/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 { a->0, b->1, c->2, d->3, f->4, g->5 }, 
it remains to prove termination of the 9-rule system
{ 0 1 2 0 -> 1 0 2 1 0 1 ,
  0 3 -> 2 ,
  0 4 4 -> 5 ,
  1 5 -> 5 1 ,
  2 -> 4 4 ,
  2 0 2 -> 1 2 0 1 2 ,
  2 3 -> 0 0 ,
  5 -> 2 0 ,
  5 -> 3 3 3 3 }


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 12 |
|  0  1 |
 \     /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /     \
|  1 18 |
|  0  1 |
 \     /
3 is interpreted by
 /   \
| 1 7 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
5 is interpreted by
 /     \
|  1 30 |
|  0  1 |
 \     /

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


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

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


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 |
 \   /

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


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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


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

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

The system is trivially terminating.