/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 { c->0, a->1, b->2 }, 
it remains to prove termination of the 6-rule system
{ 0 0 1 -> 2 1 0 ,
  2 2 2 -> 1 1 1 ,
  0 1 2 ->= 1 1 1 ,
  0 1 2 ->= 1 0 1 ,
  0 2 0 ->= 0 2 2 ,
  2 1 2 ->= 2 2 0 }


Applying context closure of depth 1 in the following form: System R over Sigma
maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n})

After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 0]->2, [0, 2]->3, [2, 1]->4, [2, 2]->5, [2, 0]->6, [1, 1]->7, [1, 2]->8 },
it remains to prove termination of the 54-rule system
{ 0 0 1 2 -> 3 4 2 0 ,
  3 5 5 6 -> 1 7 7 2 ,
  0 1 8 6 ->= 1 7 7 2 ,
  0 1 8 6 ->= 1 2 1 2 ,
  0 3 6 0 ->= 0 3 5 6 ,
  3 4 8 6 ->= 3 5 6 0 ,
  0 0 1 7 -> 3 4 2 1 ,
  3 5 5 4 -> 1 7 7 7 ,
  0 1 8 4 ->= 1 7 7 7 ,
  0 1 8 4 ->= 1 2 1 7 ,
  0 3 6 1 ->= 0 3 5 4 ,
  3 4 8 4 ->= 3 5 6 1 ,
  0 0 1 8 -> 3 4 2 3 ,
  3 5 5 5 -> 1 7 7 8 ,
  0 1 8 5 ->= 1 7 7 8 ,
  0 1 8 5 ->= 1 2 1 8 ,
  0 3 6 3 ->= 0 3 5 5 ,
  3 4 8 5 ->= 3 5 6 3 ,
  2 0 1 2 -> 8 4 2 0 ,
  8 5 5 6 -> 7 7 7 2 ,
  2 1 8 6 ->= 7 7 7 2 ,
  2 1 8 6 ->= 7 2 1 2 ,
  2 3 6 0 ->= 2 3 5 6 ,
  8 4 8 6 ->= 8 5 6 0 ,
  2 0 1 7 -> 8 4 2 1 ,
  8 5 5 4 -> 7 7 7 7 ,
  2 1 8 4 ->= 7 7 7 7 ,
  2 1 8 4 ->= 7 2 1 7 ,
  2 3 6 1 ->= 2 3 5 4 ,
  8 4 8 4 ->= 8 5 6 1 ,
  2 0 1 8 -> 8 4 2 3 ,
  8 5 5 5 -> 7 7 7 8 ,
  2 1 8 5 ->= 7 7 7 8 ,
  2 1 8 5 ->= 7 2 1 8 ,
  2 3 6 3 ->= 2 3 5 5 ,
  8 4 8 5 ->= 8 5 6 3 ,
  6 0 1 2 -> 5 4 2 0 ,
  5 5 5 6 -> 4 7 7 2 ,
  6 1 8 6 ->= 4 7 7 2 ,
  6 1 8 6 ->= 4 2 1 2 ,
  6 3 6 0 ->= 6 3 5 6 ,
  5 4 8 6 ->= 5 5 6 0 ,
  6 0 1 7 -> 5 4 2 1 ,
  5 5 5 4 -> 4 7 7 7 ,
  6 1 8 4 ->= 4 7 7 7 ,
  6 1 8 4 ->= 4 2 1 7 ,
  6 3 6 1 ->= 6 3 5 4 ,
  5 4 8 4 ->= 5 5 6 1 ,
  6 0 1 8 -> 5 4 2 3 ,
  5 5 5 5 -> 4 7 7 8 ,
  6 1 8 5 ->= 4 7 7 8 ,
  6 1 8 5 ->= 4 2 1 8 ,
  6 3 6 3 ->= 6 3 5 5 ,
  5 4 8 5 ->= 5 5 6 3 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, 
it remains to prove termination of the 49-rule system
{ 0 0 1 2 -> 3 4 2 0 ,
  3 5 5 6 -> 1 7 7 2 ,
  0 1 8 6 ->= 1 7 7 2 ,
  0 1 8 6 ->= 1 2 1 2 ,
  0 3 6 0 ->= 0 3 5 6 ,
  0 0 1 7 -> 3 4 2 1 ,
  3 5 5 4 -> 1 7 7 7 ,
  0 1 8 4 ->= 1 7 7 7 ,
  0 1 8 4 ->= 1 2 1 7 ,
  0 3 6 1 ->= 0 3 5 4 ,
  3 4 8 4 ->= 3 5 6 1 ,
  0 0 1 8 -> 3 4 2 3 ,
  3 5 5 5 -> 1 7 7 8 ,
  0 1 8 5 ->= 1 7 7 8 ,
  0 1 8 5 ->= 1 2 1 8 ,
  0 3 6 3 ->= 0 3 5 5 ,
  3 4 8 5 ->= 3 5 6 3 ,
  2 0 1 2 -> 8 4 2 0 ,
  8 5 5 6 -> 7 7 7 2 ,
  2 1 8 6 ->= 7 7 7 2 ,
  2 1 8 6 ->= 7 2 1 2 ,
  2 3 6 0 ->= 2 3 5 6 ,
  2 0 1 7 -> 8 4 2 1 ,
  8 5 5 4 -> 7 7 7 7 ,
  2 1 8 4 ->= 7 7 7 7 ,
  2 1 8 4 ->= 7 2 1 7 ,
  2 3 6 1 ->= 2 3 5 4 ,
  8 4 8 4 ->= 8 5 6 1 ,
  2 0 1 8 -> 8 4 2 3 ,
  8 5 5 5 -> 7 7 7 8 ,
  2 1 8 5 ->= 7 7 7 8 ,
  2 1 8 5 ->= 7 2 1 8 ,
  2 3 6 3 ->= 2 3 5 5 ,
  8 4 8 5 ->= 8 5 6 3 ,
  6 0 1 2 -> 5 4 2 0 ,
  5 5 5 6 -> 4 7 7 2 ,
  6 3 6 0 ->= 6 3 5 6 ,
  6 0 1 7 -> 5 4 2 1 ,
  5 5 5 4 -> 4 7 7 7 ,
  6 1 8 4 ->= 4 7 7 7 ,
  6 1 8 4 ->= 4 2 1 7 ,
  6 3 6 1 ->= 6 3 5 4 ,
  5 4 8 4 ->= 5 5 6 1 ,
  6 0 1 8 -> 5 4 2 3 ,
  5 5 5 5 -> 4 7 7 8 ,
  6 1 8 5 ->= 4 7 7 8 ,
  6 1 8 5 ->= 4 2 1 8 ,
  6 3 6 3 ->= 6 3 5 5 ,
  5 4 8 5 ->= 5 5 6 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 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 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 |
 \   /

After renaming modulo { 3->0, 5->1, 6->2, 1->3, 7->4, 2->5, 4->6, 0->7, 8->8 }, 
it remains to prove termination of the 33-rule system
{ 0 1 1 2 -> 3 4 4 5 ,
  0 1 1 6 -> 3 4 4 4 ,
  7 0 2 3 ->= 7 0 1 6 ,
  0 6 8 6 ->= 0 1 2 3 ,
  0 1 1 1 -> 3 4 4 8 ,
  7 0 2 0 ->= 7 0 1 1 ,
  0 6 8 1 ->= 0 1 2 0 ,
  5 7 3 5 -> 8 6 5 7 ,
  8 1 1 2 -> 4 4 4 5 ,
  5 3 8 2 ->= 4 4 4 5 ,
  5 3 8 2 ->= 4 5 3 5 ,
  8 1 1 6 -> 4 4 4 4 ,
  5 3 8 6 ->= 4 4 4 4 ,
  5 3 8 6 ->= 4 5 3 4 ,
  5 0 2 3 ->= 5 0 1 6 ,
  8 6 8 6 ->= 8 1 2 3 ,
  8 1 1 1 -> 4 4 4 8 ,
  5 3 8 1 ->= 4 4 4 8 ,
  5 3 8 1 ->= 4 5 3 8 ,
  5 0 2 0 ->= 5 0 1 1 ,
  8 6 8 1 ->= 8 1 2 0 ,
  2 7 3 5 -> 1 6 5 7 ,
  1 1 1 2 -> 6 4 4 5 ,
  1 1 1 6 -> 6 4 4 4 ,
  2 3 8 6 ->= 6 4 4 4 ,
  2 3 8 6 ->= 6 5 3 4 ,
  2 0 2 3 ->= 2 0 1 6 ,
  1 6 8 6 ->= 1 1 2 3 ,
  1 1 1 1 -> 6 4 4 8 ,
  2 3 8 1 ->= 6 4 4 8 ,
  2 3 8 1 ->= 6 5 3 8 ,
  2 0 2 0 ->= 2 0 1 1 ,
  1 6 8 1 ->= 1 1 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 1 |
| 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 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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


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

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


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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
1 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 |
 \         /
2 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 |
 \         /
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 |
 \         /
4 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 |
 \         /
5 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 |
 \         /
6 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 |
 \         /
7 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 |
 \         /

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

The system is trivially terminating.