/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 4-rule system
{ 0 ⟶ ,
  0 1 ⟶ 1 0 2 ,
  1 ⟶ ,
  2 2 ⟶ 1 1 0 }

The system was reversed.

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

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

After renaming modulo the bijection { (1,↑) ↦ 0, (0,↓) ↦ 1, (2,↑) ↦ 2, (1,↓) ↦ 3, (0,↑) ↦ 4, (2,↓) ↦ 5 },
it remains to prove termination of the 10-rule system
{ 0 1 ⟶ 2 1 3 ,
  0 1 ⟶ 4 3 ,
  0 1 ⟶ 0 ,
  2 5 ⟶ 4 3 3 ,
  2 5 ⟶ 0 3 ,
  2 5 ⟶ 0 ,
  1 →= ,
  3 1 →= 5 1 3 ,
  3 →= ,
  5 5 →= 1 3 3 }

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 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

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

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

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

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

After renaming modulo the bijection { (5,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (5,2) ↦ 3, (2,1) ↦ 4, (1,3) ↦ 5, (3,1) ↦ 6, (3,3) ↦ 7, (1,4) ↦ 8, (3,4) ↦ 9, (1,6) ↦ 10, (3,6) ↦ 11, (0,3) ↦ 12, (0,4) ↦ 13, (0,6) ↦ 14, (2,4) ↦ 15, (4,1) ↦ 16, (4,3) ↦ 17, (4,4) ↦ 18, (4,6) ↦ 19, (2,3) ↦ 20, (2,6) ↦ 21, (5,1) ↦ 22, (5,3) ↦ 23, (5,4) ↦ 24, (5,6) ↦ 25 },
it remains to prove termination of the 112-rule system
{ 0 1 2 ⟶ 3 4 5 6 ,
  0 1 5 ⟶ 3 4 5 7 ,
  0 1 8 ⟶ 3 4 5 9 ,
  0 1 10 ⟶ 3 4 5 11 ,
  0 1 2 ⟶ 0 1 ,
  0 1 5 ⟶ 0 12 ,
  0 1 8 ⟶ 0 13 ,
  0 1 10 ⟶ 0 14 ,
  3 15 16 ⟶ 0 12 6 ,
  3 15 17 ⟶ 0 12 7 ,
  3 15 18 ⟶ 0 12 9 ,
  3 15 19 ⟶ 0 12 11 ,
  3 15 16 ⟶ 0 1 ,
  3 15 17 ⟶ 0 12 ,
  3 15 18 ⟶ 0 13 ,
  3 15 19 ⟶ 0 14 ,
  1 2 →= 1 ,
  1 5 →= 12 ,
  1 8 →= 13 ,
  1 10 →= 14 ,
  2 2 →= 2 ,
  2 5 →= 5 ,
  2 8 →= 8 ,
  2 10 →= 10 ,
  4 2 →= 4 ,
  4 5 →= 20 ,
  4 8 →= 15 ,
  4 10 →= 21 ,
  6 2 →= 6 ,
  6 5 →= 7 ,
  6 8 →= 9 ,
  6 10 →= 11 ,
  16 2 →= 16 ,
  16 5 →= 17 ,
  16 8 →= 18 ,
  16 10 →= 19 ,
  22 2 →= 22 ,
  22 5 →= 23 ,
  22 8 →= 24 ,
  22 10 →= 25 ,
  12 6 2 →= 13 16 5 6 ,
  12 6 5 →= 13 16 5 7 ,
  12 6 8 →= 13 16 5 9 ,
  12 6 10 →= 13 16 5 11 ,
  5 6 2 →= 8 16 5 6 ,
  5 6 5 →= 8 16 5 7 ,
  5 6 8 →= 8 16 5 9 ,
  5 6 10 →= 8 16 5 11 ,
  20 6 2 →= 15 16 5 6 ,
  20 6 5 →= 15 16 5 7 ,
  20 6 8 →= 15 16 5 9 ,
  20 6 10 →= 15 16 5 11 ,
  7 6 2 →= 9 16 5 6 ,
  7 6 5 →= 9 16 5 7 ,
  7 6 8 →= 9 16 5 9 ,
  7 6 10 →= 9 16 5 11 ,
  17 6 2 →= 18 16 5 6 ,
  17 6 5 →= 18 16 5 7 ,
  17 6 8 →= 18 16 5 9 ,
  17 6 10 →= 18 16 5 11 ,
  23 6 2 →= 24 16 5 6 ,
  23 6 5 →= 24 16 5 7 ,
  23 6 8 →= 24 16 5 9 ,
  23 6 10 →= 24 16 5 11 ,
  12 6 →= 1 ,
  12 7 →= 12 ,
  12 9 →= 13 ,
  12 11 →= 14 ,
  5 6 →= 2 ,
  5 7 →= 5 ,
  5 9 →= 8 ,
  5 11 →= 10 ,
  20 6 →= 4 ,
  20 7 →= 20 ,
  20 9 →= 15 ,
  20 11 →= 21 ,
  7 6 →= 6 ,
  7 7 →= 7 ,
  7 9 →= 9 ,
  7 11 →= 11 ,
  17 6 →= 16 ,
  17 7 →= 17 ,
  17 9 →= 18 ,
  17 11 →= 19 ,
  23 6 →= 22 ,
  23 7 →= 23 ,
  23 9 →= 24 ,
  23 11 →= 25 ,
  13 18 16 →= 1 5 7 6 ,
  13 18 17 →= 1 5 7 7 ,
  13 18 18 →= 1 5 7 9 ,
  13 18 19 →= 1 5 7 11 ,
  8 18 16 →= 2 5 7 6 ,
  8 18 17 →= 2 5 7 7 ,
  8 18 18 →= 2 5 7 9 ,
  8 18 19 →= 2 5 7 11 ,
  15 18 16 →= 4 5 7 6 ,
  15 18 17 →= 4 5 7 7 ,
  15 18 18 →= 4 5 7 9 ,
  15 18 19 →= 4 5 7 11 ,
  9 18 16 →= 6 5 7 6 ,
  9 18 17 →= 6 5 7 7 ,
  9 18 18 →= 6 5 7 9 ,
  9 18 19 →= 6 5 7 11 ,
  18 18 16 →= 16 5 7 6 ,
  18 18 17 →= 16 5 7 7 ,
  18 18 18 →= 16 5 7 9 ,
  18 18 19 →= 16 5 7 11 ,
  24 18 16 →= 22 5 7 6 ,
  24 18 17 →= 22 5 7 7 ,
  24 18 18 →= 22 5 7 9 ,
  24 18 19 →= 22 5 7 11 }

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 6 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

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

5 ↦ ⎛     ⎞
    ⎜ 1 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

8 ↦ ⎛     ⎞
    ⎜ 1 4 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

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

10 ↦ ⎛     ⎞
     ⎜ 1 4 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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

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

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

15 ↦ ⎛     ⎞
     ⎜ 1 2 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

16 ↦ ⎛     ⎞
     ⎜ 1 2 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

17 ↦ ⎛     ⎞
     ⎜ 1 5 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

18 ↦ ⎛     ⎞
     ⎜ 1 6 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

20 ↦ ⎛     ⎞
     ⎜ 1 2 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

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

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

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

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

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

After renaming modulo the bijection { 16 ↦ 0, 5 ↦ 1, 17 ↦ 2, 8 ↦ 3, 18 ↦ 4, 6 ↦ 5, 2 ↦ 6, 7 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 20 ↦ 12, 23 ↦ 13 },
it remains to prove termination of the 29-rule system
{ 0 1 →= 2 ,
  0 3 →= 4 ,
  1 5 6 →= 3 0 1 5 ,
  1 5 1 →= 3 0 1 7 ,
  1 5 3 →= 3 0 1 8 ,
  1 5 9 →= 3 0 1 10 ,
  7 5 6 →= 8 0 1 5 ,
  7 5 1 →= 8 0 1 7 ,
  7 5 3 →= 8 0 1 8 ,
  7 5 9 →= 8 0 1 10 ,
  2 5 6 →= 4 0 1 5 ,
  2 5 1 →= 4 0 1 7 ,
  2 5 3 →= 4 0 1 8 ,
  2 5 9 →= 4 0 1 10 ,
  11 7 →= 11 ,
  1 5 →= 6 ,
  1 7 →= 1 ,
  1 8 →= 3 ,
  1 10 →= 9 ,
  12 7 →= 12 ,
  7 5 →= 5 ,
  7 7 →= 7 ,
  7 8 →= 8 ,
  7 10 →= 10 ,
  2 7 →= 2 ,
  2 8 →= 4 ,
  13 7 →= 13 ,
  3 4 0 →= 6 1 7 5 ,
  8 4 0 →= 5 1 7 5 }

The system is trivially terminating.