/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

After renaming modulo { c->0, a->1, b->2 }, 
it remains to prove termination of the 7-rule system
{ 0 1 1 -> 1 0 1 ,
  1 0 0 -> 1 0 2 ,
  1 2 2 -> 1 1 2 ,
  1 0 0 ->= 0 1 2 ,
  1 1 2 ->= 0 1 2 ,
  1 2 2 ->= 1 2 0 ,
  1 1 1 ->= 0 2 1 }


The length-preserving system was inverted.

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


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

After renaming modulo { 0->0, 1->1, 2->2 }, 
it remains to prove termination of the 6-rule system
{ 0 1 0 -> 1 0 0 ,
  0 0 2 -> 0 2 2 ,
  1 0 2 ->= 0 1 1 ,
  1 0 2 ->= 0 0 2 ,
  0 2 1 ->= 0 2 2 ,
  1 2 0 ->= 0 0 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, 0]->4, [2, 2]->5, [1, 1]->6, [2, 1]->7, [1, 2]->8 },
it remains to prove termination of the 54-rule system
{ 0 1 2 0 -> 1 2 0 0 ,
  0 0 3 4 -> 0 3 5 4 ,
  1 2 3 4 ->= 0 1 6 2 ,
  1 2 3 4 ->= 0 0 3 4 ,
  0 3 7 2 ->= 0 3 5 4 ,
  1 8 4 0 ->= 0 0 0 0 ,
  0 1 2 1 -> 1 2 0 1 ,
  0 0 3 7 -> 0 3 5 7 ,
  1 2 3 7 ->= 0 1 6 6 ,
  1 2 3 7 ->= 0 0 3 7 ,
  0 3 7 6 ->= 0 3 5 7 ,
  1 8 4 1 ->= 0 0 0 1 ,
  0 1 2 3 -> 1 2 0 3 ,
  0 0 3 5 -> 0 3 5 5 ,
  1 2 3 5 ->= 0 1 6 8 ,
  1 2 3 5 ->= 0 0 3 5 ,
  0 3 7 8 ->= 0 3 5 5 ,
  1 8 4 3 ->= 0 0 0 3 ,
  2 1 2 0 -> 6 2 0 0 ,
  2 0 3 4 -> 2 3 5 4 ,
  6 2 3 4 ->= 2 1 6 2 ,
  6 2 3 4 ->= 2 0 3 4 ,
  2 3 7 2 ->= 2 3 5 4 ,
  6 8 4 0 ->= 2 0 0 0 ,
  2 1 2 1 -> 6 2 0 1 ,
  2 0 3 7 -> 2 3 5 7 ,
  6 2 3 7 ->= 2 1 6 6 ,
  6 2 3 7 ->= 2 0 3 7 ,
  2 3 7 6 ->= 2 3 5 7 ,
  6 8 4 1 ->= 2 0 0 1 ,
  2 1 2 3 -> 6 2 0 3 ,
  2 0 3 5 -> 2 3 5 5 ,
  6 2 3 5 ->= 2 1 6 8 ,
  6 2 3 5 ->= 2 0 3 5 ,
  2 3 7 8 ->= 2 3 5 5 ,
  6 8 4 3 ->= 2 0 0 3 ,
  4 1 2 0 -> 7 2 0 0 ,
  4 0 3 4 -> 4 3 5 4 ,
  7 2 3 4 ->= 4 1 6 2 ,
  7 2 3 4 ->= 4 0 3 4 ,
  4 3 7 2 ->= 4 3 5 4 ,
  7 8 4 0 ->= 4 0 0 0 ,
  4 1 2 1 -> 7 2 0 1 ,
  4 0 3 7 -> 4 3 5 7 ,
  7 2 3 7 ->= 4 1 6 6 ,
  7 2 3 7 ->= 4 0 3 7 ,
  4 3 7 6 ->= 4 3 5 7 ,
  7 8 4 1 ->= 4 0 0 1 ,
  4 1 2 3 -> 7 2 0 3 ,
  4 0 3 5 -> 4 3 5 5 ,
  7 2 3 5 ->= 4 1 6 8 ,
  7 2 3 5 ->= 4 0 3 5 ,
  4 3 7 8 ->= 4 3 5 5 ,
  7 8 4 3 ->= 4 0 0 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 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 |
 \   /
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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 8->7, 6->8 }, 
it remains to prove termination of the 45-rule system
{ 0 1 2 0 -> 1 2 0 0 ,
  0 0 3 4 -> 0 3 5 4 ,
  1 2 3 4 ->= 0 0 3 4 ,
  0 3 6 2 ->= 0 3 5 4 ,
  1 7 4 0 ->= 0 0 0 0 ,
  0 1 2 1 -> 1 2 0 1 ,
  0 0 3 6 -> 0 3 5 6 ,
  1 2 3 6 ->= 0 0 3 6 ,
  0 3 6 8 ->= 0 3 5 6 ,
  1 7 4 1 ->= 0 0 0 1 ,
  0 1 2 3 -> 1 2 0 3 ,
  0 0 3 5 -> 0 3 5 5 ,
  1 2 3 5 ->= 0 0 3 5 ,
  0 3 6 7 ->= 0 3 5 5 ,
  1 7 4 3 ->= 0 0 0 3 ,
  2 1 2 0 -> 8 2 0 0 ,
  2 0 3 4 -> 2 3 5 4 ,
  8 2 3 4 ->= 2 0 3 4 ,
  2 3 6 2 ->= 2 3 5 4 ,
  8 7 4 0 ->= 2 0 0 0 ,
  2 1 2 1 -> 8 2 0 1 ,
  2 0 3 6 -> 2 3 5 6 ,
  8 2 3 6 ->= 2 0 3 6 ,
  2 3 6 8 ->= 2 3 5 6 ,
  8 7 4 1 ->= 2 0 0 1 ,
  2 1 2 3 -> 8 2 0 3 ,
  2 0 3 5 -> 2 3 5 5 ,
  8 2 3 5 ->= 2 0 3 5 ,
  2 3 6 7 ->= 2 3 5 5 ,
  8 7 4 3 ->= 2 0 0 3 ,
  4 1 2 0 -> 6 2 0 0 ,
  4 0 3 4 -> 4 3 5 4 ,
  6 2 3 4 ->= 4 0 3 4 ,
  4 3 6 2 ->= 4 3 5 4 ,
  6 7 4 0 ->= 4 0 0 0 ,
  4 1 2 1 -> 6 2 0 1 ,
  4 0 3 6 -> 4 3 5 6 ,
  6 2 3 6 ->= 4 0 3 6 ,
  4 3 6 8 ->= 4 3 5 6 ,
  6 7 4 1 ->= 4 0 0 1 ,
  4 1 2 3 -> 6 2 0 3 ,
  4 0 3 5 -> 4 3 5 5 ,
  6 2 3 5 ->= 4 0 3 5 ,
  4 3 6 7 ->= 4 3 5 5 ,
  6 7 4 3 ->= 4 0 0 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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 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, 7->5, 6->6, 5->7, 8->8 }, 
it remains to prove termination of the 27-rule system
{ 0 1 2 0 -> 1 2 0 0 ,
  1 2 3 4 ->= 0 0 3 4 ,
  1 5 4 0 ->= 0 0 0 0 ,
  0 1 2 1 -> 1 2 0 1 ,
  1 2 3 6 ->= 0 0 3 6 ,
  1 5 4 1 ->= 0 0 0 1 ,
  0 1 2 3 -> 1 2 0 3 ,
  1 2 3 7 ->= 0 0 3 7 ,
  1 5 4 3 ->= 0 0 0 3 ,
  2 1 2 0 -> 8 2 0 0 ,
  8 2 3 4 ->= 2 0 3 4 ,
  8 5 4 0 ->= 2 0 0 0 ,
  2 1 2 1 -> 8 2 0 1 ,
  8 2 3 6 ->= 2 0 3 6 ,
  8 5 4 1 ->= 2 0 0 1 ,
  2 1 2 3 -> 8 2 0 3 ,
  8 2 3 7 ->= 2 0 3 7 ,
  8 5 4 3 ->= 2 0 0 3 ,
  4 1 2 0 -> 6 2 0 0 ,
  6 2 3 4 ->= 4 0 3 4 ,
  6 5 4 0 ->= 4 0 0 0 ,
  4 1 2 1 -> 6 2 0 1 ,
  6 2 3 6 ->= 4 0 3 6 ,
  6 5 4 1 ->= 4 0 0 1 ,
  4 1 2 3 -> 6 2 0 3 ,
  6 2 3 7 ->= 4 0 3 7 ,
  6 5 4 3 ->= 4 0 0 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 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 0 |
| 0 1 |
 \   /
8 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 2 0 0 ,
  0 1 2 1 -> 1 2 0 1 ,
  0 1 2 3 -> 1 2 0 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 1 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 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 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 |
 \         /
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 1 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 -> 1 2 0 0 ,
  0 1 2 1 -> 1 2 0 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 0 0 |
| 0 1 0 0 0 |
| 0 0 1 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 1 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 |
 \         /

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

The system is trivially terminating.