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

The system was reversed.

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

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

0 ↦ ⎛       ⎞
    ⎜  1 25 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

1 ↦ ⎛       ⎞
    ⎜  1 11 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

2 ↦ ⎛       ⎞
    ⎜  1 17 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 7 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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, (3,↑) ↦ 5, (3,↓) ↦ 6 },
it remains to prove termination of the 15-rule system
{ 0 1 ⟶ 2 3 3 4 ,
  0 1 ⟶ 2 3 4 ,
  0 1 ⟶ 2 4 ,
  2 4 ⟶ 5 6 6 6 ,
  2 4 ⟶ 5 6 6 ,
  2 4 ⟶ 5 6 ,
  2 4 ⟶ 5 ,
  0 ⟶ 5 3 6 ,
  0 ⟶ 2 6 ,
  0 ⟶ 5 ,
  5 6 3 ⟶ 0 ,
  1 1 →= 3 3 3 4 ,
  3 4 →= 6 6 6 6 ,
  1 →= 6 3 6 ,
  6 6 3 →= 1 }

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

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

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

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

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

4 ↦ ⎛     ⎞
    ⎜ 1 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

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

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

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

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

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

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

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

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

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 1 0 0 ⎟
    ⎜ 0 1 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 1 0 0 0 ⎟
    ⎜ 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 ⎟
    ⎝           ⎠

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

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

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

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

The system is trivially terminating.