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

The system was reversed.

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

Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols.

After renaming modulo the bijection { (0,↑) ↦ 0, (0,↓) ↦ 1, (1,↓) ↦ 2, (2,↓) ↦ 3, (2,↑) ↦ 4 },
it remains to prove termination of the 8-rule system
{ 0 1 ⟶ 0 2 3 1 ,
  0 1 ⟶ 4 1 ,
  4 2 ⟶ 0 3 1 ,
  4 2 ⟶ 4 1 ,
  4 2 ⟶ 0 ,
  1 →= ,
  1 1 →= 1 2 3 1 ,
  3 2 →= 1 3 1 }

Applying sparse tiling TROC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo the bijection { (5,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (0,2) ↦ 3, (2,3) ↦ 4, (3,1) ↦ 5, (1,2) ↦ 6, (1,3) ↦ 7, (1,6) ↦ 8, (5,4) ↦ 9, (4,1) ↦ 10, (4,2) ↦ 11, (2,1) ↦ 12, (0,3) ↦ 13, (2,2) ↦ 14, (2,6) ↦ 15, (0,6) ↦ 16, (3,2) ↦ 17, (3,3) ↦ 18, (3,6) ↦ 19, (4,3) ↦ 20, (4,6) ↦ 21, (5,1) ↦ 22, (5,2) ↦ 23, (5,3) ↦ 24, (5,6) ↦ 25 },
it remains to prove termination of the 92-rule system
{ 0 1 2 ⟶ 0 3 4 5 2 ,
  0 1 6 ⟶ 0 3 4 5 6 ,
  0 1 7 ⟶ 0 3 4 5 7 ,
  0 1 8 ⟶ 0 3 4 5 8 ,
  0 1 2 ⟶ 9 10 2 ,
  0 1 6 ⟶ 9 10 6 ,
  0 1 7 ⟶ 9 10 7 ,
  0 1 8 ⟶ 9 10 8 ,
  9 11 12 ⟶ 0 13 5 2 ,
  9 11 14 ⟶ 0 13 5 6 ,
  9 11 4 ⟶ 0 13 5 7 ,
  9 11 15 ⟶ 0 13 5 8 ,
  9 11 12 ⟶ 9 10 2 ,
  9 11 14 ⟶ 9 10 6 ,
  9 11 4 ⟶ 9 10 7 ,
  9 11 15 ⟶ 9 10 8 ,
  9 11 12 ⟶ 0 1 ,
  9 11 14 ⟶ 0 3 ,
  9 11 4 ⟶ 0 13 ,
  9 11 15 ⟶ 0 16 ,
  1 2 →= 1 ,
  1 6 →= 3 ,
  1 7 →= 13 ,
  1 8 →= 16 ,
  2 2 →= 2 ,
  2 6 →= 6 ,
  2 7 →= 7 ,
  2 8 →= 8 ,
  12 2 →= 12 ,
  12 6 →= 14 ,
  12 7 →= 4 ,
  12 8 →= 15 ,
  5 2 →= 5 ,
  5 6 →= 17 ,
  5 7 →= 18 ,
  5 8 →= 19 ,
  10 2 →= 10 ,
  10 6 →= 11 ,
  10 7 →= 20 ,
  10 8 →= 21 ,
  22 2 →= 22 ,
  22 6 →= 23 ,
  22 7 →= 24 ,
  22 8 →= 25 ,
  1 2 2 →= 1 6 4 5 2 ,
  1 2 6 →= 1 6 4 5 6 ,
  1 2 7 →= 1 6 4 5 7 ,
  1 2 8 →= 1 6 4 5 8 ,
  2 2 2 →= 2 6 4 5 2 ,
  2 2 6 →= 2 6 4 5 6 ,
  2 2 7 →= 2 6 4 5 7 ,
  2 2 8 →= 2 6 4 5 8 ,
  12 2 2 →= 12 6 4 5 2 ,
  12 2 6 →= 12 6 4 5 6 ,
  12 2 7 →= 12 6 4 5 7 ,
  12 2 8 →= 12 6 4 5 8 ,
  5 2 2 →= 5 6 4 5 2 ,
  5 2 6 →= 5 6 4 5 6 ,
  5 2 7 →= 5 6 4 5 7 ,
  5 2 8 →= 5 6 4 5 8 ,
  10 2 2 →= 10 6 4 5 2 ,
  10 2 6 →= 10 6 4 5 6 ,
  10 2 7 →= 10 6 4 5 7 ,
  10 2 8 →= 10 6 4 5 8 ,
  22 2 2 →= 22 6 4 5 2 ,
  22 2 6 →= 22 6 4 5 6 ,
  22 2 7 →= 22 6 4 5 7 ,
  22 2 8 →= 22 6 4 5 8 ,
  13 17 12 →= 1 7 5 2 ,
  13 17 14 →= 1 7 5 6 ,
  13 17 4 →= 1 7 5 7 ,
  13 17 15 →= 1 7 5 8 ,
  7 17 12 →= 2 7 5 2 ,
  7 17 14 →= 2 7 5 6 ,
  7 17 4 →= 2 7 5 7 ,
  7 17 15 →= 2 7 5 8 ,
  4 17 12 →= 12 7 5 2 ,
  4 17 14 →= 12 7 5 6 ,
  4 17 4 →= 12 7 5 7 ,
  4 17 15 →= 12 7 5 8 ,
  18 17 12 →= 5 7 5 2 ,
  18 17 14 →= 5 7 5 6 ,
  18 17 4 →= 5 7 5 7 ,
  18 17 15 →= 5 7 5 8 ,
  20 17 12 →= 10 7 5 2 ,
  20 17 14 →= 10 7 5 6 ,
  20 17 4 →= 10 7 5 7 ,
  20 17 15 →= 10 7 5 8 ,
  24 17 12 →= 22 7 5 2 ,
  24 17 14 →= 22 7 5 6 ,
  24 17 4 →= 22 7 5 7 ,
  24 17 15 →= 22 7 5 8 }

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 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

4 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

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

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

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

12 ↦ ⎛     ⎞
     ⎜ 1 4 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

13 ↦ ⎛     ⎞
     ⎜ 1 2 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

14 ↦ ⎛     ⎞
     ⎜ 1 3 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

15 ↦ ⎛     ⎞
     ⎜ 1 4 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

16 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

17 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

18 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

19 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

20 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

21 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

22 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

24 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

25 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 5 ↦ 0, 6 ↦ 1, 17 ↦ 2, 7 ↦ 3, 18 ↦ 4, 1 ↦ 5, 2 ↦ 6, 4 ↦ 7, 8 ↦ 8, 12 ↦ 9, 10 ↦ 10, 22 ↦ 11 },
it remains to prove termination of the 30-rule system
{ 0 1 →= 2 ,
  0 3 →= 4 ,
  5 6 6 →= 5 1 7 0 6 ,
  5 6 1 →= 5 1 7 0 1 ,
  5 6 3 →= 5 1 7 0 3 ,
  5 6 8 →= 5 1 7 0 8 ,
  6 6 6 →= 6 1 7 0 6 ,
  6 6 1 →= 6 1 7 0 1 ,
  6 6 3 →= 6 1 7 0 3 ,
  6 6 8 →= 6 1 7 0 8 ,
  9 6 6 →= 9 1 7 0 6 ,
  9 6 1 →= 9 1 7 0 1 ,
  9 6 3 →= 9 1 7 0 3 ,
  9 6 8 →= 9 1 7 0 8 ,
  0 6 6 →= 0 1 7 0 6 ,
  0 6 1 →= 0 1 7 0 1 ,
  0 6 3 →= 0 1 7 0 3 ,
  0 6 8 →= 0 1 7 0 8 ,
  10 6 6 →= 10 1 7 0 6 ,
  10 6 1 →= 10 1 7 0 1 ,
  10 6 3 →= 10 1 7 0 3 ,
  10 6 8 →= 10 1 7 0 8 ,
  11 6 6 →= 11 1 7 0 6 ,
  11 6 1 →= 11 1 7 0 1 ,
  11 6 3 →= 11 1 7 0 3 ,
  11 6 8 →= 11 1 7 0 8 ,
  3 2 9 →= 6 3 0 6 ,
  3 2 7 →= 6 3 0 3 ,
  7 2 9 →= 9 3 0 6 ,
  7 2 7 →= 9 3 0 3 }

The system is trivially terminating.