/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 { a12 ↦ 0, a13 ↦ 1, a14 ↦ 2, a15 ↦ 3, a16 ↦ 4, a23 ↦ 5, a24 ↦ 6, a25 ↦ 7, a26 ↦ 8, a34 ↦ 9, a35 ↦ 10, a36 ↦ 11, a45 ↦ 12, a46 ↦ 13, a56 ↦ 14 },
it remains to prove termination of the 35-rule system
{ 0 0 ⟶ ,
  1 1 ⟶ ,
  2 2 ⟶ ,
  3 3 ⟶ ,
  4 4 ⟶ ,
  5 5 ⟶ ,
  6 6 ⟶ ,
  7 7 ⟶ ,
  8 8 ⟶ ,
  9 9 ⟶ ,
  10 10 ⟶ ,
  11 11 ⟶ ,
  12 12 ⟶ ,
  13 13 ⟶ ,
  14 14 ⟶ ,
  1 ⟶ 0 5 0 ,
  2 ⟶ 0 5 9 5 0 ,
  3 ⟶ 0 5 9 12 9 5 0 ,
  4 ⟶ 0 5 9 12 14 12 9 5 0 ,
  6 ⟶ 5 9 5 ,
  7 ⟶ 5 9 12 9 5 ,
  8 ⟶ 5 9 12 14 12 9 5 ,
  10 ⟶ 9 12 9 ,
  11 ⟶ 9 12 14 12 9 ,
  13 ⟶ 12 14 12 ,
  0 5 0 5 0 5 ⟶ ,
  5 9 5 9 5 9 ⟶ ,
  9 12 9 12 9 12 ⟶ ,
  12 14 12 14 12 14 ⟶ ,
  0 9 ⟶ 9 0 ,
  0 12 ⟶ 12 0 ,
  0 14 ⟶ 14 0 ,
  5 12 ⟶ 12 5 ,
  5 14 ⟶ 14 5 ,
  9 14 ⟶ 14 9 }

The system was reversed.

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14 },
it remains to prove termination of the 35-rule system
{ 0 0 ⟶ ,
  1 1 ⟶ ,
  2 2 ⟶ ,
  3 3 ⟶ ,
  4 4 ⟶ ,
  5 5 ⟶ ,
  6 6 ⟶ ,
  7 7 ⟶ ,
  8 8 ⟶ ,
  9 9 ⟶ ,
  10 10 ⟶ ,
  11 11 ⟶ ,
  12 12 ⟶ ,
  13 13 ⟶ ,
  14 14 ⟶ ,
  1 ⟶ 0 5 0 ,
  2 ⟶ 0 5 9 5 0 ,
  3 ⟶ 0 5 9 12 9 5 0 ,
  4 ⟶ 0 5 9 12 14 12 9 5 0 ,
  6 ⟶ 5 9 5 ,
  7 ⟶ 5 9 12 9 5 ,
  8 ⟶ 5 9 12 14 12 9 5 ,
  10 ⟶ 9 12 9 ,
  11 ⟶ 9 12 14 12 9 ,
  13 ⟶ 12 14 12 ,
  5 0 5 0 5 0 ⟶ ,
  9 5 9 5 9 5 ⟶ ,
  12 9 12 9 12 9 ⟶ ,
  14 12 14 12 14 12 ⟶ ,
  9 0 ⟶ 0 9 ,
  12 0 ⟶ 0 12 ,
  14 0 ⟶ 0 14 ,
  12 5 ⟶ 5 12 ,
  14 5 ⟶ 5 14 ,
  14 9 ⟶ 9 14 }

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 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

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

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

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

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

10 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

11 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

12 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

13 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

14 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 5 ↦ 1, 9 ↦ 2, 12 ↦ 3, 14 ↦ 4 },
it remains to prove termination of the 15-rule system
{ 0 0 ⟶ ,
  1 1 ⟶ ,
  2 2 ⟶ ,
  3 3 ⟶ ,
  4 4 ⟶ ,
  1 0 1 0 1 0 ⟶ ,
  2 1 2 1 2 1 ⟶ ,
  3 2 3 2 3 2 ⟶ ,
  4 3 4 3 4 3 ⟶ ,
  2 0 ⟶ 0 2 ,
  3 0 ⟶ 0 3 ,
  4 0 ⟶ 0 4 ,
  3 1 ⟶ 1 3 ,
  4 1 ⟶ 1 4 ,
  4 2 ⟶ 2 4 }

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 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

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.