/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 19-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 0 1 0 1 0 0 1 0 2 0 ⟶ 0 1 1 1 0 1 1 2 1 2 0 1 1 1 0 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 0 2 2 1 1 2 1 2 2 0 1 ⟶ 0 1 2 2 0 0 1 0 1 0 2 1 0 2 2 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  0 2 0 0 1 1 2 0 1 0 1 0 2 ⟶ 0 0 1 2 0 0 1 0 1 0 1 1 0 0 1 1 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 0 2 0 2 1 0 2 0 1 1 2 0 ⟶ 1 2 0 2 0 0 1 0 1 0 0 0 1 2 0 1 0 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 0 1 0 2 0 1 0 1 2 1 0 ⟶ 1 0 1 1 2 0 1 0 0 1 0 0 1 0 1 2 0 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 18-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 0 1 0 1 0 0 1 0 2 0 ⟶ 0 1 1 1 0 1 1 2 1 2 0 1 1 1 0 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 0 2 2 1 1 2 1 2 2 0 1 ⟶ 0 1 2 2 0 0 1 0 1 0 2 1 0 2 2 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 0 2 0 2 1 0 2 0 1 1 2 0 ⟶ 1 2 0 2 0 0 1 0 1 0 0 0 1 2 0 1 0 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 0 1 0 2 0 1 0 1 2 1 0 ⟶ 1 0 1 1 2 0 1 0 0 1 0 0 1 0 1 2 0 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 17-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 0 1 0 1 0 0 1 0 2 0 ⟶ 0 1 1 1 0 1 1 2 1 2 0 1 1 1 0 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 0 2 2 1 1 2 1 2 2 0 1 ⟶ 0 1 2 2 0 0 1 0 1 0 2 1 0 2 2 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 0 1 0 2 0 1 0 1 2 1 0 ⟶ 1 0 1 1 2 0 1 0 0 1 0 0 1 0 1 2 0 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 1 0 0 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 },
it remains to prove termination of the 16-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 0 1 0 1 0 0 1 0 2 0 ⟶ 0 1 1 1 0 1 1 2 1 2 0 1 1 1 0 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 0 1 0 2 0 1 0 1 2 1 0 ⟶ 1 0 1 1 2 0 1 0 0 1 0 0 1 0 1 2 0 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 15-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 0 1 0 2 0 1 0 1 2 1 0 ⟶ 1 0 1 1 2 0 1 0 0 1 0 0 1 0 1 2 0 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎝                             ⎠

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 14-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 ,
  2 2 1 1 1 1 0 1 1 2 0 1 0 ⟶ 0 1 0 1 1 1 1 1 2 2 0 1 2 1 1 1 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                             ⎠

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 13-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 0 0 2 2 0 2 2 0 1 0 1 ⟶ 2 0 0 1 1 2 1 1 2 0 0 1 2 1 2 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 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 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                             ⎠

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 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 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 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 },
it remains to prove termination of the 12-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 0 1 1 0 1 0 2 1 0 0 ⟶ 0 1 2 0 1 1 0 1 1 1 1 1 0 0 1 0 0 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 26:

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

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

2 ↦ ⎛                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 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 },
it remains to prove termination of the 11-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  1 2 1 2 0 0 0 1 1 1 0 0 1 ⟶ 1 1 1 1 0 2 0 1 1 0 1 1 2 2 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 ,
  2 1 2 2 1 1 2 2 0 1 1 0 1 ⟶ 2 1 1 1 2 0 1 2 2 0 0 0 1 1 1 0 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 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 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 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 1 0 0 0 ⎟
    ⎝                             ⎠

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

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                             ⎠

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 9-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 ,
  2 0 2 1 1 1 1 0 2 0 1 0 1 ⟶ 2 1 2 0 2 0 1 0 1 2 0 1 0 1 1 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                             ⎠

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 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 },
it remains to prove termination of the 8-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 0 1 1 1 1 1 2 1 1 2 1 1 ⟶ 0 1 2 0 1 0 0 1 2 1 0 0 1 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 26:

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

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

2 ↦ ⎛                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 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 },
it remains to prove termination of the 7-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  1 1 0 0 2 2 2 0 1 2 0 1 1 ⟶ 1 0 1 1 1 0 0 1 2 0 1 2 0 0 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 26:

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

2 ↦ ⎛                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 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 },
it remains to prove termination of the 6-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  1 0 2 0 0 2 0 1 2 0 1 0 1 ⟶ 1 1 0 0 1 0 2 1 2 0 1 1 1 0 1 1 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 26:

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

2 ↦ ⎛                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 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 },
it remains to prove termination of the 5-rule system
{ 0 0 0 1 2 1 1 1 0 0 1 0 1 ⟶ 0 0 1 0 1 1 0 2 0 0 2 0 1 0 1 0 1 ,
  0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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 },
it remains to prove termination of the 4-rule system
{ 0 0 1 0 0 1 1 1 0 1 2 0 1 ⟶ 0 1 1 0 0 1 0 1 1 1 1 0 2 0 1 1 1 ,
  0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  0 1 1 1 2 1 2 0 1 2 1 0 1 ⟶ 0 1 0 1 0 1 1 0 0 1 0 2 0 1 0 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 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 },
it remains to prove termination of the 2-rule system
{ 0 1 0 2 0 2 1 0 0 1 0 1 1 ⟶ 0 0 0 1 1 1 1 1 0 2 2 0 1 1 1 0 1 ,
  2 0 2 1 0 0 1 0 0 0 1 1 1 ⟶ 0 2 1 2 1 0 1 1 1 0 1 0 1 0 0 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

2 ↦ ⎛                             ⎞
    ⎜ 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 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, 0 ↦ 1, 1 ↦ 2 },
it remains to prove termination of the 1-rule system
{ 0 1 0 2 1 1 2 1 1 1 2 2 2 ⟶ 1 0 2 0 2 1 2 2 2 1 2 1 2 1 1 2 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

2 ↦ ⎛                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 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.