/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 { c ↦ 0, b ↦ 1, a ↦ 2 },
it remains to prove termination of the 4-rule system
{ 0 1 2 2 ⟶ 2 2 1 0 ,
  1 2 2 2 ⟶ 2 2 2 1 ,
  2 1 0 ⟶ 0 1 2 ,
  0 0 1 1 ⟶ 1 1 0 0 }

The length-preserving system was inverted.

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

The system was reversed.

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

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

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

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

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

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

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

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 },
it remains to prove termination of the 8-rule system
{ 0 1 2 2 ⟶ 3 2 1 4 ,
  5 2 2 2 ⟶ 3 2 2 1 ,
  3 1 4 ⟶ 0 1 2 ,
  0 4 1 1 ⟶ 5 1 4 4 ,
  4 1 2 2 →= 2 2 1 4 ,
  1 2 2 2 →= 2 2 2 1 ,
  2 1 4 →= 4 1 2 ,
  4 4 1 1 →= 1 1 4 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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

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

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

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

5 ↦ ⎛         ⎞
    ⎜ 1 0 0 0 ⎟
    ⎜ 0 1 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 },
it remains to prove termination of the 7-rule system
{ 0 1 2 2 ⟶ 3 2 1 4 ,
  5 2 2 2 ⟶ 3 2 2 1 ,
  0 4 1 1 ⟶ 5 1 4 4 ,
  4 1 2 2 →= 2 2 1 4 ,
  1 2 2 2 →= 2 2 2 1 ,
  2 1 4 →= 4 1 2 ,
  4 4 1 1 →= 1 1 4 4 }

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

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

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

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

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

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

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

After renaming modulo the bijection { 4 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 4-rule system
{ 0 1 2 2 →= 2 2 1 0 ,
  1 2 2 2 →= 2 2 2 1 ,
  2 1 0 →= 0 1 2 ,
  0 0 1 1 →= 1 1 0 0 }

The system is trivially terminating.