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

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

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

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

3 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 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 ⟶ 3 1 ,
  3 1 1 ⟶ 0 1 1 2 ,
  3 1 1 ⟶ 0 1 2 ,
  3 1 1 ⟶ 0 2 ,
  3 1 1 ⟶ 3 ,
  1 1 2 →= 2 1 ,
  2 1 1 →= 1 1 1 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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

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

3 ↦ ⎛         ⎞
    ⎜ 2 0 0 0 ⎟
    ⎜ 0 1 0 0 ⎟
    ⎜ 0 0 0 0 ⎟
    ⎜ 0 0 0 0 ⎟
    ⎝         ⎠

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

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

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

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

The system is trivially terminating.