/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, c ↦ 1 },
it remains to prove termination of the 3-rule system
{ 0 0 0 ⟶ 0 1 0 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, (0,3) ↦ 3, (2,0) ↦ 4, (1,1) ↦ 5, (1,3) ↦ 6, (2,1) ↦ 7, (2,3) ↦ 8 },
it remains to prove termination of the 27-rule system
{ 0 0 0 0 ⟶ 0 1 2 0 0 ,
  0 0 0 1 ⟶ 0 1 2 0 1 ,
  0 0 0 3 ⟶ 0 1 2 0 3 ,
  2 0 0 0 ⟶ 2 1 2 0 0 ,
  2 0 0 1 ⟶ 2 1 2 0 1 ,
  2 0 0 3 ⟶ 2 1 2 0 3 ,
  4 0 0 0 ⟶ 4 1 2 0 0 ,
  4 0 0 1 ⟶ 4 1 2 0 1 ,
  4 0 0 3 ⟶ 4 1 2 0 3 ,
  1 5 5 2 ⟶ 0 0 ,
  1 5 5 5 ⟶ 0 1 ,
  1 5 5 6 ⟶ 0 3 ,
  5 5 5 2 ⟶ 2 0 ,
  5 5 5 5 ⟶ 2 1 ,
  5 5 5 6 ⟶ 2 3 ,
  7 5 5 2 ⟶ 4 0 ,
  7 5 5 5 ⟶ 4 1 ,
  7 5 5 6 ⟶ 4 3 ,
  0 0 ⟶ 0 ,
  0 1 ⟶ 1 ,
  0 3 ⟶ 3 ,
  2 0 ⟶ 2 ,
  2 1 ⟶ 5 ,
  2 3 ⟶ 6 ,
  4 0 ⟶ 4 ,
  4 1 ⟶ 7 ,
  4 3 ⟶ 8 }

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 5 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

5 ↦ ⎛     ⎞
    ⎜ 1 4 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

The system is trivially terminating.