/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 { q0 ↦ 0, 0 ↦ 1, 0' ↦ 2, q1 ↦ 3, 1' ↦ 4, 1 ↦ 5, q2 ↦ 6, q3 ↦ 7, b ↦ 8, q4 ↦ 9 },
it remains to prove termination of the 16-rule system
{ 0 1 ⟶ 2 3 ,
  3 1 ⟶ 1 3 ,
  3 4 ⟶ 4 3 ,
  1 3 5 ⟶ 6 1 4 ,
  2 3 5 ⟶ 6 2 4 ,
  4 3 5 ⟶ 6 4 4 ,
  1 6 1 ⟶ 6 1 1 ,
  2 6 1 ⟶ 6 2 1 ,
  4 6 1 ⟶ 6 4 1 ,
  1 6 4 ⟶ 6 1 4 ,
  2 6 4 ⟶ 6 2 4 ,
  4 6 4 ⟶ 6 4 4 ,
  6 2 ⟶ 2 0 ,
  0 4 ⟶ 4 7 ,
  7 4 ⟶ 4 7 ,
  7 8 ⟶ 8 9 }

The system was reversed.

After renaming modulo the bijection { 1 ↦ 0, 0 ↦ 1, 3 ↦ 2, 2 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9 },
it remains to prove termination of the 16-rule system
{ 0 1 ⟶ 2 3 ,
  0 2 ⟶ 2 0 ,
  4 2 ⟶ 2 4 ,
  5 2 0 ⟶ 4 0 6 ,
  5 2 3 ⟶ 4 3 6 ,
  5 2 4 ⟶ 4 4 6 ,
  0 6 0 ⟶ 0 0 6 ,
  0 6 3 ⟶ 0 3 6 ,
  0 6 4 ⟶ 0 4 6 ,
  4 6 0 ⟶ 4 0 6 ,
  4 6 3 ⟶ 4 3 6 ,
  4 6 4 ⟶ 4 4 6 ,
  3 6 ⟶ 1 3 ,
  4 1 ⟶ 7 4 ,
  4 7 ⟶ 7 4 ,
  8 7 ⟶ 9 8 }

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

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

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

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

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

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

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

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

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

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

9 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 2 ↦ 1, 4 ↦ 2, 6 ↦ 3, 3 ↦ 4, 1 ↦ 5, 7 ↦ 6 },
it remains to prove termination of the 11-rule system
{ 0 1 ⟶ 1 0 ,
  2 1 ⟶ 1 2 ,
  0 3 0 ⟶ 0 0 3 ,
  0 3 4 ⟶ 0 4 3 ,
  0 3 2 ⟶ 0 2 3 ,
  2 3 0 ⟶ 2 0 3 ,
  2 3 4 ⟶ 2 4 3 ,
  2 3 2 ⟶ 2 2 3 ,
  4 3 ⟶ 5 4 ,
  2 5 ⟶ 6 2 ,
  2 6 ⟶ 6 2 }

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

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

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

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

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

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6 },
it remains to prove termination of the 10-rule system
{ 0 1 ⟶ 1 0 ,
  2 1 ⟶ 1 2 ,
  0 3 0 ⟶ 0 0 3 ,
  0 3 4 ⟶ 0 4 3 ,
  0 3 2 ⟶ 0 2 3 ,
  2 3 0 ⟶ 2 0 3 ,
  2 3 4 ⟶ 2 4 3 ,
  2 3 2 ⟶ 2 2 3 ,
  4 3 ⟶ 5 4 ,
  2 6 ⟶ 6 2 }

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

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

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

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

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

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

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

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 6 ↦ 5 },
it remains to prove termination of the 9-rule system
{ 0 1 ⟶ 1 0 ,
  2 1 ⟶ 1 2 ,
  0 3 0 ⟶ 0 0 3 ,
  0 3 4 ⟶ 0 4 3 ,
  0 3 2 ⟶ 0 2 3 ,
  2 3 0 ⟶ 2 0 3 ,
  2 3 4 ⟶ 2 4 3 ,
  2 3 2 ⟶ 2 2 3 ,
  2 5 ⟶ 5 2 }

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

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 5 ↦ 3 },
it remains to prove termination of the 3-rule system
{ 0 1 ⟶ 1 0 ,
  2 1 ⟶ 1 2 ,
  2 3 ⟶ 3 2 }

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

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

The system is trivially terminating.