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


The length-preserving system was inverted.

After renaming modulo { 0->0, 1->1, 2->2 }, 
it remains to prove termination of the 6-rule system
{ 0 1 1 -> 0 0 1 ,
  0 2 2 -> 2 2 1 ,
  0 1 0 ->= 1 1 2 ,
  1 0 1 ->= 2 0 1 ,
  2 2 2 ->= 1 2 1 ,
  2 0 1 ->= 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, 1]->2, [1, 0]->3, [0, 2]->4, [2, 2]->5, [2, 0]->6, [2, 1]->7, [1, 2]->8 },
it remains to prove termination of the 54-rule system
{ 0 1 2 3 -> 0 0 1 3 ,
  0 4 5 6 -> 4 5 7 3 ,
  0 1 3 0 ->= 1 2 8 6 ,
  1 3 1 3 ->= 4 6 1 3 ,
  4 5 5 6 ->= 1 8 7 3 ,
  4 6 1 3 ->= 4 5 6 0 ,
  0 1 2 2 -> 0 0 1 2 ,
  0 4 5 7 -> 4 5 7 2 ,
  0 1 3 1 ->= 1 2 8 7 ,
  1 3 1 2 ->= 4 6 1 2 ,
  4 5 5 7 ->= 1 8 7 2 ,
  4 6 1 2 ->= 4 5 6 1 ,
  0 1 2 8 -> 0 0 1 8 ,
  0 4 5 5 -> 4 5 7 8 ,
  0 1 3 4 ->= 1 2 8 5 ,
  1 3 1 8 ->= 4 6 1 8 ,
  4 5 5 5 ->= 1 8 7 8 ,
  4 6 1 8 ->= 4 5 6 4 ,
  3 1 2 3 -> 3 0 1 3 ,
  3 4 5 6 -> 8 5 7 3 ,
  3 1 3 0 ->= 2 2 8 6 ,
  2 3 1 3 ->= 8 6 1 3 ,
  8 5 5 6 ->= 2 8 7 3 ,
  8 6 1 3 ->= 8 5 6 0 ,
  3 1 2 2 -> 3 0 1 2 ,
  3 4 5 7 -> 8 5 7 2 ,
  3 1 3 1 ->= 2 2 8 7 ,
  2 3 1 2 ->= 8 6 1 2 ,
  8 5 5 7 ->= 2 8 7 2 ,
  8 6 1 2 ->= 8 5 6 1 ,
  3 1 2 8 -> 3 0 1 8 ,
  3 4 5 5 -> 8 5 7 8 ,
  3 1 3 4 ->= 2 2 8 5 ,
  2 3 1 8 ->= 8 6 1 8 ,
  8 5 5 5 ->= 2 8 7 8 ,
  8 6 1 8 ->= 8 5 6 4 ,
  6 1 2 3 -> 6 0 1 3 ,
  6 4 5 6 -> 5 5 7 3 ,
  6 1 3 0 ->= 7 2 8 6 ,
  7 3 1 3 ->= 5 6 1 3 ,
  5 5 5 6 ->= 7 8 7 3 ,
  5 6 1 3 ->= 5 5 6 0 ,
  6 1 2 2 -> 6 0 1 2 ,
  6 4 5 7 -> 5 5 7 2 ,
  6 1 3 1 ->= 7 2 8 7 ,
  7 3 1 2 ->= 5 6 1 2 ,
  5 5 5 7 ->= 7 8 7 2 ,
  5 6 1 2 ->= 5 5 6 1 ,
  6 1 2 8 -> 6 0 1 8 ,
  6 4 5 5 -> 5 5 7 8 ,
  6 1 3 4 ->= 7 2 8 5 ,
  7 3 1 8 ->= 5 6 1 8 ,
  5 5 5 5 ->= 7 8 7 8 ,
  5 6 1 8 ->= 5 5 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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 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 24-rule system
{ 0 1 2 3 -> 0 0 1 3 ,
  0 4 5 6 -> 4 5 7 3 ,
  4 5 5 6 ->= 1 8 7 3 ,
  0 1 2 2 -> 0 0 1 2 ,
  0 4 5 7 -> 4 5 7 2 ,
  4 5 5 7 ->= 1 8 7 2 ,
  4 6 1 2 ->= 4 5 6 1 ,
  0 1 2 8 -> 0 0 1 8 ,
  4 6 1 8 ->= 4 5 6 4 ,
  3 1 2 3 -> 3 0 1 3 ,
  8 5 5 6 ->= 2 8 7 3 ,
  3 1 2 2 -> 3 0 1 2 ,
  8 5 5 7 ->= 2 8 7 2 ,
  8 6 1 2 ->= 8 5 6 1 ,
  3 1 2 8 -> 3 0 1 8 ,
  8 6 1 8 ->= 8 5 6 4 ,
  6 1 2 3 -> 6 0 1 3 ,
  7 3 1 3 ->= 5 6 1 3 ,
  6 1 2 2 -> 6 0 1 2 ,
  7 3 1 2 ->= 5 6 1 2 ,
  5 6 1 2 ->= 5 5 6 1 ,
  6 1 2 8 -> 6 0 1 8 ,
  7 3 1 8 ->= 5 6 1 8 ,
  5 6 1 8 ->= 5 5 6 4 }


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 1 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
6 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 |
 \         /
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 1 0 0 0 |
 \         /
8 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, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, 
it remains to prove termination of the 23-rule system
{ 0 1 2 3 -> 0 0 1 3 ,
  0 4 5 6 -> 4 5 7 3 ,
  4 5 5 6 ->= 1 8 7 3 ,
  0 1 2 2 -> 0 0 1 2 ,
  0 4 5 7 -> 4 5 7 2 ,
  4 5 5 7 ->= 1 8 7 2 ,
  4 6 1 2 ->= 4 5 6 1 ,
  0 1 2 8 -> 0 0 1 8 ,
  4 6 1 8 ->= 4 5 6 4 ,
  3 1 2 3 -> 3 0 1 3 ,
  8 5 5 6 ->= 2 8 7 3 ,
  3 1 2 2 -> 3 0 1 2 ,
  8 6 1 2 ->= 8 5 6 1 ,
  3 1 2 8 -> 3 0 1 8 ,
  8 6 1 8 ->= 8 5 6 4 ,
  6 1 2 3 -> 6 0 1 3 ,
  7 3 1 3 ->= 5 6 1 3 ,
  6 1 2 2 -> 6 0 1 2 ,
  7 3 1 2 ->= 5 6 1 2 ,
  5 6 1 2 ->= 5 5 6 1 ,
  6 1 2 8 -> 6 0 1 8 ,
  7 3 1 8 ->= 5 6 1 8 ,
  5 6 1 8 ->= 5 5 6 4 }


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 2 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 1 0 1 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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 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 1 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 0 |
| 0 0 0 0 0 |
 \         /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 7->8 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 3 -> 0 0 1 3 ,
  4 5 5 6 ->= 1 7 8 3 ,
  0 1 2 2 -> 0 0 1 2 ,
  4 5 5 8 ->= 1 7 8 2 ,
  4 6 1 2 ->= 4 5 6 1 ,
  0 1 2 7 -> 0 0 1 7 ,
  4 6 1 7 ->= 4 5 6 4 ,
  3 1 2 3 -> 3 0 1 3 ,
  7 5 5 6 ->= 2 7 8 3 ,
  3 1 2 2 -> 3 0 1 2 ,
  7 6 1 2 ->= 7 5 6 1 ,
  3 1 2 7 -> 3 0 1 7 ,
  7 6 1 7 ->= 7 5 6 4 ,
  6 1 2 3 -> 6 0 1 3 ,
  8 3 1 3 ->= 5 6 1 3 ,
  6 1 2 2 -> 6 0 1 2 ,
  8 3 1 2 ->= 5 6 1 2 ,
  5 6 1 2 ->= 5 5 6 1 ,
  6 1 2 7 -> 6 0 1 7 ,
  8 3 1 7 ->= 5 6 1 7 ,
  5 6 1 7 ->= 5 5 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 0 |
| 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 1 |
| 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 { 4->0, 5->1, 6->2, 1->3, 7->4, 8->5, 3->6, 2->7 }, 
it remains to prove termination of the 12-rule system
{ 0 1 1 2 ->= 3 4 5 6 ,
  0 1 1 5 ->= 3 4 5 7 ,
  0 2 3 7 ->= 0 1 2 3 ,
  0 2 3 4 ->= 0 1 2 0 ,
  4 1 1 2 ->= 7 4 5 6 ,
  4 2 3 7 ->= 4 1 2 3 ,
  4 2 3 4 ->= 4 1 2 0 ,
  5 6 3 6 ->= 1 2 3 6 ,
  5 6 3 7 ->= 1 2 3 7 ,
  1 2 3 7 ->= 1 1 2 3 ,
  5 6 3 4 ->= 1 2 3 4 ,
  1 2 3 4 ->= 1 1 2 0 }

The system is trivially terminating.