/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, s ↦ 1, b ↦ 2, c ↦ 3 },
it remains to prove termination of the 5-rule system
{ 0 1 ⟶ 1 0 ,
  2 0 2 1 ⟶ 0 2 1 0 ,
  2 0 2 2 ⟶ 3 1 ,
  3 1 ⟶ 0 2 0 2 ,
  0 2 0 0 ⟶ 2 0 2 0 }

The system was reversed.

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

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

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

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 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

4 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

6 ↦ ⎛     ⎞
    ⎜ 1 7 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 5 ↦ 0, 4 ↦ 1, 1 ↦ 2, 0 ↦ 3, 6 ↦ 4, 2 ↦ 5, 3 ↦ 6 },
it remains to prove termination of the 8-rule system
{ 0 1 2 1 ⟶ 3 4 ,
  3 4 ⟶ 0 2 1 2 ,
  5 2 1 2 ⟶ 5 1 2 1 ,
  6 2 →= 2 6 ,
  6 1 2 1 →= 2 6 1 2 ,
  1 1 2 1 →= 6 4 ,
  6 4 →= 1 2 1 2 ,
  2 2 1 2 →= 2 1 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 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 ⎟
    ⎝               ⎠

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

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

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

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

6 ↦ ⎛               ⎞
    ⎜ 1 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 1 ⎟
    ⎜ 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, 4 ↦ 1, 0 ↦ 2, 2 ↦ 3, 1 ↦ 4, 5 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 7-rule system
{ 0 1 ⟶ 2 3 4 3 ,
  5 3 4 3 ⟶ 5 4 3 4 ,
  6 3 →= 3 6 ,
  6 4 3 4 →= 3 6 4 3 ,
  4 4 3 4 →= 6 1 ,
  6 1 →= 4 3 4 3 ,
  3 3 4 3 →= 3 4 3 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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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 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 1 1 ⎟
    ⎝               ⎠

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

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

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

The system is trivially terminating.