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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

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

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

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

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

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

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

The system is trivially terminating.