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

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

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

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

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

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

2 ↦ ⎛     ⎞
    ⎜ 1 7 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

The system is trivially terminating.