/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 { r->0, s->1, n->2, b->3, u->4, t->5, c->6 }, 
it remains to prove termination of the 15-rule system
{ 0 0 -> 1 0 ,
  0 1 -> 1 0 ,
  0 2 -> 1 0 ,
  0 3 -> 4 1 3 ,
  0 4 -> 4 0 ,
  1 4 -> 4 1 ,
  2 4 -> 4 2 ,
  5 0 4 -> 5 6 0 ,
  5 1 4 -> 5 6 0 ,
  5 2 4 -> 5 6 0 ,
  6 4 -> 4 6 ,
  6 1 -> 1 6 ,
  6 0 -> 0 6 ,
  6 2 -> 2 6 ,
  6 2 -> 2 }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 15-rule system
{ 0 0 -> 0 1 ,
  1 0 -> 0 1 ,
  2 0 -> 0 1 ,
  3 0 -> 3 1 4 ,
  4 0 -> 0 4 ,
  4 1 -> 1 4 ,
  4 2 -> 2 4 ,
  4 0 5 -> 0 6 5 ,
  4 1 5 -> 0 6 5 ,
  4 2 5 -> 0 6 5 ,
  4 6 -> 6 4 ,
  1 6 -> 6 1 ,
  0 6 -> 6 0 ,
  2 6 -> 6 2 ,
  2 6 -> 2 }


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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 3->2, 4->3, 2->4, 5->5, 6->6 }, 
it remains to prove termination of the 13-rule system
{ 0 0 -> 0 1 ,
  1 0 -> 0 1 ,
  2 0 -> 2 1 3 ,
  3 0 -> 0 3 ,
  3 1 -> 1 3 ,
  3 4 -> 4 3 ,
  3 0 5 -> 0 6 5 ,
  3 1 5 -> 0 6 5 ,
  3 6 -> 6 3 ,
  1 6 -> 6 1 ,
  0 6 -> 6 0 ,
  4 6 -> 6 4 ,
  4 6 -> 4 }


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 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,true)->4, (3,false)->5, (3,true)->6, (4,false)->7, (4,true)->8, (5,false)->9, (6,false)->10, (2,false)->11 },
it remains to prove termination of the 27-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 4 3 5 ,
  4 1 -> 0 5 ,
  4 1 -> 6 ,
  6 1 -> 2 5 ,
  6 1 -> 6 ,
  6 3 -> 0 5 ,
  6 3 -> 6 ,
  6 7 -> 8 5 ,
  6 7 -> 6 ,
  6 3 9 -> 2 10 9 ,
  6 10 -> 6 ,
  0 10 -> 0 ,
  2 10 -> 2 ,
  8 10 -> 8 ,
  3 1 ->= 1 3 ,
  11 1 ->= 11 3 5 ,
  5 1 ->= 1 5 ,
  5 3 ->= 3 5 ,
  5 7 ->= 7 5 ,
  5 3 9 ->= 1 10 9 ,
  5 10 ->= 10 5 ,
  3 10 ->= 10 3 ,
  1 10 ->= 10 1 ,
  7 10 ->= 10 7 ,
  7 10 ->= 7 }


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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 9->7, 10->8, 8->9, 11->10, 7->11 }, 
it remains to prove termination of the 23-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 4 3 5 ,
  6 1 -> 2 5 ,
  6 1 -> 6 ,
  6 3 -> 0 5 ,
  6 3 -> 6 ,
  6 3 7 -> 2 8 7 ,
  6 8 -> 6 ,
  0 8 -> 0 ,
  2 8 -> 2 ,
  9 8 -> 9 ,
  3 1 ->= 1 3 ,
  10 1 ->= 10 3 5 ,
  5 1 ->= 1 5 ,
  5 3 ->= 3 5 ,
  5 11 ->= 11 5 ,
  5 3 7 ->= 1 8 7 ,
  5 8 ->= 8 5 ,
  3 8 ->= 8 3 ,
  1 8 ->= 8 1 ,
  11 8 ->= 8 11 ,
  11 8 ->= 11 }


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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9, 11->10, 7->11 }, 
it remains to prove termination of the 20-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 4 3 5 ,
  6 1 -> 6 ,
  6 3 -> 6 ,
  6 7 -> 6 ,
  0 7 -> 0 ,
  2 7 -> 2 ,
  8 7 -> 8 ,
  3 1 ->= 1 3 ,
  9 1 ->= 9 3 5 ,
  5 1 ->= 1 5 ,
  5 3 ->= 3 5 ,
  5 10 ->= 10 5 ,
  5 3 11 ->= 1 7 11 ,
  5 7 ->= 7 5 ,
  3 7 ->= 7 3 ,
  1 7 ->= 7 1 ,
  10 7 ->= 7 10 ,
  10 7 ->= 10 }


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 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 4->2, 3->3, 5->4, 6->5, 7->6, 2->7, 8->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 19-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 3 4 ,
  5 1 -> 5 ,
  5 3 -> 5 ,
  5 6 -> 5 ,
  0 6 -> 0 ,
  7 6 -> 7 ,
  8 6 -> 8 ,
  3 1 ->= 1 3 ,
  9 1 ->= 9 3 4 ,
  4 1 ->= 1 4 ,
  4 3 ->= 3 4 ,
  4 10 ->= 10 4 ,
  4 3 11 ->= 1 6 11 ,
  4 6 ->= 6 4 ,
  3 6 ->= 6 3 ,
  1 6 ->= 6 1 ,
  10 6 ->= 6 10 ,
  10 6 ->= 10 }


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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 0->6, 7->7, 8->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 16-rule system
{ 0 1 -> 0 2 3 ,
  4 5 -> 4 ,
  6 5 -> 6 ,
  7 5 -> 7 ,
  8 5 -> 8 ,
  2 1 ->= 1 2 ,
  9 1 ->= 9 2 3 ,
  3 1 ->= 1 3 ,
  3 2 ->= 2 3 ,
  3 10 ->= 10 3 ,
  3 2 11 ->= 1 5 11 ,
  3 5 ->= 5 3 ,
  2 5 ->= 5 2 ,
  1 5 ->= 5 1 ,
  10 5 ->= 5 10 ,
  10 5 ->= 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /

After renaming modulo { 4->0, 5->1, 6->2, 7->3, 8->4, 2->5, 1->6, 9->7, 3->8, 10->9, 11->10 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 ->= 6 5 ,
  7 6 ->= 7 5 8 ,
  8 6 ->= 6 8 ,
  8 5 ->= 5 8 ,
  8 9 ->= 9 8 ,
  8 5 10 ->= 6 1 10 ,
  8 1 ->= 1 8 ,
  5 1 ->= 1 5 ,
  6 1 ->= 1 6 ,
  9 1 ->= 1 9 ,
  9 1 ->= 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
7 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9 }, 
it remains to prove termination of the 14-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 ->= 6 5 ,
  7 6 ->= 6 7 ,
  7 5 ->= 5 7 ,
  7 8 ->= 8 7 ,
  7 5 9 ->= 6 1 9 ,
  7 1 ->= 1 7 ,
  5 1 ->= 1 5 ,
  6 1 ->= 1 6 ,
  8 1 ->= 1 8 ,
  8 1 ->= 8 }


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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 6->1, 7->2, 8->3, 1->4 }, 
it remains to prove termination of the 8-rule system
{ 0 1 ->= 1 0 ,
  2 1 ->= 1 2 ,
  2 0 ->= 0 2 ,
  2 3 ->= 3 2 ,
  2 4 ->= 4 2 ,
  0 4 ->= 4 0 ,
  1 4 ->= 4 1 ,
  3 4 ->= 4 3 }

The system is trivially terminating.