/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 0 -> 1 1 0 ,
  2 1 1 -> 2 2 0 ,
  0 1 0 -> 1 0 0 ,
  2 0 0 -> 2 0 2 ,
  1 1 2 ->= 0 2 1 ,
  1 2 1 ->= 1 0 0 }


The system was reversed.

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


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, 1]->2, [1, 0]->3, [1, 2]->4, [2, 0]->5, [0, 2]->6, [2, 2]->7, [2, 1]->8 },
it remains to prove termination of the 54-rule system
{ 0 0 0 0 -> 0 1 2 3 ,
  1 2 4 5 -> 0 6 7 5 ,
  0 1 3 0 -> 0 0 1 3 ,
  0 0 6 5 -> 6 5 6 5 ,
  6 8 2 3 ->= 1 4 5 0 ,
  1 4 8 3 ->= 0 0 1 3 ,
  0 0 0 1 -> 0 1 2 2 ,
  1 2 4 8 -> 0 6 7 8 ,
  0 1 3 1 -> 0 0 1 2 ,
  0 0 6 8 -> 6 5 6 8 ,
  6 8 2 2 ->= 1 4 5 1 ,
  1 4 8 2 ->= 0 0 1 2 ,
  0 0 0 6 -> 0 1 2 4 ,
  1 2 4 7 -> 0 6 7 7 ,
  0 1 3 6 -> 0 0 1 4 ,
  0 0 6 7 -> 6 5 6 7 ,
  6 8 2 4 ->= 1 4 5 6 ,
  1 4 8 4 ->= 0 0 1 4 ,
  3 0 0 0 -> 3 1 2 3 ,
  2 2 4 5 -> 3 6 7 5 ,
  3 1 3 0 -> 3 0 1 3 ,
  3 0 6 5 -> 4 5 6 5 ,
  4 8 2 3 ->= 2 4 5 0 ,
  2 4 8 3 ->= 3 0 1 3 ,
  3 0 0 1 -> 3 1 2 2 ,
  2 2 4 8 -> 3 6 7 8 ,
  3 1 3 1 -> 3 0 1 2 ,
  3 0 6 8 -> 4 5 6 8 ,
  4 8 2 2 ->= 2 4 5 1 ,
  2 4 8 2 ->= 3 0 1 2 ,
  3 0 0 6 -> 3 1 2 4 ,
  2 2 4 7 -> 3 6 7 7 ,
  3 1 3 6 -> 3 0 1 4 ,
  3 0 6 7 -> 4 5 6 7 ,
  4 8 2 4 ->= 2 4 5 6 ,
  2 4 8 4 ->= 3 0 1 4 ,
  5 0 0 0 -> 5 1 2 3 ,
  8 2 4 5 -> 5 6 7 5 ,
  5 1 3 0 -> 5 0 1 3 ,
  5 0 6 5 -> 7 5 6 5 ,
  7 8 2 3 ->= 8 4 5 0 ,
  8 4 8 3 ->= 5 0 1 3 ,
  5 0 0 1 -> 5 1 2 2 ,
  8 2 4 8 -> 5 6 7 8 ,
  5 1 3 1 -> 5 0 1 2 ,
  5 0 6 8 -> 7 5 6 8 ,
  7 8 2 2 ->= 8 4 5 1 ,
  8 4 8 2 ->= 5 0 1 2 ,
  5 0 0 6 -> 5 1 2 4 ,
  8 2 4 7 -> 5 6 7 7 ,
  5 1 3 6 -> 5 0 1 4 ,
  5 0 6 7 -> 7 5 6 7 ,
  7 8 2 4 ->= 8 4 5 6 ,
  8 4 8 4 ->= 5 0 1 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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 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 1 |
| 0 1 |
 \   /

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 33-rule system
{ 0 0 0 0 -> 0 1 2 3 ,
  1 2 4 5 -> 0 6 7 5 ,
  0 1 3 0 -> 0 0 1 3 ,
  1 4 8 3 ->= 0 0 1 3 ,
  0 0 0 1 -> 0 1 2 2 ,
  1 2 4 8 -> 0 6 7 8 ,
  0 1 3 1 -> 0 0 1 2 ,
  1 4 8 2 ->= 0 0 1 2 ,
  0 0 0 6 -> 0 1 2 4 ,
  1 2 4 7 -> 0 6 7 7 ,
  0 1 3 6 -> 0 0 1 4 ,
  1 4 8 4 ->= 0 0 1 4 ,
  3 0 0 0 -> 3 1 2 3 ,
  2 2 4 5 -> 3 6 7 5 ,
  3 1 3 0 -> 3 0 1 3 ,
  2 4 8 3 ->= 3 0 1 3 ,
  3 0 0 1 -> 3 1 2 2 ,
  2 2 4 8 -> 3 6 7 8 ,
  3 1 3 1 -> 3 0 1 2 ,
  2 4 8 2 ->= 3 0 1 2 ,
  3 0 0 6 -> 3 1 2 4 ,
  2 2 4 7 -> 3 6 7 7 ,
  3 1 3 6 -> 3 0 1 4 ,
  2 4 8 4 ->= 3 0 1 4 ,
  5 0 0 0 -> 5 1 2 3 ,
  5 1 3 0 -> 5 0 1 3 ,
  5 0 6 5 -> 7 5 6 5 ,
  5 0 0 1 -> 5 1 2 2 ,
  5 1 3 1 -> 5 0 1 2 ,
  5 0 6 8 -> 7 5 6 8 ,
  5 0 0 6 -> 5 1 2 4 ,
  5 1 3 6 -> 5 0 1 4 ,
  5 0 6 7 -> 7 5 6 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 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 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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 8->5, 6->6, 5->7 }, 
it remains to prove termination of the 24-rule system
{ 0 0 0 0 -> 0 1 2 3 ,
  0 1 3 0 -> 0 0 1 3 ,
  1 4 5 3 ->= 0 0 1 3 ,
  0 0 0 1 -> 0 1 2 2 ,
  0 1 3 1 -> 0 0 1 2 ,
  1 4 5 2 ->= 0 0 1 2 ,
  0 0 0 6 -> 0 1 2 4 ,
  0 1 3 6 -> 0 0 1 4 ,
  1 4 5 4 ->= 0 0 1 4 ,
  3 0 0 0 -> 3 1 2 3 ,
  3 1 3 0 -> 3 0 1 3 ,
  2 4 5 3 ->= 3 0 1 3 ,
  3 0 0 1 -> 3 1 2 2 ,
  3 1 3 1 -> 3 0 1 2 ,
  2 4 5 2 ->= 3 0 1 2 ,
  3 0 0 6 -> 3 1 2 4 ,
  3 1 3 6 -> 3 0 1 4 ,
  2 4 5 4 ->= 3 0 1 4 ,
  7 0 0 0 -> 7 1 2 3 ,
  7 1 3 0 -> 7 0 1 3 ,
  7 0 0 1 -> 7 1 2 2 ,
  7 1 3 1 -> 7 0 1 2 ,
  7 0 0 6 -> 7 1 2 4 ,
  7 1 3 6 -> 7 0 1 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 0 |
| 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 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 7->4 }, 
it remains to prove termination of the 12-rule system
{ 0 0 0 0 -> 0 1 2 3 ,
  0 1 3 0 -> 0 0 1 3 ,
  0 0 0 1 -> 0 1 2 2 ,
  0 1 3 1 -> 0 0 1 2 ,
  3 0 0 0 -> 3 1 2 3 ,
  3 1 3 0 -> 3 0 1 3 ,
  3 0 0 1 -> 3 1 2 2 ,
  3 1 3 1 -> 3 0 1 2 ,
  4 0 0 0 -> 4 1 2 3 ,
  4 1 3 0 -> 4 0 1 3 ,
  4 0 0 1 -> 4 1 2 2 ,
  4 1 3 1 -> 4 0 1 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 1 |
| 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 |
 \   /

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

The system is trivially terminating.