/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 { f ↦ 0, b ↦ 1, a ↦ 2, c ↦ 3, d ↦ 4 },
it remains to prove termination of the 7-rule system
{ 0 0 ⟶ 1 1 1 ,
  2 0 ⟶ 0 2 2 ,
  1 1 ⟶ 3 3 2 3 ,
  4 1 ⟶ 4 2 1 ,
  3 3 ⟶ 4 4 4 ,
  1 4 ⟶ 4 1 ,
  3 4 4 ⟶ 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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛       ⎞
    ⎜  1 35 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

4 ↦ ⎛       ⎞
    ⎜  1 23 ⎟
    ⎜  0  1 ⎟
    ⎝       ⎠

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

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

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

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

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

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

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

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

The system is trivially terminating.