/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

After renaming modulo { b->0, c->1, d->2, g->3, f->4, a->5 }, 
it remains to prove termination of the 8-rule system
{ 0 0 -> 1 2 ,
  1 1 -> 2 2 2 ,
  1 -> 3 ,
  2 2 -> 1 4 ,
  2 2 2 -> 3 1 ,
  4 -> 5 3 ,
  3 -> 2 5 0 ,
  3 3 -> 0 1 }


The system was reversed.

After renaming modulo { 0->0, 2->1, 1->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 8-rule system
{ 0 0 -> 1 2 ,
  2 2 -> 1 1 1 ,
  2 -> 3 ,
  1 1 -> 4 2 ,
  1 1 1 -> 2 3 ,
  4 -> 3 5 ,
  3 -> 0 5 1 ,
  3 3 -> 2 0 }


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

After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,0)->3, (2,1)->4, (0,2)->5, (2,2)->6, (0,3)->7, (2,3)->8, (0,4)->9, (2,4)->10, (0,5)->11, (2,5)->12, (0,7)->13, (2,7)->14, (1,0)->15, (1,1)->16, (3,0)->17, (3,1)->18, (4,0)->19, (4,1)->20, (5,0)->21, (5,1)->22, (6,0)->23, (6,1)->24, (1,3)->25, (1,4)->26, (1,5)->27, (1,7)->28, (3,2)->29, (4,2)->30, (5,2)->31, (6,2)->32, (3,3)->33, (3,4)->34, (3,5)->35, (3,7)->36, (4,3)->37, (5,3)->38, (6,3)->39, (4,4)->40, (5,4)->41, (6,4)->42 },
it remains to prove termination of the 378-rule system
{ 0 0 0 -> 1 2 3 ,
  0 0 1 -> 1 2 4 ,
  0 0 5 -> 1 2 6 ,
  0 0 7 -> 1 2 8 ,
  0 0 9 -> 1 2 10 ,
  0 0 11 -> 1 2 12 ,
  0 0 13 -> 1 2 14 ,
  15 0 0 -> 16 2 3 ,
  15 0 1 -> 16 2 4 ,
  15 0 5 -> 16 2 6 ,
  15 0 7 -> 16 2 8 ,
  15 0 9 -> 16 2 10 ,
  15 0 11 -> 16 2 12 ,
  15 0 13 -> 16 2 14 ,
  3 0 0 -> 4 2 3 ,
  3 0 1 -> 4 2 4 ,
  3 0 5 -> 4 2 6 ,
  3 0 7 -> 4 2 8 ,
  3 0 9 -> 4 2 10 ,
  3 0 11 -> 4 2 12 ,
  3 0 13 -> 4 2 14 ,
  17 0 0 -> 18 2 3 ,
  17 0 1 -> 18 2 4 ,
  17 0 5 -> 18 2 6 ,
  17 0 7 -> 18 2 8 ,
  17 0 9 -> 18 2 10 ,
  17 0 11 -> 18 2 12 ,
  17 0 13 -> 18 2 14 ,
  19 0 0 -> 20 2 3 ,
  19 0 1 -> 20 2 4 ,
  19 0 5 -> 20 2 6 ,
  19 0 7 -> 20 2 8 ,
  19 0 9 -> 20 2 10 ,
  19 0 11 -> 20 2 12 ,
  19 0 13 -> 20 2 14 ,
  21 0 0 -> 22 2 3 ,
  21 0 1 -> 22 2 4 ,
  21 0 5 -> 22 2 6 ,
  21 0 7 -> 22 2 8 ,
  21 0 9 -> 22 2 10 ,
  21 0 11 -> 22 2 12 ,
  21 0 13 -> 22 2 14 ,
  23 0 0 -> 24 2 3 ,
  23 0 1 -> 24 2 4 ,
  23 0 5 -> 24 2 6 ,
  23 0 7 -> 24 2 8 ,
  23 0 9 -> 24 2 10 ,
  23 0 11 -> 24 2 12 ,
  23 0 13 -> 24 2 14 ,
  5 6 3 -> 1 16 16 15 ,
  5 6 4 -> 1 16 16 16 ,
  5 6 6 -> 1 16 16 2 ,
  5 6 8 -> 1 16 16 25 ,
  5 6 10 -> 1 16 16 26 ,
  5 6 12 -> 1 16 16 27 ,
  5 6 14 -> 1 16 16 28 ,
  2 6 3 -> 16 16 16 15 ,
  2 6 4 -> 16 16 16 16 ,
  2 6 6 -> 16 16 16 2 ,
  2 6 8 -> 16 16 16 25 ,
  2 6 10 -> 16 16 16 26 ,
  2 6 12 -> 16 16 16 27 ,
  2 6 14 -> 16 16 16 28 ,
  6 6 3 -> 4 16 16 15 ,
  6 6 4 -> 4 16 16 16 ,
  6 6 6 -> 4 16 16 2 ,
  6 6 8 -> 4 16 16 25 ,
  6 6 10 -> 4 16 16 26 ,
  6 6 12 -> 4 16 16 27 ,
  6 6 14 -> 4 16 16 28 ,
  29 6 3 -> 18 16 16 15 ,
  29 6 4 -> 18 16 16 16 ,
  29 6 6 -> 18 16 16 2 ,
  29 6 8 -> 18 16 16 25 ,
  29 6 10 -> 18 16 16 26 ,
  29 6 12 -> 18 16 16 27 ,
  29 6 14 -> 18 16 16 28 ,
  30 6 3 -> 20 16 16 15 ,
  30 6 4 -> 20 16 16 16 ,
  30 6 6 -> 20 16 16 2 ,
  30 6 8 -> 20 16 16 25 ,
  30 6 10 -> 20 16 16 26 ,
  30 6 12 -> 20 16 16 27 ,
  30 6 14 -> 20 16 16 28 ,
  31 6 3 -> 22 16 16 15 ,
  31 6 4 -> 22 16 16 16 ,
  31 6 6 -> 22 16 16 2 ,
  31 6 8 -> 22 16 16 25 ,
  31 6 10 -> 22 16 16 26 ,
  31 6 12 -> 22 16 16 27 ,
  31 6 14 -> 22 16 16 28 ,
  32 6 3 -> 24 16 16 15 ,
  32 6 4 -> 24 16 16 16 ,
  32 6 6 -> 24 16 16 2 ,
  32 6 8 -> 24 16 16 25 ,
  32 6 10 -> 24 16 16 26 ,
  32 6 12 -> 24 16 16 27 ,
  32 6 14 -> 24 16 16 28 ,
  5 3 -> 7 17 ,
  5 4 -> 7 18 ,
  5 6 -> 7 29 ,
  5 8 -> 7 33 ,
  5 10 -> 7 34 ,
  5 12 -> 7 35 ,
  5 14 -> 7 36 ,
  2 3 -> 25 17 ,
  2 4 -> 25 18 ,
  2 6 -> 25 29 ,
  2 8 -> 25 33 ,
  2 10 -> 25 34 ,
  2 12 -> 25 35 ,
  2 14 -> 25 36 ,
  6 3 -> 8 17 ,
  6 4 -> 8 18 ,
  6 6 -> 8 29 ,
  6 8 -> 8 33 ,
  6 10 -> 8 34 ,
  6 12 -> 8 35 ,
  6 14 -> 8 36 ,
  29 3 -> 33 17 ,
  29 4 -> 33 18 ,
  29 6 -> 33 29 ,
  29 8 -> 33 33 ,
  29 10 -> 33 34 ,
  29 12 -> 33 35 ,
  29 14 -> 33 36 ,
  30 3 -> 37 17 ,
  30 4 -> 37 18 ,
  30 6 -> 37 29 ,
  30 8 -> 37 33 ,
  30 10 -> 37 34 ,
  30 12 -> 37 35 ,
  30 14 -> 37 36 ,
  31 3 -> 38 17 ,
  31 4 -> 38 18 ,
  31 6 -> 38 29 ,
  31 8 -> 38 33 ,
  31 10 -> 38 34 ,
  31 12 -> 38 35 ,
  31 14 -> 38 36 ,
  32 3 -> 39 17 ,
  32 4 -> 39 18 ,
  32 6 -> 39 29 ,
  32 8 -> 39 33 ,
  32 10 -> 39 34 ,
  32 12 -> 39 35 ,
  32 14 -> 39 36 ,
  1 16 15 -> 9 30 3 ,
  1 16 16 -> 9 30 4 ,
  1 16 2 -> 9 30 6 ,
  1 16 25 -> 9 30 8 ,
  1 16 26 -> 9 30 10 ,
  1 16 27 -> 9 30 12 ,
  1 16 28 -> 9 30 14 ,
  16 16 15 -> 26 30 3 ,
  16 16 16 -> 26 30 4 ,
  16 16 2 -> 26 30 6 ,
  16 16 25 -> 26 30 8 ,
  16 16 26 -> 26 30 10 ,
  16 16 27 -> 26 30 12 ,
  16 16 28 -> 26 30 14 ,
  4 16 15 -> 10 30 3 ,
  4 16 16 -> 10 30 4 ,
  4 16 2 -> 10 30 6 ,
  4 16 25 -> 10 30 8 ,
  4 16 26 -> 10 30 10 ,
  4 16 27 -> 10 30 12 ,
  4 16 28 -> 10 30 14 ,
  18 16 15 -> 34 30 3 ,
  18 16 16 -> 34 30 4 ,
  18 16 2 -> 34 30 6 ,
  18 16 25 -> 34 30 8 ,
  18 16 26 -> 34 30 10 ,
  18 16 27 -> 34 30 12 ,
  18 16 28 -> 34 30 14 ,
  20 16 15 -> 40 30 3 ,
  20 16 16 -> 40 30 4 ,
  20 16 2 -> 40 30 6 ,
  20 16 25 -> 40 30 8 ,
  20 16 26 -> 40 30 10 ,
  20 16 27 -> 40 30 12 ,
  20 16 28 -> 40 30 14 ,
  22 16 15 -> 41 30 3 ,
  22 16 16 -> 41 30 4 ,
  22 16 2 -> 41 30 6 ,
  22 16 25 -> 41 30 8 ,
  22 16 26 -> 41 30 10 ,
  22 16 27 -> 41 30 12 ,
  22 16 28 -> 41 30 14 ,
  24 16 15 -> 42 30 3 ,
  24 16 16 -> 42 30 4 ,
  24 16 2 -> 42 30 6 ,
  24 16 25 -> 42 30 8 ,
  24 16 26 -> 42 30 10 ,
  24 16 27 -> 42 30 12 ,
  24 16 28 -> 42 30 14 ,
  1 16 16 15 -> 5 8 17 ,
  1 16 16 16 -> 5 8 18 ,
  1 16 16 2 -> 5 8 29 ,
  1 16 16 25 -> 5 8 33 ,
  1 16 16 26 -> 5 8 34 ,
  1 16 16 27 -> 5 8 35 ,
  1 16 16 28 -> 5 8 36 ,
  16 16 16 15 -> 2 8 17 ,
  16 16 16 16 -> 2 8 18 ,
  16 16 16 2 -> 2 8 29 ,
  16 16 16 25 -> 2 8 33 ,
  16 16 16 26 -> 2 8 34 ,
  16 16 16 27 -> 2 8 35 ,
  16 16 16 28 -> 2 8 36 ,
  4 16 16 15 -> 6 8 17 ,
  4 16 16 16 -> 6 8 18 ,
  4 16 16 2 -> 6 8 29 ,
  4 16 16 25 -> 6 8 33 ,
  4 16 16 26 -> 6 8 34 ,
  4 16 16 27 -> 6 8 35 ,
  4 16 16 28 -> 6 8 36 ,
  18 16 16 15 -> 29 8 17 ,
  18 16 16 16 -> 29 8 18 ,
  18 16 16 2 -> 29 8 29 ,
  18 16 16 25 -> 29 8 33 ,
  18 16 16 26 -> 29 8 34 ,
  18 16 16 27 -> 29 8 35 ,
  18 16 16 28 -> 29 8 36 ,
  20 16 16 15 -> 30 8 17 ,
  20 16 16 16 -> 30 8 18 ,
  20 16 16 2 -> 30 8 29 ,
  20 16 16 25 -> 30 8 33 ,
  20 16 16 26 -> 30 8 34 ,
  20 16 16 27 -> 30 8 35 ,
  20 16 16 28 -> 30 8 36 ,
  22 16 16 15 -> 31 8 17 ,
  22 16 16 16 -> 31 8 18 ,
  22 16 16 2 -> 31 8 29 ,
  22 16 16 25 -> 31 8 33 ,
  22 16 16 26 -> 31 8 34 ,
  22 16 16 27 -> 31 8 35 ,
  22 16 16 28 -> 31 8 36 ,
  24 16 16 15 -> 32 8 17 ,
  24 16 16 16 -> 32 8 18 ,
  24 16 16 2 -> 32 8 29 ,
  24 16 16 25 -> 32 8 33 ,
  24 16 16 26 -> 32 8 34 ,
  24 16 16 27 -> 32 8 35 ,
  24 16 16 28 -> 32 8 36 ,
  9 19 -> 7 35 21 ,
  9 20 -> 7 35 22 ,
  9 30 -> 7 35 31 ,
  9 37 -> 7 35 38 ,
  9 40 -> 7 35 41 ,
  26 19 -> 25 35 21 ,
  26 20 -> 25 35 22 ,
  26 30 -> 25 35 31 ,
  26 37 -> 25 35 38 ,
  26 40 -> 25 35 41 ,
  10 19 -> 8 35 21 ,
  10 20 -> 8 35 22 ,
  10 30 -> 8 35 31 ,
  10 37 -> 8 35 38 ,
  10 40 -> 8 35 41 ,
  34 19 -> 33 35 21 ,
  34 20 -> 33 35 22 ,
  34 30 -> 33 35 31 ,
  34 37 -> 33 35 38 ,
  34 40 -> 33 35 41 ,
  40 19 -> 37 35 21 ,
  40 20 -> 37 35 22 ,
  40 30 -> 37 35 31 ,
  40 37 -> 37 35 38 ,
  40 40 -> 37 35 41 ,
  41 19 -> 38 35 21 ,
  41 20 -> 38 35 22 ,
  41 30 -> 38 35 31 ,
  41 37 -> 38 35 38 ,
  41 40 -> 38 35 41 ,
  42 19 -> 39 35 21 ,
  42 20 -> 39 35 22 ,
  42 30 -> 39 35 31 ,
  42 37 -> 39 35 38 ,
  42 40 -> 39 35 41 ,
  7 17 -> 0 11 22 15 ,
  7 18 -> 0 11 22 16 ,
  7 29 -> 0 11 22 2 ,
  7 33 -> 0 11 22 25 ,
  7 34 -> 0 11 22 26 ,
  7 35 -> 0 11 22 27 ,
  7 36 -> 0 11 22 28 ,
  25 17 -> 15 11 22 15 ,
  25 18 -> 15 11 22 16 ,
  25 29 -> 15 11 22 2 ,
  25 33 -> 15 11 22 25 ,
  25 34 -> 15 11 22 26 ,
  25 35 -> 15 11 22 27 ,
  25 36 -> 15 11 22 28 ,
  8 17 -> 3 11 22 15 ,
  8 18 -> 3 11 22 16 ,
  8 29 -> 3 11 22 2 ,
  8 33 -> 3 11 22 25 ,
  8 34 -> 3 11 22 26 ,
  8 35 -> 3 11 22 27 ,
  8 36 -> 3 11 22 28 ,
  33 17 -> 17 11 22 15 ,
  33 18 -> 17 11 22 16 ,
  33 29 -> 17 11 22 2 ,
  33 33 -> 17 11 22 25 ,
  33 34 -> 17 11 22 26 ,
  33 35 -> 17 11 22 27 ,
  33 36 -> 17 11 22 28 ,
  37 17 -> 19 11 22 15 ,
  37 18 -> 19 11 22 16 ,
  37 29 -> 19 11 22 2 ,
  37 33 -> 19 11 22 25 ,
  37 34 -> 19 11 22 26 ,
  37 35 -> 19 11 22 27 ,
  37 36 -> 19 11 22 28 ,
  38 17 -> 21 11 22 15 ,
  38 18 -> 21 11 22 16 ,
  38 29 -> 21 11 22 2 ,
  38 33 -> 21 11 22 25 ,
  38 34 -> 21 11 22 26 ,
  38 35 -> 21 11 22 27 ,
  38 36 -> 21 11 22 28 ,
  39 17 -> 23 11 22 15 ,
  39 18 -> 23 11 22 16 ,
  39 29 -> 23 11 22 2 ,
  39 33 -> 23 11 22 25 ,
  39 34 -> 23 11 22 26 ,
  39 35 -> 23 11 22 27 ,
  39 36 -> 23 11 22 28 ,
  7 33 17 -> 5 3 0 ,
  7 33 18 -> 5 3 1 ,
  7 33 29 -> 5 3 5 ,
  7 33 33 -> 5 3 7 ,
  7 33 34 -> 5 3 9 ,
  7 33 35 -> 5 3 11 ,
  7 33 36 -> 5 3 13 ,
  25 33 17 -> 2 3 0 ,
  25 33 18 -> 2 3 1 ,
  25 33 29 -> 2 3 5 ,
  25 33 33 -> 2 3 7 ,
  25 33 34 -> 2 3 9 ,
  25 33 35 -> 2 3 11 ,
  25 33 36 -> 2 3 13 ,
  8 33 17 -> 6 3 0 ,
  8 33 18 -> 6 3 1 ,
  8 33 29 -> 6 3 5 ,
  8 33 33 -> 6 3 7 ,
  8 33 34 -> 6 3 9 ,
  8 33 35 -> 6 3 11 ,
  8 33 36 -> 6 3 13 ,
  33 33 17 -> 29 3 0 ,
  33 33 18 -> 29 3 1 ,
  33 33 29 -> 29 3 5 ,
  33 33 33 -> 29 3 7 ,
  33 33 34 -> 29 3 9 ,
  33 33 35 -> 29 3 11 ,
  33 33 36 -> 29 3 13 ,
  37 33 17 -> 30 3 0 ,
  37 33 18 -> 30 3 1 ,
  37 33 29 -> 30 3 5 ,
  37 33 33 -> 30 3 7 ,
  37 33 34 -> 30 3 9 ,
  37 33 35 -> 30 3 11 ,
  37 33 36 -> 30 3 13 ,
  38 33 17 -> 31 3 0 ,
  38 33 18 -> 31 3 1 ,
  38 33 29 -> 31 3 5 ,
  38 33 33 -> 31 3 7 ,
  38 33 34 -> 31 3 9 ,
  38 33 35 -> 31 3 11 ,
  38 33 36 -> 31 3 13 ,
  39 33 17 -> 32 3 0 ,
  39 33 18 -> 32 3 1 ,
  39 33 29 -> 32 3 5 ,
  39 33 33 -> 32 3 7 ,
  39 33 34 -> 32 3 9 ,
  39 33 35 -> 32 3 11 ,
  39 33 36 -> 32 3 13 }


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

0 is interpreted by
 /     \
|  1 30 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
2 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
3 is interpreted by
 /     \
|  1 41 |
|  0  1 |
 \     /
4 is interpreted by
 /     \
|  1 35 |
|  0  1 |
 \     /
5 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
6 is interpreted by
 /     \
|  1 35 |
|  0  1 |
 \     /
7 is interpreted by
 /     \
|  1 32 |
|  0  1 |
 \     /
8 is interpreted by
 /     \
|  1 44 |
|  0  1 |
 \     /
9 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
10 is interpreted by
 /     \
|  1 35 |
|  0  1 |
 \     /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /     \
|  1 12 |
|  0  1 |
 \     /
13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
14 is interpreted by
 /     \
|  1 12 |
|  0  1 |
 \     /
15 is interpreted by
 /     \
|  1 29 |
|  0  1 |
 \     /
16 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
17 is interpreted by
 /     \
|  1 30 |
|  0  1 |
 \     /
18 is interpreted by
 /     \
|  1 24 |
|  0  1 |
 \     /
19 is interpreted by
 /     \
|  1 16 |
|  0  1 |
 \     /
20 is interpreted by
 /     \
|  1 10 |
|  0  1 |
 \     /
21 is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
22 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
23 is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
25 is interpreted by
 /     \
|  1 32 |
|  0  1 |
 \     /
26 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /
27 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
28 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
29 is interpreted by
 /     \
|  1 24 |
|  0  1 |
 \     /
30 is interpreted by
 /     \
|  1 10 |
|  0  1 |
 \     /
31 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
32 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
33 is interpreted by
 /     \
|  1 33 |
|  0  1 |
 \     /
34 is interpreted by
 /     \
|  1 24 |
|  0  1 |
 \     /
35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
36 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
37 is interpreted by
 /     \
|  1 19 |
|  0  1 |
 \     /
38 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
39 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
40 is interpreted by
 /     \
|  1 10 |
|  0  1 |
 \     /
41 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
42 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.