/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, q0 ↦ 1, 0 ↦ 2, q1 ↦ 3, q2 ↦ 4 },
it remains to prove termination of the 7-rule system
{ 0 1 0 ⟶ 2 0 3 ,
  0 1 2 ⟶ 2 2 3 ,
  0 3 0 ⟶ 0 0 3 ,
  0 3 2 ⟶ 0 2 3 ,
  2 3 ⟶ 4 0 ,
  0 4 ⟶ 4 0 ,
  2 4 ⟶ 2 1 }

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

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

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

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

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

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

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.