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


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YES

After renaming modulo the bijection { 1 ↦ 0, 4 ↦ 1, 3 ↦ 2, 2 ↦ 3, 5 ↦ 4, 6 ↦ 5 },
it remains to prove termination of the 9-rule system
{ 0 0 ⟶ 1 2 ,
  0 3 ⟶ 3 0 ,
  3 3 ⟶ 0 0 0 ,
  2 2 ⟶ 4 5 ,
  2 1 ⟶ 0 0 ,
  1 1 ⟶ 2 ,
  4 4 ⟶ 5 3 ,
  4 5 ⟶ 0 3 ,
  5 5 ⟶ 3 0 }

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

0 ↦ ⎛       ⎞
    ⎜  1 85 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

1 ↦ ⎛       ⎞
    ⎜  1 57 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

2 ↦ ⎛         ⎞
    ⎜   1 113 ⎟
    ⎜   0   1 ⎟
    ⎝         ⎠

3 ↦ ⎛         ⎞
    ⎜   1 128 ⎟
    ⎜   0   1 ⎟
    ⎝         ⎠

4 ↦ ⎛         ⎞
    ⎜   1 118 ⎟
    ⎜   0   1 ⎟
    ⎝         ⎠

5 ↦ ⎛         ⎞
    ⎜   1 107 ⎟
    ⎜   0   1 ⎟
    ⎝         ⎠

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

Applying sparse untiling TRFCU(2) after reversal [Geser/Hofbauer/Waldmann, FSCD 2019].

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

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

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

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

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

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

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

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

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

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

The system is trivially terminating.