/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 { 1 ↦ 0, 4 ↦ 1, 3 ↦ 2, 2 ↦ 3, 5 ↦ 4, 0 ↦ 5 },
it remains to prove termination of the 19-rule system
{ 0 1 ⟶ 2 0 0 3 3 1 ,
  4 1 ⟶ 1 3 2 0 0 0 ,
  5 2 5 ⟶ 3 0 0 5 3 5 ,
  5 4 4 ⟶ 0 5 0 2 1 3 ,
  0 4 1 ⟶ 5 3 4 3 5 1 ,
  2 4 1 ⟶ 1 0 2 1 3 2 ,
  1 0 1 ⟶ 2 2 3 3 2 0 ,
  4 1 5 ⟶ 3 1 5 1 1 5 ,
  4 1 5 ⟶ 4 0 4 3 0 5 ,
  4 1 1 ⟶ 1 0 0 2 3 1 ,
  4 4 1 ⟶ 2 1 1 0 3 3 ,
  5 4 4 5 ⟶ 5 3 5 5 2 5 ,
  5 4 4 1 ⟶ 5 0 2 1 2 1 ,
  0 1 4 1 ⟶ 5 1 4 5 3 0 ,
  0 1 4 4 ⟶ 5 5 0 2 1 0 ,
  3 4 1 5 ⟶ 5 1 0 3 1 5 ,
  1 2 5 4 ⟶ 2 2 3 2 4 4 ,
  4 1 5 5 ⟶ 0 5 1 5 3 3 ,
  4 1 5 3 ⟶ 2 5 1 4 5 3 }

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

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

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 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

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

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

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

The system is trivially terminating.