/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 { f->0, n->1, c->2, s->3 }, 
it remains to prove termination of the 5-rule system
{ 0 -> 1 2 2 ,
  2 0 -> 0 2 2 ,
  2 2 -> 2 ,
  1 3 -> 0 3 3 ,
  1 0 -> 0 1 }


Applying the dependency pairs transformation.

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


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

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


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 1 |
| 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 1 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 |
 \     /

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


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 1 1 |
 \     /
3 is interpreted by
 /     \
| 1 0 1 |
| 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 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4 }, 
it remains to prove termination of the 4-rule system
{ 0 -> 1 2 2 ,
  2 3 ->= 3 2 2 ,
  2 2 ->= 2 ,
  4 3 ->= 3 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 1 |
| 0 1 |
 \   /

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

The system is trivially terminating.