/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 { a ↦ 0, b ↦ 1, c ↦ 2 },
it remains to prove termination of the 3-rule system
{ 0 0 1 1 ⟶ 1 1 2 2 0 0 ,
  1 1 2 2 ⟶ 2 2 1 1 1 1 ,
  1 1 0 0 ⟶ 0 0 2 2 1 1 }

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

After renaming modulo the bijection { (0,↑) ↦ 0, (0,↓) ↦ 1, (1,↓) ↦ 2, (1,↑) ↦ 3, (2,↓) ↦ 4 },
it remains to prove termination of the 15-rule system
{ 0 1 2 2 ⟶ 3 2 4 4 1 1 ,
  0 1 2 2 ⟶ 3 4 4 1 1 ,
  0 1 2 2 ⟶ 0 1 ,
  0 1 2 2 ⟶ 0 ,
  3 2 4 4 ⟶ 3 2 2 2 ,
  3 2 4 4 ⟶ 3 2 2 ,
  3 2 4 4 ⟶ 3 2 ,
  3 2 4 4 ⟶ 3 ,
  3 2 1 1 ⟶ 0 1 4 4 2 2 ,
  3 2 1 1 ⟶ 0 4 4 2 2 ,
  3 2 1 1 ⟶ 3 2 ,
  3 2 1 1 ⟶ 3 ,
  1 1 2 2 →= 2 2 4 4 1 1 ,
  2 2 4 4 →= 4 4 2 2 2 2 ,
  2 2 1 1 →= 1 1 4 4 2 2 }

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4 },
it remains to prove termination of the 11-rule system
{ 0 1 2 2 ⟶ 3 2 4 4 1 1 ,
  0 1 2 2 ⟶ 3 4 4 1 1 ,
  0 1 2 2 ⟶ 0 1 ,
  3 2 4 4 ⟶ 3 2 2 2 ,
  3 2 4 4 ⟶ 3 2 2 ,
  3 2 4 4 ⟶ 3 2 ,
  3 2 4 4 ⟶ 3 ,
  3 2 1 1 ⟶ 0 1 4 4 2 2 ,
  1 1 2 2 →= 2 2 4 4 1 1 ,
  2 2 4 4 →= 4 4 2 2 2 2 ,
  2 2 1 1 →= 1 1 4 4 2 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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

3 ↦ ⎛           ⎞
    ⎜ 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 ⎟
    ⎝           ⎠

4 ↦ ⎛           ⎞
    ⎜ 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 ⎟
    ⎝           ⎠

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3 },
it remains to prove termination of the 7-rule system
{ 0 1 2 2 ⟶ 0 1 1 1 ,
  0 1 2 2 ⟶ 0 1 1 ,
  0 1 2 2 ⟶ 0 1 ,
  0 1 2 2 ⟶ 0 ,
  3 3 1 1 →= 1 1 2 2 3 3 ,
  1 1 2 2 →= 2 2 1 1 1 1 ,
  1 1 3 3 →= 3 3 2 2 1 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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 ⎟
    ⎝           ⎠

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

2 ↦ ⎛           ⎞
    ⎜ 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 ⎟
    ⎝           ⎠

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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

3 ↦ ⎛           ⎞
    ⎜ 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 ⎟
    ⎝           ⎠

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

The system is trivially terminating.