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

The system was reversed.

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

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, (0,3) ↦ 4, (1,3) ↦ 5, (2,0) ↦ 6, (2,1) ↦ 7 },
it remains to prove termination of the 27-rule system
{ 0 0 0 0 ⟶ 1 2 ,
  0 0 0 1 ⟶ 1 3 ,
  0 0 0 4 ⟶ 1 5 ,
  2 0 0 0 ⟶ 3 2 ,
  2 0 0 1 ⟶ 3 3 ,
  2 0 0 4 ⟶ 3 5 ,
  6 0 0 0 ⟶ 7 2 ,
  6 0 0 1 ⟶ 7 3 ,
  6 0 0 4 ⟶ 7 5 ,
  1 3 2 ⟶ 1 2 1 2 ,
  1 3 3 ⟶ 1 2 1 3 ,
  1 3 5 ⟶ 1 2 1 5 ,
  3 3 2 ⟶ 3 2 1 2 ,
  3 3 3 ⟶ 3 2 1 3 ,
  3 3 5 ⟶ 3 2 1 5 ,
  7 3 2 ⟶ 7 2 1 2 ,
  7 3 3 ⟶ 7 2 1 3 ,
  7 3 5 ⟶ 7 2 1 5 ,
  1 3 2 ⟶ 0 0 0 ,
  1 3 3 ⟶ 0 0 1 ,
  1 3 5 ⟶ 0 0 4 ,
  3 3 2 ⟶ 2 0 0 ,
  3 3 3 ⟶ 2 0 1 ,
  3 3 5 ⟶ 2 0 4 ,
  7 3 2 ⟶ 6 0 0 ,
  7 3 3 ⟶ 6 0 1 ,
  7 3 5 ⟶ 6 0 4 }

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

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

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

2 ↦ ⎛     ⎞
    ⎜ 1 6 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛       ⎞
    ⎜  1 10 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

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

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

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

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

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

The system is trivially terminating.