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

Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,0) ↦ 2, (1,1) ↦ 3, (2,0) ↦ 4, (2,1) ↦ 5, (1,3) ↦ 6 },
it remains to prove termination of the 24-rule system
{ 0 0 0 0 ⟶ 1 2 ,
  0 0 0 1 ⟶ 1 3 ,
  2 0 0 0 ⟶ 3 2 ,
  2 0 0 1 ⟶ 3 3 ,
  4 0 0 0 ⟶ 5 2 ,
  4 0 0 1 ⟶ 5 3 ,
  1 3 2 ⟶ 1 2 1 2 ,
  1 3 3 ⟶ 1 2 1 3 ,
  1 3 6 ⟶ 1 2 1 6 ,
  3 3 2 ⟶ 3 2 1 2 ,
  3 3 3 ⟶ 3 2 1 3 ,
  3 3 6 ⟶ 3 2 1 6 ,
  5 3 2 ⟶ 5 2 1 2 ,
  5 3 3 ⟶ 5 2 1 3 ,
  5 3 6 ⟶ 5 2 1 6 ,
  1 3 3 2 ⟶ 0 1 3 2 ,
  1 3 3 3 ⟶ 0 1 3 3 ,
  1 3 3 6 ⟶ 0 1 3 6 ,
  3 3 3 2 ⟶ 2 1 3 2 ,
  3 3 3 3 ⟶ 2 1 3 3 ,
  3 3 3 6 ⟶ 2 1 3 6 ,
  5 3 3 2 ⟶ 4 1 3 2 ,
  5 3 3 3 ⟶ 4 1 3 3 ,
  5 3 3 6 ⟶ 4 1 3 6 }

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

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

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

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

3 ↦ ⎛     ⎞
    ⎜ 1 4 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

The system is trivially terminating.