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


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YES

After renaming modulo the bijection { a ↦ 0, b ↦ 1 },
it remains to prove termination of the 3-rule system
{ 0 1 1 ⟶ 0 ,
  0 0 ⟶ 1 1 1 ,
  1 1 0 ⟶ 0 1 0 }

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

After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (0,↓) ↦ 2, (1,↑) ↦ 3 },
it remains to prove termination of the 8-rule system
{ 0 1 1 ⟶ 0 ,
  0 2 ⟶ 3 1 1 ,
  0 2 ⟶ 3 1 ,
  0 2 ⟶ 3 ,
  3 1 2 ⟶ 0 1 2 ,
  2 1 1 →= 2 ,
  2 2 →= 1 1 1 ,
  1 1 2 →= 2 1 2 }

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

After renaming modulo the bijection { (4,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (1,2) ↦ 3, (0,2) ↦ 4, (1,5) ↦ 5, (0,5) ↦ 6, (2,1) ↦ 7, (4,3) ↦ 8, (3,1) ↦ 9, (2,2) ↦ 10, (2,5) ↦ 11, (3,2) ↦ 12, (3,5) ↦ 13, (4,2) ↦ 14, (4,1) ↦ 15 },
it remains to prove termination of the 60-rule system
{ 0 1 2 2 ⟶ 0 1 ,
  0 1 2 3 ⟶ 0 4 ,
  0 1 2 5 ⟶ 0 6 ,
  0 4 7 ⟶ 8 9 2 2 ,
  0 4 10 ⟶ 8 9 2 3 ,
  0 4 11 ⟶ 8 9 2 5 ,
  0 4 7 ⟶ 8 9 2 ,
  0 4 10 ⟶ 8 9 3 ,
  0 4 11 ⟶ 8 9 5 ,
  0 4 7 ⟶ 8 9 ,
  0 4 10 ⟶ 8 12 ,
  0 4 11 ⟶ 8 13 ,
  8 9 3 7 ⟶ 0 1 3 7 ,
  8 9 3 10 ⟶ 0 1 3 10 ,
  8 9 3 11 ⟶ 0 1 3 11 ,
  4 7 2 2 →= 4 7 ,
  4 7 2 3 →= 4 10 ,
  4 7 2 5 →= 4 11 ,
  3 7 2 2 →= 3 7 ,
  3 7 2 3 →= 3 10 ,
  3 7 2 5 →= 3 11 ,
  10 7 2 2 →= 10 7 ,
  10 7 2 3 →= 10 10 ,
  10 7 2 5 →= 10 11 ,
  12 7 2 2 →= 12 7 ,
  12 7 2 3 →= 12 10 ,
  12 7 2 5 →= 12 11 ,
  14 7 2 2 →= 14 7 ,
  14 7 2 3 →= 14 10 ,
  14 7 2 5 →= 14 11 ,
  4 10 7 →= 1 2 2 2 ,
  4 10 10 →= 1 2 2 3 ,
  4 10 11 →= 1 2 2 5 ,
  3 10 7 →= 2 2 2 2 ,
  3 10 10 →= 2 2 2 3 ,
  3 10 11 →= 2 2 2 5 ,
  10 10 7 →= 7 2 2 2 ,
  10 10 10 →= 7 2 2 3 ,
  10 10 11 →= 7 2 2 5 ,
  12 10 7 →= 9 2 2 2 ,
  12 10 10 →= 9 2 2 3 ,
  12 10 11 →= 9 2 2 5 ,
  14 10 7 →= 15 2 2 2 ,
  14 10 10 →= 15 2 2 3 ,
  14 10 11 →= 15 2 2 5 ,
  1 2 3 7 →= 4 7 3 7 ,
  1 2 3 10 →= 4 7 3 10 ,
  1 2 3 11 →= 4 7 3 11 ,
  2 2 3 7 →= 3 7 3 7 ,
  2 2 3 10 →= 3 7 3 10 ,
  2 2 3 11 →= 3 7 3 11 ,
  7 2 3 7 →= 10 7 3 7 ,
  7 2 3 10 →= 10 7 3 10 ,
  7 2 3 11 →= 10 7 3 11 ,
  9 2 3 7 →= 12 7 3 7 ,
  9 2 3 10 →= 12 7 3 10 ,
  9 2 3 11 →= 12 7 3 11 ,
  15 2 3 7 →= 14 7 3 7 ,
  15 2 3 10 →= 14 7 3 10 ,
  15 2 3 11 →= 14 7 3 11 }

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

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

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

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

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

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 7 ↦ 5, 8 ↦ 6, 9 ↦ 7, 10 ↦ 8, 11 ↦ 9, 5 ↦ 10, 12 ↦ 11, 14 ↦ 12, 15 ↦ 13 },
it remains to prove termination of the 58-rule system
{ 0 1 2 2 ⟶ 0 1 ,
  0 1 2 3 ⟶ 0 4 ,
  0 4 5 ⟶ 6 7 2 2 ,
  0 4 8 ⟶ 6 7 2 3 ,
  0 4 9 ⟶ 6 7 2 10 ,
  0 4 5 ⟶ 6 7 2 ,
  0 4 8 ⟶ 6 7 3 ,
  0 4 9 ⟶ 6 7 10 ,
  0 4 5 ⟶ 6 7 ,
  0 4 8 ⟶ 6 11 ,
  6 7 3 5 ⟶ 0 1 3 5 ,
  6 7 3 8 ⟶ 0 1 3 8 ,
  6 7 3 9 ⟶ 0 1 3 9 ,
  4 5 2 2 →= 4 5 ,
  4 5 2 3 →= 4 8 ,
  4 5 2 10 →= 4 9 ,
  3 5 2 2 →= 3 5 ,
  3 5 2 3 →= 3 8 ,
  3 5 2 10 →= 3 9 ,
  8 5 2 2 →= 8 5 ,
  8 5 2 3 →= 8 8 ,
  8 5 2 10 →= 8 9 ,
  11 5 2 2 →= 11 5 ,
  11 5 2 3 →= 11 8 ,
  11 5 2 10 →= 11 9 ,
  12 5 2 2 →= 12 5 ,
  12 5 2 3 →= 12 8 ,
  12 5 2 10 →= 12 9 ,
  4 8 5 →= 1 2 2 2 ,
  4 8 8 →= 1 2 2 3 ,
  4 8 9 →= 1 2 2 10 ,
  3 8 5 →= 2 2 2 2 ,
  3 8 8 →= 2 2 2 3 ,
  3 8 9 →= 2 2 2 10 ,
  8 8 5 →= 5 2 2 2 ,
  8 8 8 →= 5 2 2 3 ,
  8 8 9 →= 5 2 2 10 ,
  11 8 5 →= 7 2 2 2 ,
  11 8 8 →= 7 2 2 3 ,
  11 8 9 →= 7 2 2 10 ,
  12 8 5 →= 13 2 2 2 ,
  12 8 8 →= 13 2 2 3 ,
  12 8 9 →= 13 2 2 10 ,
  1 2 3 5 →= 4 5 3 5 ,
  1 2 3 8 →= 4 5 3 8 ,
  1 2 3 9 →= 4 5 3 9 ,
  2 2 3 5 →= 3 5 3 5 ,
  2 2 3 8 →= 3 5 3 8 ,
  2 2 3 9 →= 3 5 3 9 ,
  5 2 3 5 →= 8 5 3 5 ,
  5 2 3 8 →= 8 5 3 8 ,
  5 2 3 9 →= 8 5 3 9 ,
  7 2 3 5 →= 11 5 3 5 ,
  7 2 3 8 →= 11 5 3 8 ,
  7 2 3 9 →= 11 5 3 9 ,
  13 2 3 5 →= 12 5 3 5 ,
  13 2 3 8 →= 12 5 3 8 ,
  13 2 3 9 →= 12 5 3 9 }

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

After renaming modulo the bijection { (14,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,2) ↦ 3, (2,3) ↦ 4, (1,3) ↦ 5, (2,10) ↦ 6, (1,10) ↦ 7, (2,15) ↦ 8, (1,15) ↦ 9, (3,5) ↦ 10, (0,4) ↦ 11, (4,5) ↦ 12, (3,8) ↦ 13, (4,8) ↦ 14, (3,9) ↦ 15, (4,9) ↦ 16, (3,15) ↦ 17, (4,15) ↦ 18, (5,2) ↦ 19, (14,6) ↦ 20, (6,7) ↦ 21, (7,2) ↦ 22, (5,3) ↦ 23, (5,10) ↦ 24, (5,15) ↦ 25, (8,5) ↦ 26, (8,8) ↦ 27, (8,9) ↦ 28, (8,15) ↦ 29, (9,15) ↦ 30, (10,15) ↦ 31, (7,3) ↦ 32, (7,10) ↦ 33, (7,15) ↦ 34, (6,11) ↦ 35, (11,5) ↦ 36, (11,8) ↦ 37, (11,9) ↦ 38, (11,15) ↦ 39, (14,4) ↦ 40, (13,3) ↦ 41, (14,3) ↦ 42, (12,8) ↦ 43, (14,8) ↦ 44, (14,11) ↦ 45, (14,12) ↦ 46, (12,5) ↦ 47, (12,9) ↦ 48, (14,1) ↦ 49, (13,2) ↦ 50, (14,2) ↦ 51, (14,5) ↦ 52, (14,7) ↦ 53, (14,13) ↦ 54 },
it remains to prove termination of the 502-rule system
{ 0 1 2 3 3 ⟶ 0 1 2 ,
  0 1 2 3 4 ⟶ 0 1 5 ,
  0 1 2 3 6 ⟶ 0 1 7 ,
  0 1 2 3 8 ⟶ 0 1 9 ,
  0 1 2 4 10 ⟶ 0 11 12 ,
  0 1 2 4 13 ⟶ 0 11 14 ,
  0 1 2 4 15 ⟶ 0 11 16 ,
  0 1 2 4 17 ⟶ 0 11 18 ,
  0 11 12 19 ⟶ 20 21 22 3 3 ,
  0 11 12 23 ⟶ 20 21 22 3 4 ,
  0 11 12 24 ⟶ 20 21 22 3 6 ,
  0 11 12 25 ⟶ 20 21 22 3 8 ,
  0 11 14 26 ⟶ 20 21 22 4 10 ,
  0 11 14 27 ⟶ 20 21 22 4 13 ,
  0 11 14 28 ⟶ 20 21 22 4 15 ,
  0 11 14 29 ⟶ 20 21 22 4 17 ,
  0 11 16 30 ⟶ 20 21 22 6 31 ,
  0 11 12 19 ⟶ 20 21 22 3 ,
  0 11 12 23 ⟶ 20 21 22 4 ,
  0 11 12 24 ⟶ 20 21 22 6 ,
  0 11 12 25 ⟶ 20 21 22 8 ,
  0 11 14 26 ⟶ 20 21 32 10 ,
  0 11 14 27 ⟶ 20 21 32 13 ,
  0 11 14 28 ⟶ 20 21 32 15 ,
  0 11 14 29 ⟶ 20 21 32 17 ,
  0 11 16 30 ⟶ 20 21 33 31 ,
  0 11 12 19 ⟶ 20 21 22 ,
  0 11 12 23 ⟶ 20 21 32 ,
  0 11 12 24 ⟶ 20 21 33 ,
  0 11 12 25 ⟶ 20 21 34 ,
  0 11 14 26 ⟶ 20 35 36 ,
  0 11 14 27 ⟶ 20 35 37 ,
  0 11 14 28 ⟶ 20 35 38 ,
  0 11 14 29 ⟶ 20 35 39 ,
  20 21 32 10 19 ⟶ 0 1 5 10 19 ,
  20 21 32 10 23 ⟶ 0 1 5 10 23 ,
  20 21 32 10 24 ⟶ 0 1 5 10 24 ,
  20 21 32 10 25 ⟶ 0 1 5 10 25 ,
  20 21 32 13 26 ⟶ 0 1 5 13 26 ,
  20 21 32 13 27 ⟶ 0 1 5 13 27 ,
  20 21 32 13 28 ⟶ 0 1 5 13 28 ,
  20 21 32 13 29 ⟶ 0 1 5 13 29 ,
  20 21 32 15 30 ⟶ 0 1 5 15 30 ,
  11 12 19 3 3 →= 11 12 19 ,
  11 12 19 3 4 →= 11 12 23 ,
  11 12 19 3 6 →= 11 12 24 ,
  11 12 19 3 8 →= 11 12 25 ,
  40 12 19 3 3 →= 40 12 19 ,
  40 12 19 3 4 →= 40 12 23 ,
  40 12 19 3 6 →= 40 12 24 ,
  40 12 19 3 8 →= 40 12 25 ,
  11 12 19 4 10 →= 11 14 26 ,
  11 12 19 4 13 →= 11 14 27 ,
  11 12 19 4 15 →= 11 14 28 ,
  11 12 19 4 17 →= 11 14 29 ,
  40 12 19 4 10 →= 40 14 26 ,
  40 12 19 4 13 →= 40 14 27 ,
  40 12 19 4 15 →= 40 14 28 ,
  40 12 19 4 17 →= 40 14 29 ,
  11 12 19 6 31 →= 11 16 30 ,
  40 12 19 6 31 →= 40 16 30 ,
  5 10 19 3 3 →= 5 10 19 ,
  5 10 19 3 4 →= 5 10 23 ,
  5 10 19 3 6 →= 5 10 24 ,
  5 10 19 3 8 →= 5 10 25 ,
  4 10 19 3 3 →= 4 10 19 ,
  4 10 19 3 4 →= 4 10 23 ,
  4 10 19 3 6 →= 4 10 24 ,
  4 10 19 3 8 →= 4 10 25 ,
  23 10 19 3 3 →= 23 10 19 ,
  23 10 19 3 4 →= 23 10 23 ,
  23 10 19 3 6 →= 23 10 24 ,
  23 10 19 3 8 →= 23 10 25 ,
  32 10 19 3 3 →= 32 10 19 ,
  32 10 19 3 4 →= 32 10 23 ,
  32 10 19 3 6 →= 32 10 24 ,
  32 10 19 3 8 →= 32 10 25 ,
  41 10 19 3 3 →= 41 10 19 ,
  41 10 19 3 4 →= 41 10 23 ,
  41 10 19 3 6 →= 41 10 24 ,
  41 10 19 3 8 →= 41 10 25 ,
  42 10 19 3 3 →= 42 10 19 ,
  42 10 19 3 4 →= 42 10 23 ,
  42 10 19 3 6 →= 42 10 24 ,
  42 10 19 3 8 →= 42 10 25 ,
  5 10 19 4 10 →= 5 13 26 ,
  5 10 19 4 13 →= 5 13 27 ,
  5 10 19 4 15 →= 5 13 28 ,
  5 10 19 4 17 →= 5 13 29 ,
  4 10 19 4 10 →= 4 13 26 ,
  4 10 19 4 13 →= 4 13 27 ,
  4 10 19 4 15 →= 4 13 28 ,
  4 10 19 4 17 →= 4 13 29 ,
  23 10 19 4 10 →= 23 13 26 ,
  23 10 19 4 13 →= 23 13 27 ,
  23 10 19 4 15 →= 23 13 28 ,
  23 10 19 4 17 →= 23 13 29 ,
  32 10 19 4 10 →= 32 13 26 ,
  32 10 19 4 13 →= 32 13 27 ,
  32 10 19 4 15 →= 32 13 28 ,
  32 10 19 4 17 →= 32 13 29 ,
  41 10 19 4 10 →= 41 13 26 ,
  41 10 19 4 13 →= 41 13 27 ,
  41 10 19 4 15 →= 41 13 28 ,
  41 10 19 4 17 →= 41 13 29 ,
  42 10 19 4 10 →= 42 13 26 ,
  42 10 19 4 13 →= 42 13 27 ,
  42 10 19 4 15 →= 42 13 28 ,
  42 10 19 4 17 →= 42 13 29 ,
  5 10 19 6 31 →= 5 15 30 ,
  4 10 19 6 31 →= 4 15 30 ,
  23 10 19 6 31 →= 23 15 30 ,
  32 10 19 6 31 →= 32 15 30 ,
  41 10 19 6 31 →= 41 15 30 ,
  42 10 19 6 31 →= 42 15 30 ,
  13 26 19 3 3 →= 13 26 19 ,
  13 26 19 3 4 →= 13 26 23 ,
  13 26 19 3 6 →= 13 26 24 ,
  13 26 19 3 8 →= 13 26 25 ,
  14 26 19 3 3 →= 14 26 19 ,
  14 26 19 3 4 →= 14 26 23 ,
  14 26 19 3 6 →= 14 26 24 ,
  14 26 19 3 8 →= 14 26 25 ,
  27 26 19 3 3 →= 27 26 19 ,
  27 26 19 3 4 →= 27 26 23 ,
  27 26 19 3 6 →= 27 26 24 ,
  27 26 19 3 8 →= 27 26 25 ,
  37 26 19 3 3 →= 37 26 19 ,
  37 26 19 3 4 →= 37 26 23 ,
  37 26 19 3 6 →= 37 26 24 ,
  37 26 19 3 8 →= 37 26 25 ,
  43 26 19 3 3 →= 43 26 19 ,
  43 26 19 3 4 →= 43 26 23 ,
  43 26 19 3 6 →= 43 26 24 ,
  43 26 19 3 8 →= 43 26 25 ,
  44 26 19 3 3 →= 44 26 19 ,
  44 26 19 3 4 →= 44 26 23 ,
  44 26 19 3 6 →= 44 26 24 ,
  44 26 19 3 8 →= 44 26 25 ,
  13 26 19 4 10 →= 13 27 26 ,
  13 26 19 4 13 →= 13 27 27 ,
  13 26 19 4 15 →= 13 27 28 ,
  13 26 19 4 17 →= 13 27 29 ,
  14 26 19 4 10 →= 14 27 26 ,
  14 26 19 4 13 →= 14 27 27 ,
  14 26 19 4 15 →= 14 27 28 ,
  14 26 19 4 17 →= 14 27 29 ,
  27 26 19 4 10 →= 27 27 26 ,
  27 26 19 4 13 →= 27 27 27 ,
  27 26 19 4 15 →= 27 27 28 ,
  27 26 19 4 17 →= 27 27 29 ,
  37 26 19 4 10 →= 37 27 26 ,
  37 26 19 4 13 →= 37 27 27 ,
  37 26 19 4 15 →= 37 27 28 ,
  37 26 19 4 17 →= 37 27 29 ,
  43 26 19 4 10 →= 43 27 26 ,
  43 26 19 4 13 →= 43 27 27 ,
  43 26 19 4 15 →= 43 27 28 ,
  43 26 19 4 17 →= 43 27 29 ,
  44 26 19 4 10 →= 44 27 26 ,
  44 26 19 4 13 →= 44 27 27 ,
  44 26 19 4 15 →= 44 27 28 ,
  44 26 19 4 17 →= 44 27 29 ,
  13 26 19 6 31 →= 13 28 30 ,
  14 26 19 6 31 →= 14 28 30 ,
  27 26 19 6 31 →= 27 28 30 ,
  37 26 19 6 31 →= 37 28 30 ,
  43 26 19 6 31 →= 43 28 30 ,
  44 26 19 6 31 →= 44 28 30 ,
  35 36 19 3 3 →= 35 36 19 ,
  35 36 19 3 4 →= 35 36 23 ,
  35 36 19 3 6 →= 35 36 24 ,
  35 36 19 3 8 →= 35 36 25 ,
  45 36 19 3 3 →= 45 36 19 ,
  45 36 19 3 4 →= 45 36 23 ,
  45 36 19 3 6 →= 45 36 24 ,
  45 36 19 3 8 →= 45 36 25 ,
  35 36 19 4 10 →= 35 37 26 ,
  35 36 19 4 13 →= 35 37 27 ,
  35 36 19 4 15 →= 35 37 28 ,
  35 36 19 4 17 →= 35 37 29 ,
  45 36 19 4 10 →= 45 37 26 ,
  45 36 19 4 13 →= 45 37 27 ,
  45 36 19 4 15 →= 45 37 28 ,
  45 36 19 4 17 →= 45 37 29 ,
  35 36 19 6 31 →= 35 38 30 ,
  45 36 19 6 31 →= 45 38 30 ,
  46 47 19 3 3 →= 46 47 19 ,
  46 47 19 3 4 →= 46 47 23 ,
  46 47 19 3 6 →= 46 47 24 ,
  46 47 19 3 8 →= 46 47 25 ,
  46 47 19 4 10 →= 46 43 26 ,
  46 47 19 4 13 →= 46 43 27 ,
  46 47 19 4 15 →= 46 43 28 ,
  46 47 19 4 17 →= 46 43 29 ,
  46 47 19 6 31 →= 46 48 30 ,
  11 14 26 19 →= 1 2 3 3 3 ,
  11 14 26 23 →= 1 2 3 3 4 ,
  11 14 26 24 →= 1 2 3 3 6 ,
  11 14 26 25 →= 1 2 3 3 8 ,
  40 14 26 19 →= 49 2 3 3 3 ,
  40 14 26 23 →= 49 2 3 3 4 ,
  40 14 26 24 →= 49 2 3 3 6 ,
  40 14 26 25 →= 49 2 3 3 8 ,
  11 14 27 26 →= 1 2 3 4 10 ,
  11 14 27 27 →= 1 2 3 4 13 ,
  11 14 27 28 →= 1 2 3 4 15 ,
  11 14 27 29 →= 1 2 3 4 17 ,
  40 14 27 26 →= 49 2 3 4 10 ,
  40 14 27 27 →= 49 2 3 4 13 ,
  40 14 27 28 →= 49 2 3 4 15 ,
  40 14 27 29 →= 49 2 3 4 17 ,
  11 14 28 30 →= 1 2 3 6 31 ,
  40 14 28 30 →= 49 2 3 6 31 ,
  5 13 26 19 →= 2 3 3 3 3 ,
  5 13 26 23 →= 2 3 3 3 4 ,
  5 13 26 24 →= 2 3 3 3 6 ,
  5 13 26 25 →= 2 3 3 3 8 ,
  4 13 26 19 →= 3 3 3 3 3 ,
  4 13 26 23 →= 3 3 3 3 4 ,
  4 13 26 24 →= 3 3 3 3 6 ,
  4 13 26 25 →= 3 3 3 3 8 ,
  23 13 26 19 →= 19 3 3 3 3 ,
  23 13 26 23 →= 19 3 3 3 4 ,
  23 13 26 24 →= 19 3 3 3 6 ,
  23 13 26 25 →= 19 3 3 3 8 ,
  32 13 26 19 →= 22 3 3 3 3 ,
  32 13 26 23 →= 22 3 3 3 4 ,
  32 13 26 24 →= 22 3 3 3 6 ,
  32 13 26 25 →= 22 3 3 3 8 ,
  41 13 26 19 →= 50 3 3 3 3 ,
  41 13 26 23 →= 50 3 3 3 4 ,
  41 13 26 24 →= 50 3 3 3 6 ,
  41 13 26 25 →= 50 3 3 3 8 ,
  42 13 26 19 →= 51 3 3 3 3 ,
  42 13 26 23 →= 51 3 3 3 4 ,
  42 13 26 24 →= 51 3 3 3 6 ,
  42 13 26 25 →= 51 3 3 3 8 ,
  5 13 27 26 →= 2 3 3 4 10 ,
  5 13 27 27 →= 2 3 3 4 13 ,
  5 13 27 28 →= 2 3 3 4 15 ,
  5 13 27 29 →= 2 3 3 4 17 ,
  4 13 27 26 →= 3 3 3 4 10 ,
  4 13 27 27 →= 3 3 3 4 13 ,
  4 13 27 28 →= 3 3 3 4 15 ,
  4 13 27 29 →= 3 3 3 4 17 ,
  23 13 27 26 →= 19 3 3 4 10 ,
  23 13 27 27 →= 19 3 3 4 13 ,
  23 13 27 28 →= 19 3 3 4 15 ,
  23 13 27 29 →= 19 3 3 4 17 ,
  32 13 27 26 →= 22 3 3 4 10 ,
  32 13 27 27 →= 22 3 3 4 13 ,
  32 13 27 28 →= 22 3 3 4 15 ,
  32 13 27 29 →= 22 3 3 4 17 ,
  41 13 27 26 →= 50 3 3 4 10 ,
  41 13 27 27 →= 50 3 3 4 13 ,
  41 13 27 28 →= 50 3 3 4 15 ,
  41 13 27 29 →= 50 3 3 4 17 ,
  42 13 27 26 →= 51 3 3 4 10 ,
  42 13 27 27 →= 51 3 3 4 13 ,
  42 13 27 28 →= 51 3 3 4 15 ,
  42 13 27 29 →= 51 3 3 4 17 ,
  5 13 28 30 →= 2 3 3 6 31 ,
  4 13 28 30 →= 3 3 3 6 31 ,
  23 13 28 30 →= 19 3 3 6 31 ,
  32 13 28 30 →= 22 3 3 6 31 ,
  41 13 28 30 →= 50 3 3 6 31 ,
  42 13 28 30 →= 51 3 3 6 31 ,
  13 27 26 19 →= 10 19 3 3 3 ,
  13 27 26 23 →= 10 19 3 3 4 ,
  13 27 26 24 →= 10 19 3 3 6 ,
  13 27 26 25 →= 10 19 3 3 8 ,
  14 27 26 19 →= 12 19 3 3 3 ,
  14 27 26 23 →= 12 19 3 3 4 ,
  14 27 26 24 →= 12 19 3 3 6 ,
  14 27 26 25 →= 12 19 3 3 8 ,
  27 27 26 19 →= 26 19 3 3 3 ,
  27 27 26 23 →= 26 19 3 3 4 ,
  27 27 26 24 →= 26 19 3 3 6 ,
  27 27 26 25 →= 26 19 3 3 8 ,
  37 27 26 19 →= 36 19 3 3 3 ,
  37 27 26 23 →= 36 19 3 3 4 ,
  37 27 26 24 →= 36 19 3 3 6 ,
  37 27 26 25 →= 36 19 3 3 8 ,
  43 27 26 19 →= 47 19 3 3 3 ,
  43 27 26 23 →= 47 19 3 3 4 ,
  43 27 26 24 →= 47 19 3 3 6 ,
  43 27 26 25 →= 47 19 3 3 8 ,
  44 27 26 19 →= 52 19 3 3 3 ,
  44 27 26 23 →= 52 19 3 3 4 ,
  44 27 26 24 →= 52 19 3 3 6 ,
  44 27 26 25 →= 52 19 3 3 8 ,
  13 27 27 26 →= 10 19 3 4 10 ,
  13 27 27 27 →= 10 19 3 4 13 ,
  13 27 27 28 →= 10 19 3 4 15 ,
  13 27 27 29 →= 10 19 3 4 17 ,
  14 27 27 26 →= 12 19 3 4 10 ,
  14 27 27 27 →= 12 19 3 4 13 ,
  14 27 27 28 →= 12 19 3 4 15 ,
  14 27 27 29 →= 12 19 3 4 17 ,
  27 27 27 26 →= 26 19 3 4 10 ,
  27 27 27 27 →= 26 19 3 4 13 ,
  27 27 27 28 →= 26 19 3 4 15 ,
  27 27 27 29 →= 26 19 3 4 17 ,
  37 27 27 26 →= 36 19 3 4 10 ,
  37 27 27 27 →= 36 19 3 4 13 ,
  37 27 27 28 →= 36 19 3 4 15 ,
  37 27 27 29 →= 36 19 3 4 17 ,
  43 27 27 26 →= 47 19 3 4 10 ,
  43 27 27 27 →= 47 19 3 4 13 ,
  43 27 27 28 →= 47 19 3 4 15 ,
  43 27 27 29 →= 47 19 3 4 17 ,
  44 27 27 26 →= 52 19 3 4 10 ,
  44 27 27 27 →= 52 19 3 4 13 ,
  44 27 27 28 →= 52 19 3 4 15 ,
  44 27 27 29 →= 52 19 3 4 17 ,
  13 27 28 30 →= 10 19 3 6 31 ,
  14 27 28 30 →= 12 19 3 6 31 ,
  27 27 28 30 →= 26 19 3 6 31 ,
  37 27 28 30 →= 36 19 3 6 31 ,
  43 27 28 30 →= 47 19 3 6 31 ,
  44 27 28 30 →= 52 19 3 6 31 ,
  35 37 26 19 →= 21 22 3 3 3 ,
  35 37 26 23 →= 21 22 3 3 4 ,
  35 37 26 24 →= 21 22 3 3 6 ,
  35 37 26 25 →= 21 22 3 3 8 ,
  45 37 26 19 →= 53 22 3 3 3 ,
  45 37 26 23 →= 53 22 3 3 4 ,
  45 37 26 24 →= 53 22 3 3 6 ,
  45 37 26 25 →= 53 22 3 3 8 ,
  35 37 27 26 →= 21 22 3 4 10 ,
  35 37 27 27 →= 21 22 3 4 13 ,
  35 37 27 28 →= 21 22 3 4 15 ,
  35 37 27 29 →= 21 22 3 4 17 ,
  45 37 27 26 →= 53 22 3 4 10 ,
  45 37 27 27 →= 53 22 3 4 13 ,
  45 37 27 28 →= 53 22 3 4 15 ,
  45 37 27 29 →= 53 22 3 4 17 ,
  35 37 28 30 →= 21 22 3 6 31 ,
  45 37 28 30 →= 53 22 3 6 31 ,
  46 43 26 19 →= 54 50 3 3 3 ,
  46 43 26 23 →= 54 50 3 3 4 ,
  46 43 26 24 →= 54 50 3 3 6 ,
  46 43 26 25 →= 54 50 3 3 8 ,
  46 43 27 26 →= 54 50 3 4 10 ,
  46 43 27 27 →= 54 50 3 4 13 ,
  46 43 27 28 →= 54 50 3 4 15 ,
  46 43 27 29 →= 54 50 3 4 17 ,
  46 43 28 30 →= 54 50 3 6 31 ,
  1 2 4 10 19 →= 11 12 23 10 19 ,
  1 2 4 10 23 →= 11 12 23 10 23 ,
  1 2 4 10 24 →= 11 12 23 10 24 ,
  1 2 4 10 25 →= 11 12 23 10 25 ,
  49 2 4 10 19 →= 40 12 23 10 19 ,
  49 2 4 10 23 →= 40 12 23 10 23 ,
  49 2 4 10 24 →= 40 12 23 10 24 ,
  49 2 4 10 25 →= 40 12 23 10 25 ,
  1 2 4 13 26 →= 11 12 23 13 26 ,
  1 2 4 13 27 →= 11 12 23 13 27 ,
  1 2 4 13 28 →= 11 12 23 13 28 ,
  1 2 4 13 29 →= 11 12 23 13 29 ,
  49 2 4 13 26 →= 40 12 23 13 26 ,
  49 2 4 13 27 →= 40 12 23 13 27 ,
  49 2 4 13 28 →= 40 12 23 13 28 ,
  49 2 4 13 29 →= 40 12 23 13 29 ,
  1 2 4 15 30 →= 11 12 23 15 30 ,
  49 2 4 15 30 →= 40 12 23 15 30 ,
  2 3 4 10 19 →= 5 10 23 10 19 ,
  2 3 4 10 23 →= 5 10 23 10 23 ,
  2 3 4 10 24 →= 5 10 23 10 24 ,
  2 3 4 10 25 →= 5 10 23 10 25 ,
  3 3 4 10 19 →= 4 10 23 10 19 ,
  3 3 4 10 23 →= 4 10 23 10 23 ,
  3 3 4 10 24 →= 4 10 23 10 24 ,
  3 3 4 10 25 →= 4 10 23 10 25 ,
  19 3 4 10 19 →= 23 10 23 10 19 ,
  19 3 4 10 23 →= 23 10 23 10 23 ,
  19 3 4 10 24 →= 23 10 23 10 24 ,
  19 3 4 10 25 →= 23 10 23 10 25 ,
  22 3 4 10 19 →= 32 10 23 10 19 ,
  22 3 4 10 23 →= 32 10 23 10 23 ,
  22 3 4 10 24 →= 32 10 23 10 24 ,
  22 3 4 10 25 →= 32 10 23 10 25 ,
  50 3 4 10 19 →= 41 10 23 10 19 ,
  50 3 4 10 23 →= 41 10 23 10 23 ,
  50 3 4 10 24 →= 41 10 23 10 24 ,
  50 3 4 10 25 →= 41 10 23 10 25 ,
  51 3 4 10 19 →= 42 10 23 10 19 ,
  51 3 4 10 23 →= 42 10 23 10 23 ,
  51 3 4 10 24 →= 42 10 23 10 24 ,
  51 3 4 10 25 →= 42 10 23 10 25 ,
  2 3 4 13 26 →= 5 10 23 13 26 ,
  2 3 4 13 27 →= 5 10 23 13 27 ,
  2 3 4 13 28 →= 5 10 23 13 28 ,
  2 3 4 13 29 →= 5 10 23 13 29 ,
  3 3 4 13 26 →= 4 10 23 13 26 ,
  3 3 4 13 27 →= 4 10 23 13 27 ,
  3 3 4 13 28 →= 4 10 23 13 28 ,
  3 3 4 13 29 →= 4 10 23 13 29 ,
  19 3 4 13 26 →= 23 10 23 13 26 ,
  19 3 4 13 27 →= 23 10 23 13 27 ,
  19 3 4 13 28 →= 23 10 23 13 28 ,
  19 3 4 13 29 →= 23 10 23 13 29 ,
  22 3 4 13 26 →= 32 10 23 13 26 ,
  22 3 4 13 27 →= 32 10 23 13 27 ,
  22 3 4 13 28 →= 32 10 23 13 28 ,
  22 3 4 13 29 →= 32 10 23 13 29 ,
  50 3 4 13 26 →= 41 10 23 13 26 ,
  50 3 4 13 27 →= 41 10 23 13 27 ,
  50 3 4 13 28 →= 41 10 23 13 28 ,
  50 3 4 13 29 →= 41 10 23 13 29 ,
  51 3 4 13 26 →= 42 10 23 13 26 ,
  51 3 4 13 27 →= 42 10 23 13 27 ,
  51 3 4 13 28 →= 42 10 23 13 28 ,
  51 3 4 13 29 →= 42 10 23 13 29 ,
  2 3 4 15 30 →= 5 10 23 15 30 ,
  3 3 4 15 30 →= 4 10 23 15 30 ,
  19 3 4 15 30 →= 23 10 23 15 30 ,
  22 3 4 15 30 →= 32 10 23 15 30 ,
  50 3 4 15 30 →= 41 10 23 15 30 ,
  51 3 4 15 30 →= 42 10 23 15 30 ,
  10 19 4 10 19 →= 13 26 23 10 19 ,
  10 19 4 10 23 →= 13 26 23 10 23 ,
  10 19 4 10 24 →= 13 26 23 10 24 ,
  10 19 4 10 25 →= 13 26 23 10 25 ,
  12 19 4 10 19 →= 14 26 23 10 19 ,
  12 19 4 10 23 →= 14 26 23 10 23 ,
  12 19 4 10 24 →= 14 26 23 10 24 ,
  12 19 4 10 25 →= 14 26 23 10 25 ,
  26 19 4 10 19 →= 27 26 23 10 19 ,
  26 19 4 10 23 →= 27 26 23 10 23 ,
  26 19 4 10 24 →= 27 26 23 10 24 ,
  26 19 4 10 25 →= 27 26 23 10 25 ,
  36 19 4 10 19 →= 37 26 23 10 19 ,
  36 19 4 10 23 →= 37 26 23 10 23 ,
  36 19 4 10 24 →= 37 26 23 10 24 ,
  36 19 4 10 25 →= 37 26 23 10 25 ,
  47 19 4 10 19 →= 43 26 23 10 19 ,
  47 19 4 10 23 →= 43 26 23 10 23 ,
  47 19 4 10 24 →= 43 26 23 10 24 ,
  47 19 4 10 25 →= 43 26 23 10 25 ,
  52 19 4 10 19 →= 44 26 23 10 19 ,
  52 19 4 10 23 →= 44 26 23 10 23 ,
  52 19 4 10 24 →= 44 26 23 10 24 ,
  52 19 4 10 25 →= 44 26 23 10 25 ,
  10 19 4 13 26 →= 13 26 23 13 26 ,
  10 19 4 13 27 →= 13 26 23 13 27 ,
  10 19 4 13 28 →= 13 26 23 13 28 ,
  10 19 4 13 29 →= 13 26 23 13 29 ,
  12 19 4 13 26 →= 14 26 23 13 26 ,
  12 19 4 13 27 →= 14 26 23 13 27 ,
  12 19 4 13 28 →= 14 26 23 13 28 ,
  12 19 4 13 29 →= 14 26 23 13 29 ,
  26 19 4 13 26 →= 27 26 23 13 26 ,
  26 19 4 13 27 →= 27 26 23 13 27 ,
  26 19 4 13 28 →= 27 26 23 13 28 ,
  26 19 4 13 29 →= 27 26 23 13 29 ,
  36 19 4 13 26 →= 37 26 23 13 26 ,
  36 19 4 13 27 →= 37 26 23 13 27 ,
  36 19 4 13 28 →= 37 26 23 13 28 ,
  36 19 4 13 29 →= 37 26 23 13 29 ,
  47 19 4 13 26 →= 43 26 23 13 26 ,
  47 19 4 13 27 →= 43 26 23 13 27 ,
  47 19 4 13 28 →= 43 26 23 13 28 ,
  47 19 4 13 29 →= 43 26 23 13 29 ,
  52 19 4 13 26 →= 44 26 23 13 26 ,
  52 19 4 13 27 →= 44 26 23 13 27 ,
  52 19 4 13 28 →= 44 26 23 13 28 ,
  52 19 4 13 29 →= 44 26 23 13 29 ,
  10 19 4 15 30 →= 13 26 23 15 30 ,
  12 19 4 15 30 →= 14 26 23 15 30 ,
  26 19 4 15 30 →= 27 26 23 15 30 ,
  36 19 4 15 30 →= 37 26 23 15 30 ,
  47 19 4 15 30 →= 43 26 23 15 30 ,
  52 19 4 15 30 →= 44 26 23 15 30 ,
  21 22 4 10 19 →= 35 36 23 10 19 ,
  21 22 4 10 23 →= 35 36 23 10 23 ,
  21 22 4 10 24 →= 35 36 23 10 24 ,
  21 22 4 10 25 →= 35 36 23 10 25 ,
  53 22 4 10 19 →= 45 36 23 10 19 ,
  53 22 4 10 23 →= 45 36 23 10 23 ,
  53 22 4 10 24 →= 45 36 23 10 24 ,
  53 22 4 10 25 →= 45 36 23 10 25 ,
  21 22 4 13 26 →= 35 36 23 13 26 ,
  21 22 4 13 27 →= 35 36 23 13 27 ,
  21 22 4 13 28 →= 35 36 23 13 28 ,
  21 22 4 13 29 →= 35 36 23 13 29 ,
  53 22 4 13 26 →= 45 36 23 13 26 ,
  53 22 4 13 27 →= 45 36 23 13 27 ,
  53 22 4 13 28 →= 45 36 23 13 28 ,
  53 22 4 13 29 →= 45 36 23 13 29 ,
  21 22 4 15 30 →= 35 36 23 15 30 ,
  53 22 4 15 30 →= 45 36 23 15 30 ,
  54 50 4 10 19 →= 46 47 23 10 19 ,
  54 50 4 10 23 →= 46 47 23 10 23 ,
  54 50 4 10 24 →= 46 47 23 10 24 ,
  54 50 4 10 25 →= 46 47 23 10 25 ,
  54 50 4 13 26 →= 46 47 23 13 26 ,
  54 50 4 13 27 →= 46 47 23 13 27 ,
  54 50 4 13 28 →= 46 47 23 13 28 ,
  54 50 4 13 29 →= 46 47 23 13 29 ,
  54 50 4 15 30 →= 46 47 23 15 30 }

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

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

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

2 ↦ ⎛     ⎞
    ⎜ 1 4 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

4 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 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 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

13 ↦ ⎛     ⎞
     ⎜ 1 3 ⎟
     ⎜ 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 5 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

20 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 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 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

27 ↦ ⎛     ⎞
     ⎜ 1 5 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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

30 ↦ ⎛     ⎞
     ⎜ 1 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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

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

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

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

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

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

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

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

40 ↦ ⎛     ⎞
     ⎜ 1 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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

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

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

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

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

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

48 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

49 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

50 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

51 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

52 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

53 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

54 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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 1 ⎟
    ⎜ 0 1 0 0 1 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 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 ⎟
     ⎝             ⎠

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

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

32 ↦ ⎛             ⎞
     ⎜ 1 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 ⎟
     ⎜ 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 { 4 ↦ 0, 5 ↦ 1, 6 ↦ 2, 3 ↦ 3, 7 ↦ 4, 8 ↦ 5, 9 ↦ 6, 10 ↦ 7, 11 ↦ 8, 12 ↦ 9, 13 ↦ 10, 14 ↦ 11, 15 ↦ 12, 16 ↦ 13, 17 ↦ 14, 18 ↦ 15, 19 ↦ 16, 20 ↦ 17, 21 ↦ 18, 22 ↦ 19, 23 ↦ 20, 24 ↦ 21, 25 ↦ 22, 26 ↦ 23, 27 ↦ 24, 28 ↦ 25, 29 ↦ 26, 30 ↦ 27, 31 ↦ 28, 32 ↦ 29 },
it remains to prove termination of the 42-rule system
{ 0 1 2 3 3 →= 0 1 2 ,
  4 1 2 3 3 →= 4 1 2 ,
  5 6 2 3 3 →= 5 6 2 ,
  7 6 2 3 3 →= 7 6 2 ,
  8 6 2 3 3 →= 8 6 2 ,
  9 6 2 3 3 →= 9 6 2 ,
  10 6 2 3 3 →= 10 6 2 ,
  11 6 2 3 3 →= 11 6 2 ,
  5 6 2 7 6 →= 5 12 13 ,
  7 6 2 7 6 →= 7 12 13 ,
  8 6 2 7 6 →= 8 12 13 ,
  9 6 2 7 6 →= 9 12 13 ,
  10 6 2 7 6 →= 10 12 13 ,
  11 6 2 7 6 →= 11 12 13 ,
  12 13 2 3 3 →= 12 13 2 ,
  14 13 2 3 3 →= 14 13 2 ,
  15 13 2 3 3 →= 15 13 2 ,
  16 13 2 3 3 →= 16 13 2 ,
  17 13 2 3 3 →= 17 13 2 ,
  18 13 2 3 3 →= 18 13 2 ,
  19 20 2 3 3 →= 19 20 2 ,
  21 20 2 3 3 →= 21 20 2 ,
  22 23 2 3 3 →= 22 23 2 ,
  8 12 13 8 →= 2 3 3 3 7 ,
  3 3 7 6 2 →= 7 6 8 6 2 ,
  3 3 7 6 8 →= 7 6 8 6 8 ,
  3 3 7 6 24 →= 7 6 8 6 24 ,
  3 3 7 6 25 →= 7 6 8 6 25 ,
  3 3 7 12 13 →= 7 6 8 12 13 ,
  3 3 7 12 15 →= 7 6 8 12 15 ,
  3 3 7 12 26 →= 7 6 8 12 26 ,
  3 3 7 12 27 →= 7 6 8 12 27 ,
  3 3 7 28 29 →= 7 6 8 28 29 ,
  6 2 7 6 2 →= 12 13 8 6 2 ,
  6 2 7 6 8 →= 12 13 8 6 8 ,
  6 2 7 6 24 →= 12 13 8 6 24 ,
  6 2 7 6 25 →= 12 13 8 6 25 ,
  6 2 7 12 13 →= 12 13 8 12 13 ,
  6 2 7 12 15 →= 12 13 8 12 15 ,
  6 2 7 12 26 →= 12 13 8 12 26 ,
  6 2 7 12 27 →= 12 13 8 12 27 ,
  6 2 7 28 29 →= 12 13 8 28 29 }

The system is trivially terminating.