/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 { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 10-rule system
{ 0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ,
  0 1 2 1 ⟶ 1 2 1 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 }

The system was reversed.

After renaming modulo the bijection { 1 ↦ 0, 2 ↦ 1, 0 ↦ 2 },
it remains to prove termination of the 10-rule system
{ 0 1 0 2 ⟶ 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 1 0 ,
  0 1 0 2 ⟶ 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 2 0 0 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, (2,0) ↦ 4, (2,1) ↦ 5, (1,1) ↦ 6 },
it remains to prove termination of the 60-rule system
{ 0 1 2 3 4 ⟶ 1 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 4 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 }

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

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

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 0 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 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 ⎟
    ⎝             ⎠

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 ⎟
    ⎝             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 50-rule system
{ 0 1 2 3 4 ⟶ 1 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  0 1 2 3 5 ⟶ 1 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  2 1 2 3 4 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 0 ,
  2 1 2 3 5 ⟶ 6 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 ,
  4 1 2 3 5 ⟶ 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 5 2 3 4 0 1 2 1 }

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 0 0 0 0 0 ⎟
    ⎝             ⎠

4 ↦ ⎛             ⎞
    ⎜ 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 ⎟
    ⎝             ⎠

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 ⎟
    ⎝             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 5 ↦ 4, 4 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 40-rule system
{ 0 1 2 3 4 ⟶ 1 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  5 1 2 3 4 ⟶ 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 }

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

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

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 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 1 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 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 ⎟
    ⎝             ⎠

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 ⎟
    ⎝             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 30-rule system
{ 0 1 2 3 4 ⟶ 1 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  0 1 2 3 4 ⟶ 1 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 ,
  2 1 2 3 5 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 0 ,
  2 1 2 3 4 ⟶ 6 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 5 0 1 2 1 }

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 1 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 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 1 0 0 0 0 ⎟
    ⎝             ⎠

5 ↦ ⎛             ⎞
    ⎜ 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 ⎟
    ⎝             ⎠

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 ⎟
    ⎝             ⎠

After renaming modulo the bijection { 2 ↦ 0, 1 ↦ 1, 3 ↦ 2, 5 ↦ 3, 6 ↦ 4, 4 ↦ 5, 0 ↦ 6 },
it remains to prove termination of the 20-rule system
{ 0 1 0 2 3 ⟶ 4 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 6 ,
  0 1 0 2 5 ⟶ 4 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 5 0 2 3 6 1 0 1 }

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 1 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 1 ⎟
    ⎜ 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 1 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 ⎟
    ⎝             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 5 ↦ 3, 4 ↦ 4, 3 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 10-rule system
{ 0 1 0 2 3 ⟶ 4 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 ,
  0 1 0 2 3 ⟶ 4 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2 5 6 1 0 1 }

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 1 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 1 ⎟
    ⎜ 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 1 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 ⎟
    ⎝             ⎠

After renaming modulo the bijection {  },
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.