/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 { a ↦ 0, b ↦ 1, c ↦ 2, d ↦ 3, e ↦ 4 },
it remains to prove termination of the 8-rule system
{ 0 0 ⟶ 1 1 1 ,
  0 ⟶ 2 3 ,
  1 1 ⟶ 2 2 2 ,
  2 2 ⟶ 3 3 3 ,
  4 3 ⟶ 0 1 2 3 4 ,
  1 ⟶ 3 3 ,
  4 2 ⟶ 1 0 0 4 ,
  2 3 3 ⟶ 0 }

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

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

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

0 ↦ ⎛       ⎞
    ⎜  1 80 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

1 ↦ ⎛       ⎞
    ⎜  1 53 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

2 ↦ ⎛       ⎞
    ⎜  1 35 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

3 ↦ ⎛       ⎞
    ⎜  1 23 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

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

The system is trivially terminating.