/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, c ↦ 3, A ↦ 4, B ↦ 5 },
it remains to prove termination of the 24-rule system
{ 0 1 ⟶ 2 ,
  1 3 ⟶ 4 ,
  3 0 ⟶ 5 ,
  4 2 ⟶ 1 ,
  2 5 ⟶ 0 ,
  5 4 ⟶ 3 ,
  0 0 0 0 ⟶ 4 4 4 ,
  4 4 4 4 ⟶ 0 0 0 ,
  1 1 1 1 ⟶ 5 5 5 ,
  5 5 5 5 ⟶ 1 1 1 ,
  3 3 3 3 ⟶ 2 2 2 ,
  2 2 2 2 ⟶ 3 3 3 ,
  5 0 0 0 ⟶ 3 4 4 4 ,
  4 4 4 1 ⟶ 0 0 0 2 ,
  2 1 1 1 ⟶ 0 5 5 5 ,
  5 5 5 3 ⟶ 1 1 1 4 ,
  4 3 3 3 ⟶ 1 2 2 2 ,
  2 2 2 0 ⟶ 3 3 3 5 ,
  0 4 ⟶ ,
  4 0 ⟶ ,
  1 5 ⟶ ,
  5 1 ⟶ ,
  3 2 ⟶ ,
  2 3 ⟶ }

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 { 5 ↦ 0, 0 ↦ 1, 3 ↦ 2, 4 ↦ 3, 1 ↦ 4, 2 ↦ 5 },
it remains to prove termination of the 6-rule system
{ 0 1 1 1 ⟶ 2 3 3 3 ,
  3 3 3 4 ⟶ 1 1 1 5 ,
  5 4 4 4 ⟶ 1 0 0 0 ,
  0 0 0 2 ⟶ 4 4 4 3 ,
  3 2 2 2 ⟶ 4 5 5 5 ,
  5 5 5 1 ⟶ 2 2 2 0 }

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

After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (3,↑) ↦ 2, (3,↓) ↦ 3, (4,↓) ↦ 4, (5,↑) ↦ 5, (0,↓) ↦ 6, (2,↓) ↦ 7, (5,↓) ↦ 8 },
it remains to prove termination of the 18-rule system
{ 0 1 1 1 ⟶ 2 3 3 ,
  0 1 1 1 ⟶ 2 3 ,
  0 1 1 1 ⟶ 2 ,
  2 3 3 4 ⟶ 5 ,
  5 4 4 4 ⟶ 0 6 6 ,
  5 4 4 4 ⟶ 0 6 ,
  5 4 4 4 ⟶ 0 ,
  0 6 6 7 ⟶ 2 ,
  2 7 7 7 ⟶ 5 8 8 ,
  2 7 7 7 ⟶ 5 8 ,
  2 7 7 7 ⟶ 5 ,
  5 8 8 1 ⟶ 0 ,
  6 1 1 1 →= 7 3 3 3 ,
  3 3 3 4 →= 1 1 1 8 ,
  8 4 4 4 →= 1 6 6 6 ,
  6 6 6 7 →= 4 4 4 3 ,
  3 7 7 7 →= 4 8 8 8 ,
  8 8 8 1 →= 7 7 7 6 }

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 ⎟
    ⎝     ⎠

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

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

8 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 6 ↦ 0, 1 ↦ 1, 7 ↦ 2, 3 ↦ 3, 4 ↦ 4, 8 ↦ 5 },
it remains to prove termination of the 6-rule system
{ 0 1 1 1 →= 2 3 3 3 ,
  3 3 3 4 →= 1 1 1 5 ,
  5 4 4 4 →= 1 0 0 0 ,
  0 0 0 2 →= 4 4 4 3 ,
  3 2 2 2 →= 4 5 5 5 ,
  5 5 5 1 →= 2 2 2 0 }

The system is trivially terminating.