 3 9 3 ,
  11 1 2 5 ⟶ 23 2 0 3 9 5 ,
  11 1 2 6 ⟶ 23 2 0 3 9 6 ,
  11 1 2 7 ⟶ 23 2 0 3 9 7 ,
  11 1 2 8 ⟶ 23 2 0 3 9 8 ,
  12 1 2 0 ⟶ 24 2 0 3 9 0 ,
  12 1 2 1 ⟶ 24 2 0 3 9 1 ,
  12 1 2 3 ⟶ 24 2 0 3 9 3 ,
  12 1 2 5 ⟶ 24 2 0 3 9 5 ,
  12 1 2 6 ⟶ 24 2 0 3 9 6 ,
  12 1 2 7 ⟶ 24 2 0 3 9 7 ,
  12 1 2 8 ⟶ 24 2 0 3 9 8 ,
  13 1 2 0 ⟶ 25 2 0 3 9 0 ,
  13 1 2 1 ⟶ 25 2 0 3 9 1 ,
  13 1 2 3 ⟶ 25 2 0 3 9 3 ,
  13 1 2 5 ⟶ 25 2 0 3 9 5 ,
  13 1 2 6 ⟶ 25 2 0 3 9 6 ,
  13 1 2 7 ⟶ 25 2 0 3 9 7 ,
  13 1 2 8 ⟶ 25 2 0 3 9 8 ,
  0 1 2 0 ⟶ 1 2 6 26 9 0 ,
  0 1 2 1 ⟶ 1 2 6 26 9 1 ,
  0 1 2 3 ⟶ 1 2 6 26 9 3 ,
  0 1 2 5 ⟶ 1 2 6 26 9 5 ,
  0 1 2 6 ⟶ 1 2 6 26 9 6 ,
  0 1 2 7 ⟶ 1 2 6 26 9 7 ,
  0 1 2 8 ⟶ 1 2 6 26 9 8 ,
  2 1 2 0 ⟶ 21 2 6 26 9 0 ,
  2 1 2 1 ⟶ 21 2 6 26 9 1 ,
  2 1 2 3 ⟶ 21 2 6 26 9 3 ,
  2 1 2 5 ⟶ 21 2 6 26 9 5 ,
  2 1 2 6 ⟶ 21 2 6 26 9 6 ,
  2 1 2 7 ⟶ 21 2 6 26 9 7 ,
  2 1 2 8 ⟶ 21 2 6 26 9 8 ,
  9 1 2 0 ⟶ 4 2 6 26 9 0 ,
  9 1 2 1 ⟶ 4 2 6 26 9 1 ,
  9 1 2 3 ⟶ 4 2 6 26 9 3 ,
  9 1 2 5 ⟶ 4 2 6 26 9 5 ,
  9 1 2 6 ⟶ 4 2 6 26 9 6 ,
  9 1 2 7 ⟶ 4 2 6 26 9 7 ,
  9 1 2 8 ⟶ 4 2 6 26 9 8 ,
  10 1 2 0 ⟶ 22 2 6 26 9 0 ,
  10 1 2 1 ⟶ 22 2 6 26 9 1 ,
  10 1 2 3 ⟶ 22 2 6 26 9 3 ,
  10 1 2 5 ⟶ 22 2 6 26 9 5 ,
  10 1 2 6 ⟶ 22 2 6 26 9 6 ,
  10 1 2 7 ⟶ 22 2 6 26 9 7 ,
  10 1 2 8 ⟶ 22 2 6 26 9 8 ,
  11 1 2 0 ⟶ 23 2 6 26 9 0 ,
  11 1 2 1 ⟶ 23 2 6 26 9 1 ,
  11 1 2 3 ⟶ 23 2 6 26 9 3 ,
  11 1 2 5 ⟶ 23 2 6 26 9 5 ,
  11 1 2 6 ⟶ 23 2 6 26 9 6 ,
  11 1 2 7 ⟶ 23 2 6 26 9 7 ,
  11 1 2 8 ⟶ 23 2 6 26 9 8 ,
  12 1 2 0 ⟶ 24 2 6 26 9 0 ,
  12 1 2 1 ⟶ 24 2 6 26 9 1 ,
  12 1 2 3 ⟶ 24 2 6 26 9 3 ,
  12 1 2 5 ⟶ 24 2 6 26 9 5 ,
  12 1 2 6 ⟶ 24 2 6 26 9 6 ,
  12 1 2 7 ⟶ 24 2 6 26 9 7 ,
  12 1 2 8 ⟶ 24 2 6 26 9 8 ,
  13 1 2 0 ⟶ 25 2 6 26 9 0 ,
  13 1 2 1 ⟶ 25 2 6 26 9 1 ,
  13 1 2 3 ⟶ 25 2 6 26 9 3 ,
  13 1 2 5 ⟶ 25 2 6 26 9 5 ,
  13 1 2 6 ⟶ 25 2 6 26 9 6 ,
  13 1 2 7 ⟶ 25 2 6 26 9 7 ,
  13 1 2 8 ⟶ 25 2 6 26 9 8 ,
  0 1 2 0 ⟶ 1 27 11 6 11 0 ,
  0 1 2 1 ⟶ 1 27 11 6 11 1 ,
  0 1 2 3 ⟶ 1 27 11 6 11 3 ,
  0 1 2 5 ⟶ 1 27 11 6 11 5 ,
  0 1 2 6 ⟶ 1 27 11 6 11 6 ,
  0 1 2 7 ⟶ 1 27 11 6 11 7 ,
  0 1 2 8 ⟶ 1 27 11 6 11 8 ,
  2 1 2 0 ⟶ 21 27 11 6 11 0 ,
  2 1 2 1 ⟶ 21 27 11 6 11 1 ,
  2 1 2 3 ⟶ 21 27 11 6 11 3 ,
  2 1 2 5 ⟶ 21 27 11 6 11 5 ,
  2 1 2 6 ⟶ 21 27 11 6 11 6 ,
  2 1 2 7 ⟶ 21 27 11 6 11 7 ,
  2 1 2 8 ⟶ 21 27 11 6 11 8 ,
  9 1 2 0 ⟶ 4 27 11 6 11 0 ,
  9 1 2 1 ⟶ 4 27 11 6 11 1 ,
  9 1 2 3 ⟶ 4 27 11 6 11 3 ,
  9 1 2 5 ⟶ 4 27 11 6 11 5 ,
  9 1 2 6 ⟶ 4 27 11 6 11 6 ,
  9 1 2 7 ⟶ 4 27 11 6 11 7 ,
  9 1 2 8 ⟶ 4 27 11 6 11 8 ,
  10 1 2 0 ⟶ 22 27 11 6 11 0 ,
  10 1 2 1 ⟶ 22 27 11 6 11 1 ,
  10 1 2 3 ⟶ 22 27 11 6 11 3 ,
  10 1 2 5 ⟶ 22 27 11 6 11 5 ,
  10 1 2 6 ⟶ 22 27 11 6 11 6 ,
  10 1 2 7 ⟶ 22 27 11 6 11 7 ,
  10 1 2 8 ⟶ 22 27 11 6 11 8 ,
  11 1 2 0 ⟶ 23 27 11 6 11 0 ,
  11 1 2 1 ⟶ 23 27 11 6 11 1 ,
  11 1 2 3 ⟶ 23 27 11 6 11 3 ,
  11 1 2 5 ⟶ 23 27 11 6 11 5 ,
  11 1 2 6 ⟶ 23 27 11 6 11 6 ,
  11 1 2 7 ⟶ 23 27 11 6 11 7 ,
  11 1 2 8 ⟶ 23 27 11 6 11 8 ,
  12 1 2 0 ⟶ 24 27 11 6 11 0 ,
  12 1 2 1 ⟶ 24 27 11 6 11 1 ,
  12 1 2 3 ⟶ 24 27 11 6 11 3 ,
  12 1 2 5 ⟶ 24 27 11 6 11 5 ,
  12 1 2 6 ⟶ 24 27 11 6 11 6 ,
  12 1 2 7 ⟶ 24 27 11 6 11 7 ,
  12 1 2 8 ⟶ 24 27 11 6 11 8 ,
  13 1 2 0 ⟶ 25 27 11 6 11 0 ,
  13 1 2 1 ⟶ 25 27 11 6 11 1 ,
  13 1 2 3 ⟶ 25 27 11 6 11 3 ,
  13 1 2 5 ⟶ 25 27 11 6 11 5 ,
  13 1 2 6 ⟶ 25 27 11 6 11 6 ,
  13 1 2 7 ⟶ 25 27 11 6 11 7 ,
  13 1 2 8 ⟶ 25 27 11 6 11 8 ,
  0 1 2 0 ⟶ 6 11 0 3 4 2 ,
  0 1 2 1 ⟶ 6 11 0 3 4 21 ,
  0 1 2 3 ⟶ 6 11 0 3 4 14 ,
  0 1 2 5 ⟶ 6 11 0 3 4 28 ,
  0 1 2 6 ⟶ 6 11 0 3 4 27 ,
  0 1 2 7 ⟶ 6 11 0 3 4 29 ,
  0 1 2 8 ⟶ 6 11 0 3 4 30 ,
  2 1 2 0 ⟶ 27 11 0 3 4 2 ,
  2 1 2 1 ⟶ 27 11 0 3 4 21 ,
  2 1 2 3 ⟶ 27 11 0 3 4 14 ,
  2 1 2 5 ⟶ 27 11 0 3 4 28 ,
  2 1 2 6 ⟶ 27 11 0 3 4 27 ,
  2 1 2 7 ⟶ 27 11 0 3 4 29 ,
  2 1 2 8 ⟶ 27 11 0 3 4 30 ,
  9 1 2 0 ⟶ 17 11 0 3 4 2 ,
  9 1 2 1 ⟶ 17 11 0 3 4 21 ,
  9 1 2 3 ⟶ 17 11 0 3 4 14 ,
  9 1 2 5 ⟶ 17 11 0 3 4 28 ,
  9 1 2 6 ⟶ 17 11 0 3 4 27 ,
  9 1 2 7 ⟶ 17 11 0 3 4 29 ,
  9 1 2 8 ⟶ 17 11 0 3 4 30 ,
  10 1 2 0 ⟶ 31 11 0 3 4 2 ,
  10 1 2 1 ⟶ 31 11 0 3 4 21 ,
  10 1 2 3 ⟶ 31 11 0 3 4 14 ,
  10 1 2 5 ⟶ 31 11 0 3 4 28 ,
  10 1 2 6 ⟶ 31 11 0 3 4 27 ,
  10 1 2 7 ⟶ 31 11 0 3 4 29 ,
  10 1 2 8 ⟶ 31 11 0 3 4 30 ,
  11 1 2 0 ⟶ 32 11 0 3 4 2 ,
  11 1 2 1 ⟶ 32 11 0 3 4 21 ,
  11 1 2 3 ⟶ 32 11 0 3 4 14 ,
  11 1 2 5 ⟶ 32 11 0 3 4 28 ,
  11 1 2 6 ⟶ 32 11 0 3 4 27 ,
  11 1 2 7 ⟶ 32 11 0 3 4 29 ,
  11 1 2 8 ⟶ 32 11 0 3 4 30 ,
  12 1 2 0 ⟶ 33 11 0 3 4 2 ,
  12 1 2 1 ⟶ 33 11 0 3 4 21 ,
  12 1 2 3 ⟶ 33 11 0 3 4 14 ,
  12 1 2 5 ⟶ 33 11 0 3 4 28 ,
  12 1 2 6 ⟶ 33 11 0 3 4 27 ,
  12 1 2 7 ⟶ 33 11 0 3 4 29 ,
  12 1 2 8 ⟶ 33 11 0 3 4 30 ,
  13 1 2 0 ⟶ 34 11 0 3 4 2 ,
  13 1 2 1 ⟶ 34 11 0 3 4 21 ,
  13 1 2 3 ⟶ 34 11 0 3 4 14 ,
  13 1 2 5 ⟶ 34 11 0 3 4 28 ,
  13 1 2 6 ⟶ 34 11 0 3 4 27 ,
  13 1 2 7 ⟶ 34 11 0 3 4 29 ,
  13 1 2 8 ⟶ 34 11 0 3 4 30 ,
  0 1 2 0 ⟶ 7 12 0 6 23 2 ,
  0 1 2 1 ⟶ 7 12 0 6 23 21 ,
  0 1 2 3 ⟶ 7 12 0 6 23 14 ,
  0 1 2 5 ⟶ 7 12 0 6 23 28 ,
  0 1 2 6 ⟶ 7 12 0 6 23 27 ,
  0 1 2 7 ⟶ 7 12 0 6 23 29 ,
  0 1 2 8 ⟶ 7 12 0 6 23 30 ,
  2 1 2 0 ⟶ 29 12 0 6 23 2 ,
  2 1 2 1 ⟶ 29 12 0 6 23 21 ,
  2 1 2 3 ⟶ 29 12 0 6 23 14 ,
  2 1 2 5 ⟶ 29 12 0 6 23 28 ,
  2 1 2 6 ⟶ 29 12 0 6 23 27 ,
  2 1 2 7 ⟶ 29 12 0 6 23 29 ,
  2 1 2 8 ⟶ 29 12 0 6 23 30 ,
  9 1 2 0 ⟶ 18 12 0 6 23 2 ,
  9 1 2 1 ⟶ 18 12 0 6 23 21 ,
  9 1 2 3 ⟶ 18 12 0 6 23 14 ,
  9 1 2 5 ⟶ 18 12 0 6 23 28 ,
  9 1 2 6 ⟶ 18 12 0 6 23 27 ,
  9 1 2 7 ⟶ 18 12 0 6 23 29 ,
  9 1 2 8 ⟶ 18 12 0 6 23 30 ,
  10 1 2 0 ⟶ 35 12 0 6 23 2 ,
  10 1 2 1 ⟶ 35 12 0 6 23 21 ,
  10 1 2 3 ⟶ 35 12 0 6 23 14 ,
  10 1 2 5 ⟶ 35 12 0 6 23 28 ,
  10 1 2 6 ⟶ 35 12 0 6 23 27 ,
  10 1 2 7 ⟶ 35 12 0 6 23 29 ,
  10 1 2 8 ⟶ 35 12 0 6 23 30 ,
  11 1 2 0 ⟶ 36 12 0 6 23 2 ,
  11 1 2 1 ⟶ 36 12 0 6 23 21 ,
  11 1 2 3 ⟶ 36 12 0 6 23 14 ,
  11 1 2 5 ⟶ 36 12 0 6 23 28 ,
  11 1 2 6 ⟶ 36 12 0 6 23 27 ,
  11 1 2 7 ⟶ 36 12 0 6 23 29 ,
  11 1 2 8 ⟶ 36 12 0 6 23 30 ,
  12 1 2 0 ⟶ 37 12 0 6 23 2 ,
  12 1 2 1 ⟶ 37 12 0 6 23 21 ,
  12 1 2 3 ⟶ 37 12 0 6 23 14 ,
  12 1 2 5 ⟶ 37 12 0 6 23 28 ,
  12 1 2 6 ⟶ 37 12 0 6 23 27 ,
  12 1 2 7 ⟶ 37 12 0 6 23 29 ,
  12 1 2 8 ⟶ 37 12 0 6 23 30 ,
  13 1 2 0 ⟶ 38 12 0 6 23 2 ,
  13 1 2 1 ⟶ 38 12 0 6 23 21 ,
  13 1 2 3 ⟶ 38 12 0 6 23 14 ,
  13 1 2 5 ⟶ 38 12 0 6 23 28 ,
  13 1 2 6 ⟶ 38 12 0 6 23 27 ,
  13 1 2 7 ⟶ 38 12 0 6 23 29 ,
  13 1 2 8 ⟶ 38 12 0 6 23 30 ,
  0 1 2 0 ⟶ 7 24 2 6 11 0 ,
  0 1 2 1 ⟶ 7 24 2 6 11 1 ,
  0 1 2 3 ⟶ 7 24 2 6 11 3 ,
  0 1 2 5 ⟶ 7 24 2 6 11 5 ,
  0 1 2 6 ⟶ 7 24 2 6 11 6 ,
  0 1 2 7 ⟶ 7 24 2 6 11 7 ,
  0 1 2 8 ⟶ 7 24 2 6 11 8 ,
  2 1 2 0 ⟶ 29 24 2 6 11 0 ,
  2 1 2 1 ⟶ 29 24 2 6 11 1 ,
  2 1 2 3 ⟶ 29 24 2 6 11 3 ,
  2 1 2 5 ⟶ 29 24 2 6 11 5 ,
  2 1 2 6 ⟶ 29 24 2 6 11 6 ,
  2 1 2 7 ⟶ 29 24 2 6 11 7 ,
  2 1 2 8 ⟶ 29 24 2 6 11 8 ,
  9 1 2 0 ⟶ 18 24 2 6 11 0 ,
  9 1 2 1 ⟶ 18 24 2 6 11 1 ,
  9 1 2 3 ⟶ 18 24 2 6 11 3 ,
  9 1 2 5 ⟶ 18 24 2 6 11 5 ,
  9 1 2 6 ⟶ 18 24 2 6 11 6 ,
  9 1 2 7 ⟶ 18 24 2 6 11 7 ,
  9 1 2 8 ⟶ 18 24 2 6 11 8 ,
  10 1 2 0 ⟶ 35 24 2 6 11 0 ,
  10 1 2 1 ⟶ 35 24 2 6 11 1 ,
  10 1 2 3 ⟶ 35 24 2 6 11 3 ,
  10 1 2 5 ⟶ 35 24 2 6 11 5 ,
  10 1 2 6 ⟶ 35 24 2 6 11 6 ,
  10 1 2 7 ⟶ 35 24 2 6 11 7 ,
  10 1 2 8 ⟶ 35 24 2 6 11 8 ,
  11 1 2 0 ⟶ 36 24 2 6 11 0 ,
  11 1 2 1 ⟶ 36 24 2 6 11 1 ,
  11 1 2 3 ⟶ 36 24 2 6 11 3 ,
  11 1 2 5 ⟶ 36 24 2 6 11 5 ,
  11 1 2 6 ⟶ 36 24 2 6 11 6 ,
  11 1 2 7 ⟶ 36 24 2 6 11 7 ,
  11 1 2 8 ⟶ 36 24 2 6 11 8 ,
  12 1 2 0 ⟶ 37 24 2 6 11 0 ,
  12 1 2 1 ⟶ 37 24 2 6 11 1 ,
  12 1 2 3 ⟶ 37 24 2 6 11 3 ,
  12 1 2 5 ⟶ 37 24 2 6 11 5 ,
  12 1 2 6 ⟶ 37 24 2 6 11 6 ,
  12 1 2 7 ⟶ 37 24 2 6 11 7 ,
  12 1 2 8 ⟶ 37 24 2 6 11 8 ,
  13 1 2 0 ⟶ 38 24 2 6 11 0 ,
  13 1 2 1 ⟶ 38 24 2 6 11 1 ,
  13 1 2 3 ⟶ 38 24 2 6 11 3 ,
  13 1 2 5 ⟶ 38 24 2 6 11 5 ,
  13 1 2 6 ⟶ 38 24 2 6 11 6 ,
  13 1 2 7 ⟶ 38 24 2 6 11 7 ,
  13 1 2 8 ⟶ 38 24 2 6 11 8 ,
  0 1 2 0 ⟶ 0 3 4 2 5 20 9 ,
  0 1 2 1 ⟶ 0 3 4 2 5 20 4 ,
  0 1 2 3 ⟶ 0 3 4 2 5 20 15 ,
  0 1 2 5 ⟶ 0 3 4 2 5 20 16 ,
  0 1 2 6 ⟶ 0 3 4 2 5 20 17 ,
  0 1 2 7 ⟶ 0 3 4 2 5 20 18 ,
  0 1 2 8 ⟶ 0 3 4 2 5 20 19 ,
  2 1 2 0 ⟶ 2 3 4 2 5 20 9 ,
  2 1 2 1 ⟶ 2 3 4 2 5 20 4 ,
  2 1 2 3 ⟶ 2 3 4 2 5 20 15 ,
  2 1 2 5 ⟶ 2 3 4 2 5 20 16 ,
  2 1 2 6 ⟶ 2 3 4 2 5 20 17 ,
  2 1 2 7 ⟶ 2 3 4 2 5 20 18 ,
  2 1 2 8 ⟶ 2 3 4 2 5 20 19 ,
  9 1 2 0 ⟶ 9 3 4 2 5 20 9 ,
  9 1 2 1 ⟶ 9 3 4 2 5 20 4 ,
  9 1 2 3 ⟶ 9 3 4 2 5 20 15 ,
  9 1 2 5 ⟶ 9 3 4 2 5 20 16 ,
  9 1 2 6 ⟶ 9 3 4 2 5 20 17 ,
  9 1 2 7 ⟶ 9 3 4 2 5 20 18 ,
  9 1 2 8 ⟶ 9 3 4 2 5 20 19 ,
  10 1 2 0 ⟶ 10 3 4 2 5 20 9 ,
  10 1 2 1 ⟶ 10 3 4 2 5 20 4 ,
  10 1 2 3 ⟶ 10 3 4 2 5 20 15 ,
  10 1 2 5 ⟶ 10 3 4 2 5 20 16 ,
  10 1 2 6 ⟶ 10 3 4 2 5 20 17 ,
  10 1 2 7 ⟶ 10 3 4 2 5 20 18 ,
  10 1 2 8 ⟶ 10 3 4 2 5 20 19 ,
  11 1 2 0 ⟶ 11 3 4 2 5 20 9 ,
  11 1 2 1 ⟶ 11 3 4 2 5 20 4 ,
  11 1 2 3 ⟶ 11 3 4 2 5 20 15 ,
  11 1 2 5 ⟶ 11 3 4 2 5 20 16 ,
  11 1 2 6 ⟶ 11 3 4 2 5 20 17 ,
  11 1 2 7 ⟶ 11 3 4 2 5 20 18 ,
  11 1 2 8 ⟶ 11 3 4 2 5 20 19 ,
  12 1 2 0 ⟶ 12 3 4 2 5 20 9 ,
  12 1 2 1 ⟶ 12 3 4 2 5 20 4 ,
  12 1 2 3 ⟶ 12 3 4 2 5 20 15 ,
  12 1 2 5 ⟶ 12 3 4 2 5 20 16 ,
  12 1 2 6 ⟶ 12 3 4 2 5 20 17 ,
  12 1 2 7 ⟶ 12 3 4 2 5 20 18 ,
  12 1 2 8 ⟶ 12 3 4 2 5 20 19 ,
  13 1 2 0 ⟶ 13 3 4 2 5 20 9 ,
  13 1 2 1 ⟶ 13 3 4 2 5 20 4 ,
  13 1 2 3 ⟶ 13 3 4 2 5 20 15 ,
  13 1 2 5 ⟶ 13 3 4 2 5 20 16 ,
  13 1 2 6 ⟶ 13 3 4 2 5 20 17 ,
  13 1 2 7 ⟶ 13 3 4 2 5 20 18 ,
  13 1 2 8 ⟶ 13 3 4 2 5 20 19 ,
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  0 1 2 1 ⟶ 0 6 11 6 23 28 22 ,
  0 1 2 3 ⟶ 0 6 11 6 23 28 20 ,
  0 1 2 5 ⟶ 0 6 11 6 23 28 39 ,
  0 1 2 6 ⟶ 0 6 11 6 23 28 31 ,
  0 1 2 7 ⟶ 0 6 11 6 23 28 35 ,
  0 1 2 8 ⟶ 0 6 11 6 23 28 40 ,
  2 1 2 0 ⟶ 2 6 11 6 23 28 10 ,
  2 1 2 1 ⟶ 2 6 11 6 23 28 22 ,
  2 1 2 3 ⟶ 2 6 11 6 23 28 20 ,
  2 1 2 5 ⟶ 2 6 11 6 23 28 39 ,
  2 1 2 6 ⟶ 2 6 11 6 23 28 31 ,
  2 1 2 7 ⟶ 2 6 11 6 23 28 35 ,
  2 1 2 8 ⟶ 2 6 11 6 23 28 40 ,
  9 1 2 0 ⟶ 9 6 11 6 23 28 10 ,
  9 1 2 1 ⟶ 9 6 11 6 23 28 22 ,
  9 1 2 3 ⟶ 9 6 11 6 23 28 20 ,
  9 1 2 5 ⟶ 9 6 11 6 23 28 39 ,
  9 1 2 6 ⟶ 9 6 11 6 23 28 31 ,
  9 1 2 7 ⟶ 9 6 11 6 23 28 35 ,
  9 1 2 8 ⟶ 9 6 11 6 23 28 40 ,
  10 1 2 0 ⟶ 10 6 11 6 23 28 10 ,
  10 1 2 1 ⟶ 10 6 11 6 23 28 22 ,
  10 1 2 3 ⟶ 10 6 11 6 23 28 20 ,
  10 1 2 5 ⟶ 10 6 11 6 23 28 39 ,
  10 1 2 6 ⟶ 10 6 11 6 23 28 31 ,
  10 1 2 7 ⟶ 10 6 11 6 23 28 35 ,
  10 1 2 8 ⟶ 10 6 11 6 23 28 40 ,
  11 1 2 0 ⟶ 11 6 11 6 23 28 10 ,
  11 1 2 1 ⟶ 11 6 11 6 23 28 22 ,
  11 1 2 3 ⟶ 11 6 11 6 23 28 20 ,
  11 1 2 5 ⟶ 11 6 11 6 23 28 39 ,
  11 1 2 6 ⟶ 11 6 11 6 23 28 31 ,
  11 1 2 7 ⟶ 11 6 11 6 23 28 35 ,
  11 1 2 8 ⟶ 11 6 11 6 23 28 40 ,
  12 1 2 0 ⟶ 12 6 11 6 23 28 10 ,
  12 1 2 1 ⟶ 12 6 11 6 23 28 22 ,
  12 1 2 3 ⟶ 12 6 11 6 23 28 20 ,
  12 1 2 5 ⟶ 12 6 11 6 23 28 39 ,
  12 1 2 6 ⟶ 12 6 11 6 23 28 31 ,
  12 1 2 7 ⟶ 12 6 11 6 23 28 35 ,
  12 1 2 8 ⟶ 12 6 11 6 23 28 40 ,
  13 1 2 0 ⟶ 13 6 11 6 23 28 10 ,
  13 1 2 1 ⟶ 13 6 11 6 23 28 22 ,
  13 1 2 3 ⟶ 13 6 11 6 23 28 20 ,
  13 1 2 5 ⟶ 13 6 11 6 23 28 39 ,
  13 1 2 6 ⟶ 13 6 11 6 23 28 31 ,
  13 1 2 7 ⟶ 13 6 11 6 23 28 35 ,
  13 1 2 8 ⟶ 13 6 11 6 23 28 40 ,
  0 1 2 0 ⟶ 0 6 26 15 4 2 0 ,
  0 1 2 1 ⟶ 0 6 26 15 4 2 1 ,
  0 1 2 3 ⟶ 0 6 26 15 4 2 3 ,
  0 1 2 5 ⟶ 0 6 26 15 4 2 5 ,
  0 1 2 6 ⟶ 0 6 26 15 4 2 6 ,
  0 1 2 7 ⟶ 0 6 26 15 4 2 7 ,
  0 1 2 8 ⟶ 0 6 26 15 4 2 8 ,
  2 1 2 0 ⟶ 2 6 26 15 4 2 0 ,
  2 1 2 1 ⟶ 2 6 26 15 4 2 1 ,
  2 1 2 3 ⟶ 2 6 26 15 4 2 3 ,
  2 1 2 5 ⟶ 2 6 26 15 4 2 5 ,
  2 1 2 6 ⟶ 2 6 26 15 4 2 6 ,
  2 1 2 7 ⟶ 2 6 26 15 4 2 7 ,
  2 1 2 8 ⟶ 2 6 26 15 4 2 8 ,
  9 1 2 0 ⟶ 9 6 26 15 4 2 0 ,
  9 1 2 1 ⟶ 9 6 26 15 4 2 1 ,
  9 1 2 3 ⟶ 9 6 26 15 4 2 3 ,
  9 1 2 5 ⟶ 9 6 26 15 4 2 5 ,
  9 1 2 6 ⟶ 9 6 26 15 4 2 6 ,
  9 1 2 7 ⟶ 9 6 26 15 4 2 7 ,
  9 1 2 8 ⟶ 9 6 26 15 4 2 8 ,
  10 1 2 0 ⟶ 10 6 26 15 4 2 0 ,
  10 1 2 1 ⟶ 10 6 26 15 4 2 1 ,
  10 1 2 3 ⟶ 10 6 26 15 4 2 3 ,
  10 1 2 5 ⟶ 10 6 26 15 4 2 5 ,
  10 1 2 6 ⟶ 10 6 26 15 4 2 6 ,
  10 1 2 7 ⟶ 10 6 26 15 4 2 7 ,
  10 1 2 8 ⟶ 10 6 26 15 4 2 8 ,
  11 1 2 0 ⟶ 11 6 26 15 4 2 0 ,
  11 1 2 1 ⟶ 11 6 26 15 4 2 1 ,
  11 1 2 3 ⟶ 11 6 26 15 4 2 3 ,
  11 1 2 5 ⟶ 11 6 26 15 4 2 5 ,
  11 1 2 6 ⟶ 11 6 26 15 4 2 6 ,
  11 1 2 7 ⟶ 11 6 26 15 4 2 7 ,
  11 1 2 8 ⟶ 11 6 26 15 4 2 8 ,
  12 1 2 0 ⟶ 12 6 26 15 4 2 0 ,
  12 1 2 1 ⟶ 12 6 26 15 4 2 1 ,
  12 1 2 3 ⟶ 12 6 26 15 4 2 3 ,
  12 1 2 5 ⟶ 12 6 26 15 4 2 5 ,
  12 1 2 6 ⟶ 12 6 26 15 4 2 6 ,
  12 1 2 7 ⟶ 12 6 26 15 4 2 7 ,
  12 1 2 8 ⟶ 12 6 26 15 4 2 8 ,
  13 1 2 0 ⟶ 13 6 26 15 4 2 0 ,
  13 1 2 1 ⟶ 13 6 26 15 4 2 1 ,
  13 1 2 3 ⟶ 13 6 26 15 4 2 3 ,
  13 1 2 5 ⟶ 13 6 26 15 4 2 5 ,
  13 1 2 6 ⟶ 13 6 26 15 4 2 6 ,
  13 1 2 7 ⟶ 13 6 26 15 4 2 7 ,
  13 1 2 8 ⟶ 13 6 26 15 4 2 8 ,
  0 1 2 0 ⟶ 0 7 41 4 14 9 0 ,
  0 1 2 1 ⟶ 0 7 41 4 14 9 1 ,
  0 1 2 3 ⟶ 0 7 41 4 14 9 3 ,
  0 1 2 5 ⟶ 0 7 41 4 14 9 5 ,
  0 1 2 6 ⟶ 0 7 41 4 14 9 6 ,
  0 1 2 7 ⟶ 0 7 41 4 14 9 7 ,
  0 1 2 8 ⟶ 0 7 41 4 14 9 8 ,
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  2 1 2 1 ⟶ 2 7 41 4 14 9 1 ,
  2 1 2 3 ⟶ 2 7 41 4 14 9 3 ,
  2 1 2 5 ⟶ 2 7 41 4 14 9 5 ,
  2 1 2 6 ⟶ 2 7 41 4 14 9 6 ,
  2 1 2 7 ⟶ 2 7 41 4 14 9 7 ,
  2 1 2 8 ⟶ 2 7 41 4 14 9 8 ,
  9 1 2 0 ⟶ 9 7 41 4 14 9 0 ,
  9 1 2 1 ⟶ 9 7 41 4 14 9 1 ,
  9 1 2 3 ⟶ 9 7 41 4 14 9 3 ,
  9 1 2 5 ⟶ 9 7 41 4 14 9 5 ,
  9 1 2 6 ⟶ 9 7 41 4 14 9 6 ,
  9 1 2 7 ⟶ 9 7 41 4 14 9 7 ,
  9 1 2 8 ⟶ 9 7 41 4 14 9 8 ,
  10 1 2 0 ⟶ 10 7 41 4 14 9 0 ,
  10 1 2 1 ⟶ 10 7 41 4 14 9 1 ,
  10 1 2 3 ⟶ 10 7 41 4 14 9 3 ,
  10 1 2 5 ⟶ 10 7 41 4 14 9 5 ,
  10 1 2 6 ⟶ 10 7 41 4 14 9 6 ,
  10 1 2 7 ⟶ 10 7 41 4 14 9 7 ,
  10 1 2 8 ⟶ 10 7 41 4 14 9 8 ,
  11 1 2 0 ⟶ 11 7 41 4 14 9 0 ,
  11 1 2 1 ⟶ 11 7 41 4 14 9 1 ,
  11 1 2 3 ⟶ 11 7 41 4 14 9 3 ,
  11 1 2 5 ⟶ 11 7 41 4 14 9 5 ,
  11 1 2 6 ⟶ 11 7 41 4 14 9 6 ,
  11 1 2 7 ⟶ 11 7 41 4 14 9 7 ,
  11 1 2 8 ⟶ 11 7 41 4 14 9 8 ,
  12 1 2 0 ⟶ 12 7 41 4 14 9 0 ,
  12 1 2 1 ⟶ 12 7 41 4 14 9 1 ,
  12 1 2 3 ⟶ 12 7 41 4 14 9 3 ,
  12 1 2 5 ⟶ 12 7 41 4 14 9 5 ,
  12 1 2 6 ⟶ 12 7 41 4 14 9 6 ,
  12 1 2 7 ⟶ 12 7 41 4 14 9 7 ,
  12 1 2 8 ⟶ 12 7 41 4 14 9 8 ,
  13 1 2 0 ⟶ 13 7 41 4 14 9 0 ,
  13 1 2 1 ⟶ 13 7 41 4 14 9 1 ,
  13 1 2 3 ⟶ 13 7 41 4 14 9 3 ,
  13 1 2 5 ⟶ 13 7 41 4 14 9 5 ,
  13 1 2 6 ⟶ 13 7 41 4 14 9 6 ,
  13 1 2 7 ⟶ 13 7 41 4 14 9 7 ,
  13 1 2 8 ⟶ 13 7 41 4 14 9 8 ,
  0 1 2 0 ⟶ 0 7 41 18 24 2 0 ,
  0 1 2 1 ⟶ 0 7 41 18 24 2 1 ,
  0 1 2 3 ⟶ 0 7 41 18 24 2 3 ,
  0 1 2 5 ⟶ 0 7 41 18 24 2 5 ,
  0 1 2 6 ⟶ 0 7 41 18 24 2 6 ,
  0 1 2 7 ⟶ 0 7 41 18 24 2 7 ,
  0 1 2 8 ⟶ 0 7 41 18 24 2 8 ,
  2 1 2 0 ⟶ 2 7 41 18 24 2 0 ,
  2 1 2 1 ⟶ 2 7 41 18 24 2 1 ,
  2 1 2 3 ⟶ 2 7 41 18 24 2 3 ,
  2 1 2 5 ⟶ 2 7 41 18 24 2 5 ,
  2 1 2 6 ⟶ 2 7 41 18 24 2 6 ,
  2 1 2 7 ⟶ 2 7 41 18 24 2 7 ,
  2 1 2 8 ⟶ 2 7 41 18 24 2 8 ,
  9 1 2 0 ⟶ 9 7 41 18 24 2 0 ,
  9 1 2 1 ⟶ 9 7 41 18 24 2 1 ,
  9 1 2 3 ⟶ 9 7 41 18 24 2 3 ,
  9 1 2 5 ⟶ 9 7 41 18 24 2 5 ,
  9 1 2 6 ⟶ 9 7 41 18 24 2 6 ,
  9 1 2 7 ⟶ 9 7 41 18 24 2 7 ,
  9 1 2 8 ⟶ 9 7 41 18 24 2 8 ,
  10 1 2 0 ⟶ 10 7 41 18 24 2 0 ,
  10 1 2 1 ⟶ 10 7 41 18 24 2 1 ,
  10 1 2 3 ⟶ 10 7 41 18 24 2 3 ,
  10 1 2 5 ⟶ 10 7 41 18 24 2 5 ,
  10 1 2 6 ⟶ 10 7 41 18 24 2 6 ,
  10 1 2 7 ⟶ 10 7 41 18 24 2 7 ,
  10 1 2 8 ⟶ 10 7 41 18 24 2 8 ,
  11 1 2 0 ⟶ 11 7 41 18 24 2 0 ,
  11 1 2 1 ⟶ 11 7 41 18 24 2 1 ,
  11 1 2 3 ⟶ 11 7 41 18 24 2 3 ,
  11 1 2 5 ⟶ 11 7 41 18 24 2 5 ,
  11 1 2 6 ⟶ 11 7 41 18 24 2 6 ,
  11 1 2 7 ⟶ 11 7 41 18 24 2 7 ,
  11 1 2 8 ⟶ 11 7 41 18 24 2 8 ,
  12 1 2 0 ⟶ 12 7 41 18 24 2 0 ,
  12 1 2 1 ⟶ 12 7 41 18 24 2 1 ,
  12 1 2 3 ⟶ 12 7 41 18 24 2 3 ,
  12 1 2 5 ⟶ 12 7 41 18 24 2 5 ,
  12 1 2 6 ⟶ 12 7 41 18 24 2 6 ,
  12 1 2 7 ⟶ 12 7 41 18 24 2 7 ,
  12 1 2 8 ⟶ 12 7 41 18 24 2 8 ,
  13 1 2 0 ⟶ 13 7 41 18 24 2 0 ,
  13 1 2 1 ⟶ 13 7 41 18 24 2 1 ,
  13 1 2 3 ⟶ 13 7 41 18 24 2 3 ,
  13 1 2 5 ⟶ 13 7 41 18 24 2 5 ,
  13 1 2 6 ⟶ 13 7 41 18 24 2 6 ,
  13 1 2 7 ⟶ 13 7 41 18 24 2 7 ,
  13 1 2 8 ⟶ 13 7 41 18 24 2 8 ,
  0 1 2 0 ⟶ 1 2 0 7 33 32 11 ,
  0 1 2 1 ⟶ 1 2 0 7 33 32 23 ,
  0 1 2 3 ⟶ 1 2 0 7 33 32 26 ,
  0 1 2 5 ⟶ 1 2 0 7 33 32 42 ,
  0 1 2 6 ⟶ 1 2 0 7 33 32 32 ,
  0 1 2 7 ⟶ 1 2 0 7 33 32 36 ,
  0 1 2 8 ⟶ 1 2 0 7 33 32 43 ,
  2 1 2 0 ⟶ 21 2 0 7 33 32 11 ,
  2 1 2 1 ⟶ 21 2 0 7 33 32 23 ,
  2 1 2 3 ⟶ 21 2 0 7 33 32 26 ,
  2 1 2 5 ⟶ 21 2 0 7 33 32 42 ,
  2 1 2 6 ⟶ 21 2 0 7 33 32 32 ,
  2 1 2 7 ⟶ 21 2 0 7 33 32 36 ,
  2 1 2 8 ⟶ 21 2 0 7 33 32 43 ,
  9 1 2 0 ⟶ 4 2 0 7 33 32 11 ,
  9 1 2 1 ⟶ 4 2 0 7 33 32 23 ,
  9 1 2 3 ⟶ 4 2 0 7 33 32 26 ,
  9 1 2 5 ⟶ 4 2 0 7 33 32 42 ,
  9 1 2 6 ⟶ 4 2 0 7 33 32 32 ,
  9 1 2 7 ⟶ 4 2 0 7 33 32 36 ,
  9 1 2 8 ⟶ 4 2 0 7 33 32 43 ,
  10 1 2 0 ⟶ 22 2 0 7 33 32 11 ,
  10 1 2 1 ⟶ 22 2 0 7 33 32 23 ,
  10 1 2 3 ⟶ 22 2 0 7 33 32 26 ,
  10 1 2 5 ⟶ 22 2 0 7 33 32 42 ,
  10 1 2 6 ⟶ 22 2 0 7 33 32 32 ,
  10 1 2 7 ⟶ 22 2 0 7 33 32 36 ,
  10 1 2 8 ⟶ 22 2 0 7 33 32 43 ,
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  9 1 14 18 12 0 ⟶ 4 2 3 9 7 33 11 ,
  9 1 14 18 12 1 ⟶ 4 2 3 9 7 33 23 ,
  9 1 14 18 12 3 ⟶ 4 2 3 9 7 33 26 ,
  9 1 14 18 12 5 ⟶ 4 2 3 9 7 33 42 ,
  9 1 14 18 12 6 ⟶ 4 2 3 9 7 33 32 ,
  9 1 14 18 12 7 ⟶ 4 2 3 9 7 33 36 ,
  9 1 14 18 12 8 ⟶ 4 2 3 9 7 33 43 ,
  10 1 14 18 12 0 ⟶ 22 2 3 9 7 33 11 ,
  10 1 14 18 12 1 ⟶ 22 2 3 9 7 33 23 ,
  10 1 14 18 12 3 ⟶ 22 2 3 9 7 33 26 ,
  10 1 14 18 12 5 ⟶ 22 2 3 9 7 33 42 ,
  10 1 14 18 12 6 ⟶ 22 2 3 9 7 33 32 ,
  10 1 14 18 12 7 ⟶ 22 2 3 9 7 33 36 ,
  10 1 14 18 12 8 ⟶ 22 2 3 9 7 33 43 ,
  11 1 14 18 12 0 ⟶ 23 2 3 9 7 33 11 ,
  11 1 14 18 12 1 ⟶ 23 2 3 9 7 33 23 ,
  11 1 14 18 12 3 ⟶ 23 2 3 9 7 33 26 ,
  11 1 14 18 12 5 ⟶ 23 2 3 9 7 33 42 ,
  11 1 14 18 12 6 ⟶ 23 2 3 9 7 33 32 ,
  11 1 14 18 12 7 ⟶ 23 2 3 9 7 33 36 ,
  11 1 14 18 12 8 ⟶ 23 2 3 9 7 33 43 ,
  12 1 14 18 12 0 ⟶ 24 2 3 9 7 33 11 ,
  12 1 14 18 12 1 ⟶ 24 2 3 9 7 33 23 ,
  12 1 14 18 12 3 ⟶ 24 2 3 9 7 33 26 ,
  12 1 14 18 12 5 ⟶ 24 2 3 9 7 33 42 ,
  12 1 14 18 12 6 ⟶ 24 2 3 9 7 33 32 ,
  12 1 14 18 12 7 ⟶ 24 2 3 9 7 33 36 ,
  12 1 14 18 12 8 ⟶ 24 2 3 9 7 33 43 ,
  13 1 14 18 12 0 ⟶ 25 2 3 9 7 33 11 ,
  13 1 14 18 12 1 ⟶ 25 2 3 9 7 33 23 ,
  13 1 14 18 12 3 ⟶ 25 2 3 9 7 33 26 ,
  13 1 14 18 12 5 ⟶ 25 2 3 9 7 33 42 ,
  13 1 14 18 12 6 ⟶ 25 2 3 9 7 33 32 ,
  13 1 14 18 12 7 ⟶ 25 2 3 9 7 33 36 ,
  13 1 14 18 12 8 ⟶ 25 2 3 9 7 33 43 ,
  0 1 27 11 0 0 ⟶ 0 0 0 6 23 2 0 ,
  0 1 27 11 0 1 ⟶ 0 0 0 6 23 2 1 ,
  0 1 27 11 0 3 ⟶ 0 0 0 6 23 2 3 ,
  0 1 27 11 0 5 ⟶ 0 0 0 6 23 2 5 ,
  0 1 27 11 0 6 ⟶ 0 0 0 6 23 2 6 ,
  0 1 27 11 0 7 ⟶ 0 0 0 6 23 2 7 ,
  0 1 27 11 0 8 ⟶ 0 0 0 6 23 2 8 ,
  2 1 27 11 0 0 ⟶ 2 0 0 6 23 2 0 ,
  2 1 27 11 0 1 ⟶ 2 0 0 6 23 2 1 ,
  2 1 27 11 0 3 ⟶ 2 0 0 6 23 2 3 ,
  2 1 27 11 0 5 ⟶ 2 0 0 6 23 2 5 ,
  2 1 27 11 0 6 ⟶ 2 0 0 6 23 2 6 ,
  2 1 27 11 0 7 ⟶ 2 0 0 6 23 2 7 ,
  2 1 27 11 0 8 ⟶ 2 0 0 6 23 2 8 ,
  9 1 27 11 0 0 ⟶ 9 0 0 6 23 2 0 ,
  9 1 27 11 0 1 ⟶ 9 0 0 6 23 2 1 ,
  9 1 27 11 0 3 ⟶ 9 0 0 6 23 2 3 ,
  9 1 27 11 0 5 ⟶ 9 0 0 6 23 2 5 ,
  9 1 27 11 0 6 ⟶ 9 0 0 6 23 2 6 ,
  9 1 27 11 0 7 ⟶ 9 0 0 6 23 2 7 ,
  9 1 27 11 0 8 ⟶ 9 0 0 6 23 2 8 ,
  10 1 27 11 0 0 ⟶ 10 0 0 6 23 2 0 ,
  10 1 27 11 0 1 ⟶ 10 0 0 6 23 2 1 ,
  10 1 27 11 0 3 ⟶ 10 0 0 6 23 2 3 ,
  10 1 27 11 0 5 ⟶ 10 0 0 6 23 2 5 ,
  10 1 27 11 0 6 ⟶ 10 0 0 6 23 2 6 ,
  10 1 27 11 0 7 ⟶ 10 0 0 6 23 2 7 ,
  10 1 27 11 0 8 ⟶ 10 0 0 6 23 2 8 ,
  11 1 27 11 0 0 ⟶ 11 0 0 6 23 2 0 ,
  11 1 27 11 0 1 ⟶ 11 0 0 6 23 2 1 ,
  11 1 27 11 0 3 ⟶ 11 0 0 6 23 2 3 ,
  11 1 27 11 0 5 ⟶ 11 0 0 6 23 2 5 ,
  11 1 27 11 0 6 ⟶ 11 0 0 6 23 2 6 ,
  11 1 27 11 0 7 ⟶ 11 0 0 6 23 2 7 ,
  11 1 27 11 0 8 ⟶ 11 0 0 6 23 2 8 ,
  12 1 27 11 0 0 ⟶ 12 0 0 6 23 2 0 ,
  12 1 27 11 0 1 ⟶ 12 0 0 6 23 2 1 ,
  12 1 27 11 0 3 ⟶ 12 0 0 6 23 2 3 ,
  12 1 27 11 0 5 ⟶ 12 0 0 6 23 2 5 ,
  12 1 27 11 0 6 ⟶ 12 0 0 6 23 2 6 ,
  12 1 27 11 0 7 ⟶ 12 0 0 6 23 2 7 ,
  12 1 27 11 0 8 ⟶ 12 0 0 6 23 2 8 ,
  13 1 27 11 0 0 ⟶ 13 0 0 6 23 2 0 ,
  13 1 27 11 0 1 ⟶ 13 0 0 6 23 2 1 ,
  13 1 27 11 0 3 ⟶ 13 0 0 6 23 2 3 ,
  13 1 27 11 0 5 ⟶ 13 0 0 6 23 2 5 ,
  13 1 27 11 0 6 ⟶ 13 0 0 6 23 2 6 ,
  13 1 27 11 0 7 ⟶ 13 0 0 6 23 2 7 ,
  13 1 27 11 0 8 ⟶ 13 0 0 6 23 2 8 ,
  0 1 27 36 12 0 ⟶ 1 29 12 0 6 26 9 ,
  0 1 27 36 12 1 ⟶ 1 29 12 0 6 26 4 ,
  0 1 27 36 12 3 ⟶ 1 29 12 0 6 26 15 ,
  0 1 27 36 12 5 ⟶ 1 29 12 0 6 26 16 ,
  0 1 27 36 12 6 ⟶ 1 29 12 0 6 26 17 ,
  0 1 27 36 12 7 ⟶ 1 29 12 0 6 26 18 ,
  0 1 27 36 12 8 ⟶ 1 29 12 0 6 26 19 ,
  2 1 27 36 12 0 ⟶ 21 29 12 0 6 26 9 ,
  2 1 27 36 12 1 ⟶ 21 29 12 0 6 26 4 ,
  2 1 27 36 12 3 ⟶ 21 29 12 0 6 26 15 ,
  2 1 27 36 12 5 ⟶ 21 29 12 0 6 26 16 ,
  2 1 27 36 12 6 ⟶ 21 29 12 0 6 26 17 ,
  2 1 27 36 12 7 ⟶ 21 29 12 0 6 26 18 ,
  2 1 27 36 12 8 ⟶ 21 29 12 0 6 26 19 ,
  9 1 27 36 12 0 ⟶ 4 29 12 0 6 26 9 ,
  9 1 27 36 12 1 ⟶ 4 29 12 0 6 26 4 ,
  9 1 27 36 12 3 ⟶ 4 29 12 0 6 26 15 ,
  9 1 27 36 12 5 ⟶ 4 29 12 0 6 26 16 ,
  9 1 27 36 12 6 ⟶ 4 29 12 0 6 26 17 ,
  9 1 27 36 12 7 ⟶ 4 29 12 0 6 26 18 ,
  9 1 27 36 12 8 ⟶ 4 29 12 0 6 26 19 ,
  10 1 27 36 12 0 ⟶ 22 29 12 0 6 26 9 ,
  10 1 27 36 12 1 ⟶ 22 29 12 0 6 26 4 ,
  10 1 27 36 12 3 ⟶ 22 29 12 0 6 26 15 ,
  10 1 27 36 12 5 ⟶ 22 29 12 0 6 26 16 ,
  10 1 27 36 12 6 ⟶ 22 29 12 0 6 26 17 ,
  10 1 27 36 12 7 ⟶ 22 29 12 0 6 26 18 ,
  10 1 27 36 12 8 ⟶ 22 29 12 0 6 26 19 ,
  11 1 27 36 12 0 ⟶ 23 29 12 0 6 26 9 ,
  11 1 27 36 12 1 ⟶ 23 29 12 0 6 26 4 ,
  11 1 27 36 12 3 ⟶ 23 29 12 0 6 26 15 ,
  11 1 27 36 12 5 ⟶ 23 29 12 0 6 26 16 ,
  11 1 27 36 12 6 ⟶ 23 29 12 0 6 26 17 ,
  11 1 27 36 12 7 ⟶ 23 29 12 0 6 26 18 ,
  11 1 27 36 12 8 ⟶ 23 29 12 0 6 26 19 ,
  12 1 27 36 12 0 ⟶ 24 29 12 0 6 26 9 ,
  12 1 27 36 12 1 ⟶ 24 29 12 0 6 26 4 ,
  12 1 27 36 12 3 ⟶ 24 29 12 0 6 26 15 ,
  12 1 27 36 12 5 ⟶ 24 29 12 0 6 26 16 ,
  12 1 27 36 12 6 ⟶ 24 29 12 0 6 26 17 ,
  12 1 27 36 12 7 ⟶ 24 29 12 0 6 26 18 ,
  12 1 27 36 12 8 ⟶ 24 29 12 0 6 26 19 ,
  13 1 27 36 12 0 ⟶ 25 29 12 0 6 26 9 ,
  13 1 27 36 12 1 ⟶ 25 29 12 0 6 26 4 ,
  13 1 27 36 12 3 ⟶ 25 29 12 0 6 26 15 ,
  13 1 27 36 12 5 ⟶ 25 29 12 0 6 26 16 ,
  13 1 27 36 12 6 ⟶ 25 29 12 0 6 26 17 ,
  13 1 27 36 12 7 ⟶ 25 29 12 0 6 26 18 ,
  13 1 27 36 12 8 ⟶ 25 29 12 0 6 26 19 ,
  0 5 10 1 2 0 ⟶ 0 5 10 0 3 4 2 ,
  0 5 10 1 2 1 ⟶ 0 5 10 0 3 4 21 ,
  0 5 10 1 2 3 ⟶ 0 5 10 0 3 4 14 ,
  0 5 10 1 2 5 ⟶ 0 5 10 0 3 4 28 ,
  0 5 10 1 2 6 ⟶ 0 5 10 0 3 4 27 ,
  0 5 10 1 2 7 ⟶ 0 5 10 0 3 4 29 ,
  0 5 10 1 2 8 ⟶ 0 5 10 0 3 4 30 ,
  2 5 10 1 2 0 ⟶ 2 5 10 0 3 4 2 ,
  2 5 10 1 2 1 ⟶ 2 5 10 0 3 4 21 ,
  2 5 10 1 2 3 ⟶ 2 5 10 0 3 4 14 ,
  2 5 10 1 2 5 ⟶ 2 5 10 0 3 4 28 ,
  2 5 10 1 2 6 ⟶ 2 5 10 0 3 4 27 ,
  2 5 10 1 2 7 ⟶ 2 5 10 0 3 4 29 ,
  2 5 10 1 2 8 ⟶ 2 5 10 0 3 4 30 ,
  9 5 10 1 2 0 ⟶ 9 5 10 0 3 4 2 ,
  9 5 10 1 2 1 ⟶ 9 5 10 0 3 4 21 ,
  9 5 10 1 2 3 ⟶ 9 5 10 0 3 4 14 ,
  9 5 10 1 2 5 ⟶ 9 5 10 0 3 4 28 ,
  9 5 10 1 2 6 ⟶ 9 5 10 0 3 4 27 ,
  9 5 10 1 2 7 ⟶ 9 5 10 0 3 4 29 ,
  9 5 10 1 2 8 ⟶ 9 5 10 0 3 4 30 ,
  10 5 10 1 2 0 ⟶ 10 5 10 0 3 4 2 ,
  10 5 10 1 2 1 ⟶ 10 5 10 0 3 4 21 ,
  10 5 10 1 2 3 ⟶ 10 5 10 0 3 4 14 ,
  10 5 10 1 2 5 ⟶ 10 5 10 0 3 4 28 ,
  10 5 10 1 2 6 ⟶ 10 5 10 0 3 4 27 ,
  10 5 10 1 2 7 ⟶ 10 5 10 0 3 4 29 ,
  10 5 10 1 2 8 ⟶ 10 5 10 0 3 4 30 ,
  11 5 10 1 2 0 ⟶ 11 5 10 0 3 4 2 ,
  11 5 10 1 2 1 ⟶ 11 5 10 0 3 4 21 ,
  11 5 10 1 2 3 ⟶ 11 5 10 0 3 4 14 ,
  11 5 10 1 2 5 ⟶ 11 5 10 0 3 4 28 ,
  11 5 10 1 2 6 ⟶ 11 5 10 0 3 4 27 ,
  11 5 10 1 2 7 ⟶ 11 5 10 0 3 4 29 ,
  11 5 10 1 2 8 ⟶ 11 5 10 0 3 4 30 ,
  12 5 10 1 2 0 ⟶ 12 5 10 0 3 4 2 ,
  12 5 10 1 2 1 ⟶ 12 5 10 0 3 4 21 ,
  12 5 10 1 2 3 ⟶ 12 5 10 0 3 4 14 ,
  12 5 10 1 2 5 ⟶ 12 5 10 0 3 4 28 ,
  12 5 10 1 2 6 ⟶ 12 5 10 0 3 4 27 ,
  12 5 10 1 2 7 ⟶ 12 5 10 0 3 4 29 ,
  12 5 10 1 2 8 ⟶ 12 5 10 0 3 4 30 ,
  13 5 10 1 2 0 ⟶ 13 5 10 0 3 4 2 ,
  13 5 10 1 2 1 ⟶ 13 5 10 0 3 4 21 ,
  13 5 10 1 2 3 ⟶ 13 5 10 0 3 4 14 ,
  13 5 10 1 2 5 ⟶ 13 5 10 0 3 4 28 ,
  13 5 10 1 2 6 ⟶ 13 5 10 0 3 4 27 ,
  13 5 10 1 2 7 ⟶ 13 5 10 0 3 4 29 ,
  13 5 10 1 2 8 ⟶ 13 5 10 0 3 4 30 ,
  5 10 5 22 2 0 ⟶ 0 1 28 20 16 10 0 ,
  5 10 5 22 2 1 ⟶ 0 1 28 20 16 10 1 ,
  5 10 5 22 2 3 ⟶ 0 1 28 20 16 10 3 ,
  5 10 5 22 2 5 ⟶ 0 1 28 20 16 10 5 ,
  5 10 5 22 2 6 ⟶ 0 1 28 20 16 10 6 ,
  5 10 5 22 2 7 ⟶ 0 1 28 20 16 10 7 ,
  5 10 5 22 2 8 ⟶ 0 1 28 20 16 10 8 ,
  28 10 5 22 2 0 ⟶ 2 1 28 20 16 10 0 ,
  28 10 5 22 2 1 ⟶ 2 1 28 20 16 10 1 ,
  28 10 5 22 2 3 ⟶ 2 1 28 20 16 10 3 ,
  28 10 5 22 2 5 ⟶ 2 1 28 20 16 10 5 ,
  28 10 5 22 2 6 ⟶ 2 1 28 20 16 10 6 ,
  28 10 5 22 2 7 ⟶ 2 1 28 20 16 10 7 ,
  28 10 5 22 2 8 ⟶ 2 1 28 20 16 10 8 ,
  16 10 5 22 2 0 ⟶ 9 1 28 20 16 10 0 ,
  16 10 5 22 2 1 ⟶ 9 1 28 20 16 10 1 ,
  16 10 5 22 2 3 ⟶ 9 1 28 20 16 10 3 ,
  16 10 5 22 2 5 ⟶ 9 1 28 20 16 10 5 ,
  16 10 5 22 2 6 ⟶ 9 1 28 20 16 10 6 ,
  16 10 5 22 2 7 ⟶ 9 1 28 20 16 10 7 ,
  16 10 5 22 2 8 ⟶ 9 1 28 20 16 10 8 ,
  39 10 5 22 2 0 ⟶ 10 1 28 20 16 10 0 ,
  39 10 5 22 2 1 ⟶ 10 1 28 20 16 10 1 ,
  39 10 5 22 2 3 ⟶ 10 1 28 20 16 10 3 ,
  39 10 5 22 2 5 ⟶ 10 1 28 20 16 10 5 ,
  39 10 5 22 2 6 ⟶ 10 1 28 20 16 10 6 ,
  39 10 5 22 2 7 ⟶ 10 1 28 20 16 10 7 ,
  39 10 5 22 2 8 ⟶ 10 1 28 20 16 10 8 ,
  42 10 5 22 2 0 ⟶ 11 1 28 20 16 10 0 ,
  42 10 5 22 2 1 ⟶ 11 1 28 20 16 10 1 ,
  42 10 5 22 2 3 ⟶ 11 1 28 20 16 10 3 ,
  42 10 5 22 2 5 ⟶ 11 1 28 20 16 10 5 ,
  42 10 5 22 2 6 ⟶ 11 1 28 20 16 10 6 ,
  42 10 5 22 2 7 ⟶ 11 1 28 20 16 10 7 ,
  42 10 5 22 2 8 ⟶ 11 1 28 20 16 10 8 ,
  44 10 5 22 2 0 ⟶ 12 1 28 20 16 10 0 ,
  44 10 5 22 2 1 ⟶ 12 1 28 20 16 10 1 ,
  44 10 5 22 2 3 ⟶ 12 1 28 20 16 10 3 ,
  44 10 5 22 2 5 ⟶ 12 1 28 20 16 10 5 ,
  44 10 5 22 2 6 ⟶ 12 1 28 20 16 10 6 ,
  44 10 5 22 2 7 ⟶ 12 1 28 20 16 10 7 ,
  44 10 5 22 2 8 ⟶ 12 1 28 20 16 10 8 ,
  45 10 5 22 2 0 ⟶ 13 1 28 20 16 10 0 ,
  45 10 5 22 2 1 ⟶ 13 1 28 20 16 10 1 ,
  45 10 5 22 2 3 ⟶ 13 1 28 20 16 10 3 ,
  45 10 5 22 2 5 ⟶ 13 1 28 20 16 10 5 ,
  45 10 5 22 2 6 ⟶ 13 1 28 20 16 10 6 ,
  45 10 5 22 2 7 ⟶ 13 1 28 20 16 10 7 ,
  45 10 5 22 2 8 ⟶ 13 1 28 20 16 10 8 ,
  7 12 1 14 9 0 ⟶ 0 0 7 41 4 2 0 ,
  7 12 1 14 9 1 ⟶ 0 0 7 41 4 2 1 ,
  7 12 1 14 9 3 ⟶ 0 0 7 41 4 2 3 ,
  7 12 1 14 9 5 ⟶ 0 0 7 41 4 2 5 ,
  7 12 1 14 9 6 ⟶ 0 0 7 41 4 2 6 ,
  7 12 1 14 9 7 ⟶ 0 0 7 41 4 2 7 ,
  7 12 1 14 9 8 ⟶ 0 0 7 41 4 2 8 ,
  29 12 1 14 9 0 ⟶ 2 0 7 41 4 2 0 ,
  29 12 1 14 9 1 ⟶ 2 0 7 41 4 2 1 ,
  29 12 1 14 9 3 ⟶ 2 0 7 41 4 2 3 ,
  29 12 1 14 9 5 ⟶ 2 0 7 41 4 2 5 ,
  29 12 1 14 9 6 ⟶ 2 0 7 41 4 2 6 ,
  29 12 1 14 9 7 ⟶ 2 0 7 41 4 2 7 ,
  29 12 1 14 9 8 ⟶ 2 0 7 41 4 2 8 ,
  18 12 1 14 9 0 ⟶ 9 0 7 41 4 2 0 ,
  18 12 1 14 9 1 ⟶ 9 0 7 41 4 2 1 ,
  18 12 1 14 9 3 ⟶ 9 0 7 41 4 2 3 ,
  18 12 1 14 9 5 ⟶ 9 0 7 41 4 2 5 ,
  18 12 1 14 9 6 ⟶ 9 0 7 41 4 2 6 ,
  18 12 1 14 9 7 ⟶ 9 0 7 41 4 2 7 ,
  18 12 1 14 9 8 ⟶ 9 0 7 41 4 2 8 ,
  35 12 1 14 9 0 ⟶ 10 0 7 41 4 2 0 ,
  35 12 1 14 9 1 ⟶ 10 0 7 41 4 2 1 ,
  35 12 1 14 9 3 ⟶ 10 0 7 41 4 2 3 ,
  35 12 1 14 9 5 ⟶ 10 0 7 41 4 2 5 ,
  35 12 1 14 9 6 ⟶ 10 0 7 41 4 2 6 ,
  35 12 1 14 9 7 ⟶ 10 0 7 41 4 2 7 ,
  35 12 1 14 9 8 ⟶ 10 0 7 41 4 2 8 ,
  36 12 1 14 9 0 ⟶ 11 0 7 41 4 2 0 ,
  36 12 1 14 9 1 ⟶ 11 0 7 41 4 2 1 ,
  36 12 1 14 9 3 ⟶ 11 0 7 41 4 2 3 ,
  36 12 1 14 9 5 ⟶ 11 0 7 41 4 2 5 ,
  36 12 1 14 9 6 ⟶ 11 0 7 41 4 2 6 ,
  36 12 1 14 9 7 ⟶ 11 0 7 41 4 2 7 ,
  36 12 1 14 9 8 ⟶ 11 0 7 41 4 2 8 ,
  37 12 1 14 9 0 ⟶ 12 0 7 41 4 2 0 ,
  37 12 1 14 9 1 ⟶ 12 0 7 41 4 2 1 ,
  37 12 1 14 9 3 ⟶ 12 0 7 41 4 2 3 ,
  37 12 1 14 9 5 ⟶ 12 0 7 41 4 2 5 ,
  37 12 1 14 9 6 ⟶ 12 0 7 41 4 2 6 ,
  37 12 1 14 9 7 ⟶ 12 0 7 41 4 2 7 ,
  37 12 1 14 9 8 ⟶ 12 0 7 41 4 2 8 ,
  38 12 1 14 9 0 ⟶ 13 0 7 41 4 2 0 ,
  38 12 1 14 9 1 ⟶ 13 0 7 41 4 2 1 ,
  38 12 1 14 9 3 ⟶ 13 0 7 41 4 2 3 ,
  38 12 1 14 9 5 ⟶ 13 0 7 41 4 2 5 ,
  38 12 1 14 9 6 ⟶ 13 0 7 41 4 2 6 ,
  38 12 1 14 9 7 ⟶ 13 0 7 41 4 2 7 ,
  38 12 1 14 9 8 ⟶ 13 0 7 41 4 2 8 }

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 5 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 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 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

15 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

16 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

17 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

18 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

19 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

20 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

21 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

22 ↦ ⎛     ⎞
     ⎜ 1 5 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

23 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

24 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

25 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

26 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

27 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

28 ↦ ⎛     ⎞
     ⎜ 1 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

29 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

30 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

31 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

32 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

33 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

34 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

35 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

36 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

37 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

38 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

39 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

40 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

41 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

42 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

43 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

44 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

45 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

46 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

47 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 9 ↦ 4, 15 ↦ 5, 6 ↦ 6, 17 ↦ 7, 7 ↦ 8, 18 ↦ 9, 10 ↦ 10, 22 ↦ 11, 5 ↦ 12, 8 ↦ 13, 26 ↦ 14, 33 ↦ 15, 32 ↦ 16, 11 ↦ 17, 36 ↦ 18, 39 ↦ 19, 20 ↦ 20, 16 ↦ 21, 44 ↦ 22, 14 ↦ 23, 21 ↦ 24, 28 ↦ 25, 29 ↦ 26, 12 ↦ 27, 27 ↦ 28, 24 ↦ 29 },
it remains to prove termination of the 170-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 13 ⟶ 1 2 0 3 4 13 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  0 1 2 13 ⟶ 1 2 6 14 4 13 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  0 1 2 13 ⟶ 1 2 6 16 16 17 13 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 0 1 2 13 ⟶ 1 2 0 3 4 13 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 0 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 20 ⟶ 1 2 12 19 10 3 5 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 21 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 20 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 21 ,
  0 1 2 12 19 ⟶ 1 2 8 22 20 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 20 4 12 ,
  0 1 23 4 0 ⟶ 1 24 2 3 4 0 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 3 ⟶ 1 24 2 3 4 3 ,
  0 1 23 4 12 ⟶ 1 24 2 3 4 12 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 0 ⟶ 1 24 23 4 6 17 0 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 3 ⟶ 1 24 23 4 6 17 3 ,
  0 1 23 4 12 ⟶ 1 24 23 4 6 17 12 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  21 10 12 11 2 0 ⟶ 4 1 25 20 21 10 0 ,
  21 10 12 11 2 1 ⟶ 4 1 25 20 21 10 1 ,
  21 10 12 11 2 3 ⟶ 4 1 25 20 21 10 3 ,
  21 10 12 11 2 12 ⟶ 4 1 25 20 21 10 12 ,
  21 10 12 11 2 6 ⟶ 4 1 25 20 21 10 6 ,
  21 10 12 11 2 8 ⟶ 4 1 25 20 21 10 8 ,
  21 10 12 11 2 13 ⟶ 4 1 25 20 21 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 20 21 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 20 21 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 20 21 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 20 21 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 20 21 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 20 21 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 20 21 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 20 21 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 20 21 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 20 21 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 20 21 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 20 21 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 20 21 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 20 21 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 ↦ ⎛           ⎞
    ⎜ 1 0 1 0 0 ⎟
    ⎜ 0 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

2 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

3 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 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 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎝           ⎠

14 ↦ ⎛           ⎞
     ⎜ 1 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 0 0 0 ⎟
     ⎜ 0 1 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 1 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 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 1 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 1 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 1 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 1 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 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

23 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

24 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

25 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

26 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

27 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

28 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

29 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 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, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 165-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 20 ⟶ 1 2 12 19 10 3 5 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 21 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 20 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 21 ,
  0 1 2 12 19 ⟶ 1 2 8 22 20 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 20 4 12 ,
  0 1 23 4 0 ⟶ 1 24 2 3 4 0 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 3 ⟶ 1 24 2 3 4 3 ,
  0 1 23 4 12 ⟶ 1 24 2 3 4 12 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 0 ⟶ 1 24 23 4 6 17 0 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 3 ⟶ 1 24 23 4 6 17 3 ,
  0 1 23 4 12 ⟶ 1 24 23 4 6 17 12 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  21 10 12 11 2 0 ⟶ 4 1 25 20 21 10 0 ,
  21 10 12 11 2 1 ⟶ 4 1 25 20 21 10 1 ,
  21 10 12 11 2 3 ⟶ 4 1 25 20 21 10 3 ,
  21 10 12 11 2 12 ⟶ 4 1 25 20 21 10 12 ,
  21 10 12 11 2 6 ⟶ 4 1 25 20 21 10 6 ,
  21 10 12 11 2 8 ⟶ 4 1 25 20 21 10 8 ,
  21 10 12 11 2 13 ⟶ 4 1 25 20 21 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 20 21 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 20 21 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 20 21 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 20 21 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 20 21 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 20 21 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 20 21 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 20 21 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 20 21 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 20 21 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 20 21 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 20 21 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 20 21 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 20 21 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

3 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 21 ↦ 20, 20 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 164-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 0 ⟶ 1 24 2 3 4 0 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 3 ⟶ 1 24 2 3 4 3 ,
  0 1 23 4 12 ⟶ 1 24 2 3 4 12 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 0 ⟶ 1 24 23 4 6 17 0 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 3 ⟶ 1 24 23 4 6 17 3 ,
  0 1 23 4 12 ⟶ 1 24 23 4 6 17 12 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

1 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 162-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 3 ⟶ 1 24 2 3 4 3 ,
  0 1 23 4 12 ⟶ 1 24 2 3 4 12 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 3 ⟶ 1 24 23 4 6 17 3 ,
  0 1 23 4 12 ⟶ 1 24 23 4 6 17 12 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 160-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 12 ⟶ 1 24 2 3 4 12 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 12 ⟶ 1 24 23 4 6 17 12 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 158-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 6 ⟶ 1 24 2 3 4 6 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 6 ⟶ 1 24 23 4 6 17 6 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 156-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 8 ⟶ 1 24 2 3 4 8 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 8 ⟶ 1 24 23 4 6 17 8 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 154-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  0 1 23 4 13 ⟶ 1 24 2 3 4 13 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  0 1 23 4 13 ⟶ 1 24 23 4 6 17 13 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 152-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 0 ⟶ 1 2 12 10 3 4 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

1 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 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 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 151-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 3 ⟶ 1 2 12 10 3 5 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 150-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 6 ⟶ 1 2 12 10 3 7 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 149-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  0 1 25 10 8 ⟶ 1 2 12 10 3 9 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 148-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  10 1 2 0 ⟶ 11 2 0 0 3 4 ,
  10 1 2 3 ⟶ 11 2 0 0 3 5 ,
  10 1 2 6 ⟶ 11 2 0 0 3 7 ,
  10 1 2 8 ⟶ 11 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 1 2 8 ⟶ 11 2 0 3 4 8 ,
  10 1 2 13 ⟶ 11 2 0 3 4 13 ,
  0 1 2 0 ⟶ 1 2 6 14 4 0 ,
  0 1 2 1 ⟶ 1 2 6 14 4 1 ,
  0 1 2 3 ⟶ 1 2 6 14 4 3 ,
  0 1 2 12 ⟶ 1 2 6 14 4 12 ,
  0 1 2 6 ⟶ 1 2 6 14 4 6 ,
  0 1 2 8 ⟶ 1 2 6 14 4 8 ,
  10 1 2 0 ⟶ 11 2 6 14 4 0 ,
  10 1 2 1 ⟶ 11 2 6 14 4 1 ,
  10 1 2 3 ⟶ 11 2 6 14 4 3 ,
  10 1 2 12 ⟶ 11 2 6 14 4 12 ,
  10 1 2 6 ⟶ 11 2 6 14 4 6 ,
  10 1 2 8 ⟶ 11 2 6 14 4 8 ,
  10 1 2 13 ⟶ 11 2 6 14 4 13 ,
  0 1 2 0 ⟶ 1 2 0 8 15 16 17 ,
  0 1 2 3 ⟶ 1 2 0 8 15 16 14 ,
  0 1 2 6 ⟶ 1 2 0 8 15 16 16 ,
  0 1 2 8 ⟶ 1 2 0 8 15 16 18 ,
  10 1 2 0 ⟶ 11 2 0 8 15 16 17 ,
  10 1 2 3 ⟶ 11 2 0 8 15 16 14 ,
  10 1 2 6 ⟶ 11 2 0 8 15 16 16 ,
  10 1 2 8 ⟶ 11 2 0 8 15 16 18 ,
  0 1 2 0 ⟶ 1 2 6 16 16 17 0 ,
  0 1 2 1 ⟶ 1 2 6 16 16 17 1 ,
  0 1 2 3 ⟶ 1 2 6 16 16 17 3 ,
  0 1 2 12 ⟶ 1 2 6 16 16 17 12 ,
  0 1 2 6 ⟶ 1 2 6 16 16 17 6 ,
  0 1 2 8 ⟶ 1 2 6 16 16 17 8 ,
  10 1 2 0 ⟶ 11 2 6 16 16 17 0 ,
  10 1 2 1 ⟶ 11 2 6 16 16 17 1 ,
  10 1 2 3 ⟶ 11 2 6 16 16 17 3 ,
  10 1 2 12 ⟶ 11 2 6 16 16 17 12 ,
  10 1 2 6 ⟶ 11 2 6 16 16 17 6 ,
  10 1 2 8 ⟶ 11 2 6 16 16 17 8 ,
  10 1 2 13 ⟶ 11 2 6 16 16 17 13 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 12 ⟶ 1 2 0 3 4 12 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  10 0 1 2 0 ⟶ 11 2 0 3 4 0 ,
  10 0 1 2 1 ⟶ 11 2 0 3 4 1 ,
  10 0 1 2 3 ⟶ 11 2 0 3 4 3 ,
  10 0 1 2 12 ⟶ 11 2 0 3 4 12 ,
  10 0 1 2 6 ⟶ 11 2 0 3 4 6 ,
  10 0 1 2 8 ⟶ 11 2 0 3 4 8 ,
  0 1 2 12 10 ⟶ 1 2 12 19 10 3 4 ,
  0 1 2 12 19 ⟶ 1 2 12 19 10 3 20 ,
  10 1 2 12 10 ⟶ 11 2 12 19 10 3 4 ,
  10 1 2 12 21 ⟶ 11 2 12 19 10 3 5 ,
  10 1 2 12 19 ⟶ 11 2 12 19 10 3 20 ,
  0 1 2 12 19 ⟶ 1 2 8 22 21 4 12 ,
  10 1 2 12 19 ⟶ 11 2 8 22 21 4 12 ,
  0 1 23 4 1 ⟶ 1 24 2 3 4 1 ,
  10 1 23 4 0 ⟶ 11 24 2 3 4 0 ,
  10 1 23 4 1 ⟶ 11 24 2 3 4 1 ,
  10 1 23 4 3 ⟶ 11 24 2 3 4 3 ,
  10 1 23 4 12 ⟶ 11 24 2 3 4 12 ,
  10 1 23 4 6 ⟶ 11 24 2 3 4 6 ,
  10 1 23 4 8 ⟶ 11 24 2 3 4 8 ,
  10 1 23 4 13 ⟶ 11 24 2 3 4 13 ,
  0 1 23 4 1 ⟶ 1 24 23 4 6 17 1 ,
  10 1 23 4 0 ⟶ 11 24 23 4 6 17 0 ,
  10 1 23 4 1 ⟶ 11 24 23 4 6 17 1 ,
  10 1 23 4 3 ⟶ 11 24 23 4 6 17 3 ,
  10 1 23 4 12 ⟶ 11 24 23 4 6 17 12 ,
  10 1 23 4 6 ⟶ 11 24 23 4 6 17 6 ,
  10 1 23 4 8 ⟶ 11 24 23 4 6 17 8 ,
  10 1 23 4 13 ⟶ 11 24 23 4 6 17 13 ,
  10 1 25 10 0 ⟶ 11 2 12 10 3 4 ,
  10 1 25 10 3 ⟶ 11 2 12 10 3 5 ,
  10 1 25 10 6 ⟶ 11 2 12 10 3 7 ,
  10 1 25 10 8 ⟶ 11 2 12 10 3 9 ,
  0 1 26 27 0 ⟶ 1 26 22 10 3 4 0 ,
  0 1 26 27 1 ⟶ 1 26 22 10 3 4 1 ,
  0 1 26 27 3 ⟶ 1 26 22 10 3 4 3 ,
  0 1 26 27 12 ⟶ 1 26 22 10 3 4 12 ,
  0 1 26 27 6 ⟶ 1 26 22 10 3 4 6 ,
  0 1 26 27 8 ⟶ 1 26 22 10 3 4 8 ,
  0 1 26 27 13 ⟶ 1 26 22 10 3 4 13 ,
  10 1 26 27 0 ⟶ 11 26 22 10 3 4 0 ,
  10 1 26 27 1 ⟶ 11 26 22 10 3 4 1 ,
  10 1 26 27 3 ⟶ 11 26 22 10 3 4 3 ,
  10 1 26 27 12 ⟶ 11 26 22 10 3 4 12 ,
  10 1 26 27 6 ⟶ 11 26 22 10 3 4 6 ,
  10 1 26 27 8 ⟶ 11 26 22 10 3 4 8 ,
  10 1 26 27 13 ⟶ 11 26 22 10 3 4 13 ,
  8 27 1 2 0 ⟶ 1 28 17 0 8 29 2 ,
  8 27 1 2 3 ⟶ 1 28 17 0 8 29 23 ,
  8 27 1 2 12 ⟶ 1 28 17 0 8 29 25 ,
  0 1 23 9 27 0 ⟶ 1 2 3 4 8 15 17 ,
  0 1 23 9 27 3 ⟶ 1 2 3 4 8 15 14 ,
  0 1 23 9 27 6 ⟶ 1 2 3 4 8 15 16 ,
  0 1 23 9 27 8 ⟶ 1 2 3 4 8 15 18 ,
  10 1 23 9 27 0 ⟶ 11 2 3 4 8 15 17 ,
  10 1 23 9 27 3 ⟶ 11 2 3 4 8 15 14 ,
  10 1 23 9 27 6 ⟶ 11 2 3 4 8 15 16 ,
  10 1 23 9 27 8 ⟶ 11 2 3 4 8 15 18 ,
  0 1 28 18 27 0 ⟶ 1 26 27 0 6 14 4 ,
  0 1 28 18 27 3 ⟶ 1 26 27 0 6 14 5 ,
  0 1 28 18 27 6 ⟶ 1 26 27 0 6 14 7 ,
  0 1 28 18 27 8 ⟶ 1 26 27 0 6 14 9 ,
  10 1 28 18 27 0 ⟶ 11 26 27 0 6 14 4 ,
  10 1 28 18 27 3 ⟶ 11 26 27 0 6 14 5 ,
  10 1 28 18 27 6 ⟶ 11 26 27 0 6 14 7 ,
  10 1 28 18 27 8 ⟶ 11 26 27 0 6 14 9 ,
  20 10 12 11 2 0 ⟶ 4 1 25 21 20 10 0 ,
  20 10 12 11 2 1 ⟶ 4 1 25 21 20 10 1 ,
  20 10 12 11 2 3 ⟶ 4 1 25 21 20 10 3 ,
  20 10 12 11 2 12 ⟶ 4 1 25 21 20 10 12 ,
  20 10 12 11 2 6 ⟶ 4 1 25 21 20 10 6 ,
  20 10 12 11 2 8 ⟶ 4 1 25 21 20 10 8 ,
  20 10 12 11 2 13 ⟶ 4 1 25 21 20 10 13 ,
  19 10 12 11 2 0 ⟶ 10 1 25 21 20 10 0 ,
  19 10 12 11 2 1 ⟶ 10 1 25 21 20 10 1 ,
  19 10 12 11 2 3 ⟶ 10 1 25 21 20 10 3 ,
  19 10 12 11 2 12 ⟶ 10 1 25 21 20 10 12 ,
  19 10 12 11 2 6 ⟶ 10 1 25 21 20 10 6 ,
  19 10 12 11 2 8 ⟶ 10 1 25 21 20 10 8 ,
  19 10 12 11 2 13 ⟶ 10 1 25 21 20 10 13 ,
  22 10 12 11 2 0 ⟶ 27 1 25 21 20 10 0 ,
  22 10 12 11 2 1 ⟶ 27 1 25 21 20 10 1 ,
  22 10 12 11 2 3 ⟶ 27 1 25 21 20 10 3 ,
  22 10 12 11 2 12 ⟶ 27 1 25 21 20 10 12 ,
  22 10 12 11 2 6 ⟶ 27 1 25 21 20 10 6 ,
  22 10 12 11 2 8 ⟶ 27 1 25 21 20 10 8 ,
  22 10 12 11 2 13 ⟶ 27 1 25 21 20 10 13 }

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

9 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

10 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

11 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

12 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

13 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

14 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

15 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

16 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

17 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 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 ⎟
     ⎝     ⎠

23 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

24 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

25 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

26 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

27 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

28 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

29 ↦ ⎛     ⎞
     ⎜ 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, 12 ↦ 10, 14 ↦ 11, 15 ↦ 12, 16 ↦ 13, 17 ↦ 14, 18 ↦ 15, 10 ↦ 16, 19 ↦ 17, 20 ↦ 18, 22 ↦ 19, 21 ↦ 20, 23 ↦ 21, 24 ↦ 22, 25 ↦ 23, 11 ↦ 24, 26 ↦ 25, 27 ↦ 26, 13 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 79-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  0 1 25 26 3 ⟶ 1 25 19 16 3 4 3 ,
  0 1 25 26 10 ⟶ 1 25 19 16 3 4 10 ,
  0 1 25 26 6 ⟶ 1 25 19 16 3 4 6 ,
  0 1 25 26 8 ⟶ 1 25 19 16 3 4 8 ,
  0 1 25 26 27 ⟶ 1 25 19 16 3 4 27 ,
  8 26 1 2 0 ⟶ 1 28 14 0 8 29 2 ,
  8 26 1 2 3 ⟶ 1 28 14 0 8 29 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 28 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 28 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 28 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 28 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 27 ⟶ 4 1 23 20 18 16 27 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 27 ⟶ 16 1 23 20 18 16 27 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 27 ⟶ 26 1 23 20 18 16 27 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

6 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 78-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  0 1 25 26 10 ⟶ 1 25 19 16 3 4 10 ,
  0 1 25 26 6 ⟶ 1 25 19 16 3 4 6 ,
  0 1 25 26 8 ⟶ 1 25 19 16 3 4 8 ,
  0 1 25 26 27 ⟶ 1 25 19 16 3 4 27 ,
  8 26 1 2 0 ⟶ 1 28 14 0 8 29 2 ,
  8 26 1 2 3 ⟶ 1 28 14 0 8 29 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 28 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 28 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 28 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 28 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 27 ⟶ 4 1 23 20 18 16 27 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 27 ⟶ 16 1 23 20 18 16 27 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 27 ⟶ 26 1 23 20 18 16 27 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 77-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  0 1 25 26 6 ⟶ 1 25 19 16 3 4 6 ,
  0 1 25 26 8 ⟶ 1 25 19 16 3 4 8 ,
  0 1 25 26 27 ⟶ 1 25 19 16 3 4 27 ,
  8 26 1 2 0 ⟶ 1 28 14 0 8 29 2 ,
  8 26 1 2 3 ⟶ 1 28 14 0 8 29 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 28 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 28 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 28 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 28 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 27 ⟶ 4 1 23 20 18 16 27 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 27 ⟶ 16 1 23 20 18 16 27 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 27 ⟶ 26 1 23 20 18 16 27 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

7 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

8 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 76-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  0 1 25 26 8 ⟶ 1 25 19 16 3 4 8 ,
  0 1 25 26 27 ⟶ 1 25 19 16 3 4 27 ,
  8 26 1 2 0 ⟶ 1 28 14 0 8 29 2 ,
  8 26 1 2 3 ⟶ 1 28 14 0 8 29 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 28 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 28 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 28 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 28 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 27 ⟶ 4 1 23 20 18 16 27 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 27 ⟶ 16 1 23 20 18 16 27 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 27 ⟶ 26 1 23 20 18 16 27 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎝             ⎠

9 ↦ ⎛             ⎞
    ⎜ 1 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 ⎟
    ⎝             ⎠

10 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

11 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

12 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

13 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

14 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

15 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

16 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

17 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

18 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

19 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

20 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

21 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

22 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 75-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  0 1 25 26 27 ⟶ 1 25 19 16 3 4 27 ,
  8 26 1 2 0 ⟶ 1 28 14 0 8 29 2 ,
  8 26 1 2 3 ⟶ 1 28 14 0 8 29 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 28 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 28 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 28 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 28 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 27 ⟶ 4 1 23 20 18 16 27 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 27 ⟶ 16 1 23 20 18 16 27 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 27 ⟶ 26 1 23 20 18 16 27 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 ↦ ⎛             ⎞
    ⎜ 1 0 1 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 ⎟
    ⎜ 0 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
    ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 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 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

23 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

24 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

25 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

26 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

27 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎝             ⎠

28 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

29 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 ⎟
     ⎝             ⎠

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, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 28 ↦ 27, 29 ↦ 28, 27 ↦ 29 },
it remains to prove termination of the 74-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  8 26 1 2 0 ⟶ 1 27 14 0 8 28 2 ,
  8 26 1 2 3 ⟶ 1 27 14 0 8 28 21 ,
  0 1 21 9 26 0 ⟶ 1 2 3 4 8 12 14 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 27 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 27 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 27 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 27 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 29 ⟶ 4 1 23 20 18 16 29 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 29 ⟶ 16 1 23 20 18 16 29 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 29 ⟶ 26 1 23 20 18 16 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

0 ↦ ⎛               ⎞
    ⎜ 1 0 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎝               ⎠

1 ↦ ⎛               ⎞
    ⎜ 1 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎝               ⎠

10 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

22 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

23 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

24 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

25 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

26 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

27 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

28 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

29 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 73-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  8 26 1 2 0 ⟶ 1 27 14 0 8 28 2 ,
  8 26 1 2 3 ⟶ 1 27 14 0 8 28 21 ,
  0 1 21 9 26 3 ⟶ 1 2 3 4 8 12 11 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 27 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 27 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 27 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 27 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 29 ⟶ 4 1 23 20 18 16 29 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 29 ⟶ 16 1 23 20 18 16 29 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 29 ⟶ 26 1 23 20 18 16 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

0 ↦ ⎛               ⎞
    ⎜ 1 0 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎝               ⎠

4 ↦ ⎛               ⎞
    ⎜ 1 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎝               ⎠

10 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

22 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

23 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

24 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

25 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

26 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

27 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

28 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

29 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 72-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  8 26 1 2 0 ⟶ 1 27 14 0 8 28 2 ,
  8 26 1 2 3 ⟶ 1 27 14 0 8 28 21 ,
  0 1 21 9 26 6 ⟶ 1 2 3 4 8 12 13 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 27 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 27 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 27 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 27 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 29 ⟶ 4 1 23 20 18 16 29 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 29 ⟶ 16 1 23 20 18 16 29 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 29 ⟶ 26 1 23 20 18 16 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

0 ↦ ⎛               ⎞
    ⎜ 1 0 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎝               ⎠

7 ↦ ⎛               ⎞
    ⎜ 1 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎝               ⎠

10 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

22 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

23 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

24 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

25 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

26 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

27 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

28 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

29 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 71-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  8 26 1 2 0 ⟶ 1 27 14 0 8 28 2 ,
  8 26 1 2 3 ⟶ 1 27 14 0 8 28 21 ,
  0 1 21 9 26 8 ⟶ 1 2 3 4 8 12 15 ,
  0 1 27 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 27 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 27 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 27 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 29 ⟶ 4 1 23 20 18 16 29 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 29 ⟶ 16 1 23 20 18 16 29 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 29 ⟶ 26 1 23 20 18 16 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

0 ↦ ⎛               ⎞
    ⎜ 1 0 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎝               ⎠

9 ↦ ⎛               ⎞
    ⎜ 1 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 ⎟
    ⎝               ⎠

10 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 1 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

22 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

23 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

24 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

25 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

26 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 1 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

27 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

28 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎝               ⎠

29 ↦ ⎛               ⎞
     ⎜ 1 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 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, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 70-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 3 ⟶ 1 2 0 0 3 5 ,
  0 1 2 6 ⟶ 1 2 0 0 3 7 ,
  0 1 2 8 ⟶ 1 2 0 0 3 9 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 0 ⟶ 1 2 6 11 4 0 ,
  0 1 2 1 ⟶ 1 2 6 11 4 1 ,
  0 1 2 3 ⟶ 1 2 6 11 4 3 ,
  0 1 2 10 ⟶ 1 2 6 11 4 10 ,
  0 1 2 6 ⟶ 1 2 6 11 4 6 ,
  0 1 2 8 ⟶ 1 2 6 11 4 8 ,
  0 1 2 0 ⟶ 1 2 0 8 12 13 14 ,
  0 1 2 3 ⟶ 1 2 0 8 12 13 11 ,
  0 1 2 6 ⟶ 1 2 0 8 12 13 13 ,
  0 1 2 8 ⟶ 1 2 0 8 12 13 15 ,
  0 1 2 0 ⟶ 1 2 6 13 13 14 0 ,
  0 1 2 1 ⟶ 1 2 6 13 13 14 1 ,
  0 1 2 3 ⟶ 1 2 6 13 13 14 3 ,
  0 1 2 10 ⟶ 1 2 6 13 13 14 10 ,
  0 1 2 6 ⟶ 1 2 6 13 13 14 6 ,
  0 1 2 8 ⟶ 1 2 6 13 13 14 8 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 3 ⟶ 1 2 0 3 4 3 ,
  0 0 1 2 10 ⟶ 1 2 0 3 4 10 ,
  0 0 1 2 6 ⟶ 1 2 0 3 4 6 ,
  0 0 1 2 8 ⟶ 1 2 0 3 4 8 ,
  0 1 2 10 16 ⟶ 1 2 10 17 16 3 4 ,
  0 1 2 10 17 ⟶ 1 2 10 17 16 3 18 ,
  0 1 2 10 17 ⟶ 1 2 8 19 20 4 10 ,
  0 1 21 4 1 ⟶ 1 22 2 3 4 1 ,
  0 1 21 4 1 ⟶ 1 22 21 4 6 14 1 ,
  16 1 23 16 0 ⟶ 24 2 10 16 3 4 ,
  16 1 23 16 3 ⟶ 24 2 10 16 3 5 ,
  16 1 23 16 6 ⟶ 24 2 10 16 3 7 ,
  16 1 23 16 8 ⟶ 24 2 10 16 3 9 ,
  0 1 25 26 0 ⟶ 1 25 19 16 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 19 16 3 4 1 ,
  8 26 1 2 0 ⟶ 1 27 14 0 8 28 2 ,
  8 26 1 2 3 ⟶ 1 27 14 0 8 28 21 ,
  0 1 27 15 26 0 ⟶ 1 25 26 0 6 11 4 ,
  0 1 27 15 26 3 ⟶ 1 25 26 0 6 11 5 ,
  0 1 27 15 26 6 ⟶ 1 25 26 0 6 11 7 ,
  0 1 27 15 26 8 ⟶ 1 25 26 0 6 11 9 ,
  18 16 10 24 2 0 ⟶ 4 1 23 20 18 16 0 ,
  18 16 10 24 2 1 ⟶ 4 1 23 20 18 16 1 ,
  18 16 10 24 2 3 ⟶ 4 1 23 20 18 16 3 ,
  18 16 10 24 2 10 ⟶ 4 1 23 20 18 16 10 ,
  18 16 10 24 2 6 ⟶ 4 1 23 20 18 16 6 ,
  18 16 10 24 2 8 ⟶ 4 1 23 20 18 16 8 ,
  18 16 10 24 2 29 ⟶ 4 1 23 20 18 16 29 ,
  17 16 10 24 2 0 ⟶ 16 1 23 20 18 16 0 ,
  17 16 10 24 2 1 ⟶ 16 1 23 20 18 16 1 ,
  17 16 10 24 2 3 ⟶ 16 1 23 20 18 16 3 ,
  17 16 10 24 2 10 ⟶ 16 1 23 20 18 16 10 ,
  17 16 10 24 2 6 ⟶ 16 1 23 20 18 16 6 ,
  17 16 10 24 2 8 ⟶ 16 1 23 20 18 16 8 ,
  17 16 10 24 2 29 ⟶ 16 1 23 20 18 16 29 ,
  19 16 10 24 2 0 ⟶ 26 1 23 20 18 16 0 ,
  19 16 10 24 2 1 ⟶ 26 1 23 20 18 16 1 ,
  19 16 10 24 2 3 ⟶ 26 1 23 20 18 16 3 ,
  19 16 10 24 2 10 ⟶ 26 1 23 20 18 16 10 ,
  19 16 10 24 2 6 ⟶ 26 1 23 20 18 16 6 ,
  19 16 10 24 2 8 ⟶ 26 1 23 20 18 16 8 ,
  19 16 10 24 2 29 ⟶ 26 1 23 20 18 16 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 ↦ ⎛           ⎞
    ⎜ 1 0 1 0 0 ⎟
    ⎜ 0 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

2 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

3 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎝           ⎠

4 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 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 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 1 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 1 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 1 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 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 1 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 1 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 1 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 1 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 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

23 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

24 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

25 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

26 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

27 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

28 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

29 ↦ ⎛           ⎞
     ⎜ 1 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 ⎟
     ⎝           ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 6 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 13 ↦ 12, 14 ↦ 13, 15 ↦ 14, 16 ↦ 15, 17 ↦ 16, 18 ↦ 17, 19 ↦ 18, 20 ↦ 19, 21 ↦ 20, 22 ↦ 21, 23 ↦ 22, 24 ↦ 23, 5 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29 },
it remains to prove termination of the 64-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 5 ⟶ 1 2 0 0 3 6 ,
  0 1 2 7 ⟶ 1 2 0 0 3 8 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 9 ⟶ 1 2 0 3 4 9 ,
  0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 1 2 7 ⟶ 1 2 0 3 4 7 ,
  0 1 2 0 ⟶ 1 2 5 10 4 0 ,
  0 1 2 1 ⟶ 1 2 5 10 4 1 ,
  0 1 2 9 ⟶ 1 2 5 10 4 9 ,
  0 1 2 5 ⟶ 1 2 5 10 4 5 ,
  0 1 2 7 ⟶ 1 2 5 10 4 7 ,
  0 1 2 0 ⟶ 1 2 0 7 11 12 13 ,
  0 1 2 5 ⟶ 1 2 0 7 11 12 12 ,
  0 1 2 7 ⟶ 1 2 0 7 11 12 14 ,
  0 1 2 0 ⟶ 1 2 5 12 12 13 0 ,
  0 1 2 1 ⟶ 1 2 5 12 12 13 1 ,
  0 1 2 9 ⟶ 1 2 5 12 12 13 9 ,
  0 1 2 5 ⟶ 1 2 5 12 12 13 5 ,
  0 1 2 7 ⟶ 1 2 5 12 12 13 7 ,
  0 0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 0 1 2 9 ⟶ 1 2 0 3 4 9 ,
  0 0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 0 1 2 7 ⟶ 1 2 0 3 4 7 ,
  0 1 2 9 15 ⟶ 1 2 9 16 15 3 4 ,
  0 1 2 9 16 ⟶ 1 2 9 16 15 3 17 ,
  0 1 2 9 16 ⟶ 1 2 7 18 19 4 9 ,
  0 1 20 4 1 ⟶ 1 21 2 3 4 1 ,
  0 1 20 4 1 ⟶ 1 21 20 4 5 13 1 ,
  15 1 22 15 0 ⟶ 23 2 9 15 3 4 ,
  15 1 22 15 3 ⟶ 23 2 9 15 3 24 ,
  15 1 22 15 5 ⟶ 23 2 9 15 3 6 ,
  15 1 22 15 7 ⟶ 23 2 9 15 3 8 ,
  0 1 25 26 0 ⟶ 1 25 18 15 3 4 0 ,
  0 1 25 26 1 ⟶ 1 25 18 15 3 4 1 ,
  7 26 1 2 0 ⟶ 1 27 13 0 7 28 2 ,
  7 26 1 2 3 ⟶ 1 27 13 0 7 28 20 ,
  0 1 27 14 26 0 ⟶ 1 25 26 0 5 10 4 ,
  0 1 27 14 26 3 ⟶ 1 25 26 0 5 10 24 ,
  0 1 27 14 26 5 ⟶ 1 25 26 0 5 10 6 ,
  0 1 27 14 26 7 ⟶ 1 25 26 0 5 10 8 ,
  17 15 9 23 2 0 ⟶ 4 1 22 19 17 15 0 ,
  17 15 9 23 2 1 ⟶ 4 1 22 19 17 15 1 ,
  17 15 9 23 2 3 ⟶ 4 1 22 19 17 15 3 ,
  17 15 9 23 2 9 ⟶ 4 1 22 19 17 15 9 ,
  17 15 9 23 2 5 ⟶ 4 1 22 19 17 15 5 ,
  17 15 9 23 2 7 ⟶ 4 1 22 19 17 15 7 ,
  17 15 9 23 2 29 ⟶ 4 1 22 19 17 15 29 ,
  16 15 9 23 2 0 ⟶ 15 1 22 19 17 15 0 ,
  16 15 9 23 2 1 ⟶ 15 1 22 19 17 15 1 ,
  16 15 9 23 2 3 ⟶ 15 1 22 19 17 15 3 ,
  16 15 9 23 2 9 ⟶ 15 1 22 19 17 15 9 ,
  16 15 9 23 2 5 ⟶ 15 1 22 19 17 15 5 ,
  16 15 9 23 2 7 ⟶ 15 1 22 19 17 15 7 ,
  16 15 9 23 2 29 ⟶ 15 1 22 19 17 15 29 ,
  18 15 9 23 2 0 ⟶ 26 1 22 19 17 15 0 ,
  18 15 9 23 2 1 ⟶ 26 1 22 19 17 15 1 ,
  18 15 9 23 2 3 ⟶ 26 1 22 19 17 15 3 ,
  18 15 9 23 2 9 ⟶ 26 1 22 19 17 15 9 ,
  18 15 9 23 2 5 ⟶ 26 1 22 19 17 15 5 ,
  18 15 9 23 2 7 ⟶ 26 1 22 19 17 15 7 ,
  18 15 9 23 2 29 ⟶ 26 1 22 19 17 15 29 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 8 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 7 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 8 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 8 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 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 7 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

16 ↦ ⎛     ⎞
     ⎜ 1 7 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

17 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 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 ⎟
     ⎝     ⎠

24 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

25 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

26 ↦ ⎛       ⎞
     ⎜  1 11 ⎟
     ⎜  0  1 ⎟
     ⎝       ⎠

27 ↦ ⎛     ⎞
     ⎜ 1 9 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

28 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

29 ↦ ⎛     ⎞
     ⎜ 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, 20 ↦ 15, 21 ↦ 16 },
it remains to prove termination of the 22-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 5 ⟶ 1 2 0 0 3 6 ,
  0 1 2 7 ⟶ 1 2 0 0 3 8 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 9 ⟶ 1 2 0 3 4 9 ,
  0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 1 2 7 ⟶ 1 2 0 3 4 7 ,
  0 1 2 0 ⟶ 1 2 5 10 4 0 ,
  0 1 2 1 ⟶ 1 2 5 10 4 1 ,
  0 1 2 9 ⟶ 1 2 5 10 4 9 ,
  0 1 2 5 ⟶ 1 2 5 10 4 5 ,
  0 1 2 7 ⟶ 1 2 5 10 4 7 ,
  0 1 2 0 ⟶ 1 2 0 7 11 12 13 ,
  0 1 2 5 ⟶ 1 2 0 7 11 12 12 ,
  0 1 2 7 ⟶ 1 2 0 7 11 12 14 ,
  0 1 2 0 ⟶ 1 2 5 12 12 13 0 ,
  0 1 2 1 ⟶ 1 2 5 12 12 13 1 ,
  0 1 2 9 ⟶ 1 2 5 12 12 13 9 ,
  0 1 2 5 ⟶ 1 2 5 12 12 13 5 ,
  0 1 2 7 ⟶ 1 2 5 12 12 13 7 ,
  0 1 15 4 1 ⟶ 1 16 15 4 5 13 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 ↦ ⎛           ⎞
    ⎜ 1 0 1 0 0 ⎟
    ⎜ 0 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

2 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

3 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎝           ⎠

8 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 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 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 1 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 1 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 1 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, 9 ↦ 7, 10 ↦ 8, 7 ↦ 9, 11 ↦ 10, 12 ↦ 11, 13 ↦ 12, 15 ↦ 13, 16 ↦ 14 },
it remains to prove termination of the 17-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 5 ⟶ 1 2 0 0 3 6 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 7 ⟶ 1 2 0 3 4 7 ,
  0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 1 2 0 ⟶ 1 2 5 8 4 0 ,
  0 1 2 1 ⟶ 1 2 5 8 4 1 ,
  0 1 2 7 ⟶ 1 2 5 8 4 7 ,
  0 1 2 5 ⟶ 1 2 5 8 4 5 ,
  0 1 2 0 ⟶ 1 2 0 9 10 11 12 ,
  0 1 2 5 ⟶ 1 2 0 9 10 11 11 ,
  0 1 2 0 ⟶ 1 2 5 11 11 12 0 ,
  0 1 2 1 ⟶ 1 2 5 11 11 12 1 ,
  0 1 2 7 ⟶ 1 2 5 11 11 12 7 ,
  0 1 2 5 ⟶ 1 2 5 11 11 12 5 ,
  0 1 13 4 1 ⟶ 1 14 13 4 5 12 1 }

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 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 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 11 ↦ 9, 12 ↦ 10, 13 ↦ 11, 14 ↦ 12 },
it remains to prove termination of the 15-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 5 ⟶ 1 2 0 0 3 6 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 7 ⟶ 1 2 0 3 4 7 ,
  0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 1 2 0 ⟶ 1 2 5 8 4 0 ,
  0 1 2 1 ⟶ 1 2 5 8 4 1 ,
  0 1 2 7 ⟶ 1 2 5 8 4 7 ,
  0 1 2 5 ⟶ 1 2 5 8 4 5 ,
  0 1 2 0 ⟶ 1 2 5 9 9 10 0 ,
  0 1 2 1 ⟶ 1 2 5 9 9 10 1 ,
  0 1 2 7 ⟶ 1 2 5 9 9 10 7 ,
  0 1 2 5 ⟶ 1 2 5 9 9 10 5 ,
  0 1 11 4 1 ⟶ 1 12 11 4 5 10 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 ↦ ⎛           ⎞
    ⎜ 1 0 1 0 0 ⎟
    ⎜ 0 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

2 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

3 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎝           ⎠

8 ↦ ⎛           ⎞
    ⎜ 1 0 0 0 0 ⎟
    ⎜ 0 1 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 1 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 1 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 1 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 1 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, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11 },
it remains to prove termination of the 12-rule system
{ 0 1 2 0 ⟶ 1 2 0 0 3 4 ,
  0 1 2 5 ⟶ 1 2 0 0 3 6 ,
  0 1 2 0 ⟶ 1 2 0 3 4 0 ,
  0 1 2 1 ⟶ 1 2 0 3 4 1 ,
  0 1 2 5 ⟶ 1 2 0 3 4 5 ,
  0 1 2 0 ⟶ 1 2 5 7 4 0 ,
  0 1 2 1 ⟶ 1 2 5 7 4 1 ,
  0 1 2 5 ⟶ 1 2 5 7 4 5 ,
  0 1 2 0 ⟶ 1 2 5 8 8 9 0 ,
  0 1 2 1 ⟶ 1 2 5 8 8 9 1 ,
  0 1 2 5 ⟶ 1 2 5 8 8 9 5 ,
  0 1 10 4 1 ⟶ 1 11 10 4 5 9 1 }

Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols.

After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (2,↓) ↦ 2, (0,↓) ↦ 3, (3,↓) ↦ 4, (4,↓) ↦ 5, (5,↓) ↦ 6, (6,↓) ↦ 7, (7,↓) ↦ 8, (8,↓) ↦ 9, (9,↓) ↦ 10, (10,↓) ↦ 11, (11,↓) ↦ 12 },
it remains to prove termination of the 19-rule system
{ 0 1 2 3 ⟶ 0 3 4 5 ,
  0 1 2 3 ⟶ 0 4 5 ,
  0 1 2 6 ⟶ 0 3 4 7 ,
  0 1 2 6 ⟶ 0 4 7 ,
  0 1 2 3 ⟶ 0 4 5 3 ,
  0 1 2 1 ⟶ 0 4 5 1 ,
  0 1 2 6 ⟶ 0 4 5 6 ,
  3 1 2 3 →= 1 2 3 3 4 5 ,
  3 1 2 6 →= 1 2 3 3 4 7 ,
  3 1 2 3 →= 1 2 3 4 5 3 ,
  3 1 2 1 →= 1 2 3 4 5 1 ,
  3 1 2 6 →= 1 2 3 4 5 6 ,
  3 1 2 3 →= 1 2 6 8 5 3 ,
  3 1 2 1 →= 1 2 6 8 5 1 ,
  3 1 2 6 →= 1 2 6 8 5 6 ,
  3 1 2 3 →= 1 2 6 9 9 10 3 ,
  3 1 2 1 →= 1 2 6 9 9 10 1 ,
  3 1 2 6 →= 1 2 6 9 9 10 6 ,
  3 1 11 5 1 →= 1 12 11 5 6 10 1 }

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

9 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

10 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

11 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

12 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 3 ↦ 0, 1 ↦ 1, 2 ↦ 2, 4 ↦ 3, 5 ↦ 4, 6 ↦ 5, 7 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11 },
it remains to prove termination of the 12-rule system
{ 0 1 2 0 →= 1 2 0 0 3 4 ,
  0 1 2 5 →= 1 2 0 0 3 6 ,
  0 1 2 0 →= 1 2 0 3 4 0 ,
  0 1 2 1 →= 1 2 0 3 4 1 ,
  0 1 2 5 →= 1 2 0 3 4 5 ,
  0 1 2 0 →= 1 2 5 7 4 0 ,
  0 1 2 1 →= 1 2 5 7 4 1 ,
  0 1 2 5 →= 1 2 5 7 4 5 ,
  0 1 2 0 →= 1 2 5 8 8 9 0 ,
  0 1 2 1 →= 1 2 5 8 8 9 1 ,
  0 1 2 5 →= 1 2 5 8 8 9 5 ,
  0 1 10 4 1 →= 1 11 10 4 5 9 1 }

The system is trivially terminating.