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


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YES

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

The system was reversed.

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

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

After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (2,↓) ↦ 2, (1,↑) ↦ 3, (2,↑) ↦ 4, (0,↓) ↦ 5 },
it remains to prove termination of the 17-rule system
{ 0 1 1 ⟶ 0 1 2 ,
  0 1 1 ⟶ 3 2 ,
  0 1 1 ⟶ 4 ,
  4 5 1 2 ⟶ 3 1 5 ,
  4 5 1 2 ⟶ 3 5 ,
  4 5 1 2 ⟶ 0 ,
  3 2 5 ⟶ 4 1 5 2 ,
  3 2 5 ⟶ 3 5 2 ,
  3 2 5 ⟶ 0 2 ,
  3 2 5 ⟶ 4 ,
  4 1 5 ⟶ 0 2 1 ,
  4 1 5 ⟶ 4 1 ,
  4 1 5 ⟶ 3 ,
  5 1 1 →= 5 1 2 ,
  2 5 1 2 →= 1 1 5 ,
  1 2 5 →= 2 1 5 2 ,
  2 1 5 →= 5 2 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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 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 11-rule system
{ 0 1 1 ⟶ 0 1 2 ,
  0 1 1 ⟶ 3 2 ,
  0 1 1 ⟶ 4 ,
  4 5 1 2 ⟶ 3 1 5 ,
  4 5 1 2 ⟶ 3 5 ,
  3 2 5 ⟶ 4 1 5 2 ,
  3 2 5 ⟶ 3 5 2 ,
  5 1 1 →= 5 1 2 ,
  2 5 1 2 →= 1 1 5 ,
  1 2 5 →= 2 1 5 2 ,
  2 1 5 →= 5 2 1 }

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

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

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

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

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 4 ↦ 3, 5 ↦ 4, 3 ↦ 5 },
it remains to prove termination of the 9-rule system
{ 0 1 1 ⟶ 0 1 2 ,
  3 4 1 2 ⟶ 5 1 4 ,
  3 4 1 2 ⟶ 5 4 ,
  5 2 4 ⟶ 3 1 4 2 ,
  5 2 4 ⟶ 5 4 2 ,
  4 1 1 →= 4 1 2 ,
  2 4 1 2 →= 1 1 4 ,
  1 2 4 →= 2 1 4 2 ,
  2 1 4 →= 4 2 1 }

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 0 ⎟
    ⎜ 0 0 1 0 ⎟
    ⎝         ⎠

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

3 ↦ ⎛         ⎞
    ⎜ 1 0 0 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 1 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 1 ⟶ 0 1 2 ,
  3 4 1 2 ⟶ 5 1 4 ,
  3 4 1 2 ⟶ 5 4 ,
  4 1 1 →= 4 1 2 ,
  2 4 1 2 →= 1 1 4 ,
  1 2 4 →= 2 1 4 2 ,
  2 1 4 →= 4 2 1 }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The system is trivially terminating.