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


The length-preserving system was inverted.

After renaming modulo { 2->0, 0->1, 1->2 }, 
it remains to prove termination of the 6-rule system
{ 0 1 0 -> 1 2 0 ,
  2 2 2 -> 0 0 0 ,
  0 1 0 -> 0 0 0 ,
  2 0 2 ->= 2 2 0 ,
  1 2 2 ->= 1 0 1 ,
  0 2 1 ->= 2 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, 0]->2, [1, 2]->3, [2, 0]->4, [0, 2]->5, [2, 2]->6, [2, 1]->7, [1, 1]->8 },
it remains to prove termination of the 54-rule system
{ 0 1 2 0 -> 1 3 4 0 ,
  5 6 6 4 -> 0 0 0 0 ,
  0 1 2 0 -> 0 0 0 0 ,
  5 4 5 4 ->= 5 6 4 0 ,
  1 3 6 4 ->= 1 2 1 2 ,
  0 5 7 2 ->= 5 4 1 2 ,
  0 1 2 1 -> 1 3 4 1 ,
  5 6 6 7 -> 0 0 0 1 ,
  0 1 2 1 -> 0 0 0 1 ,
  5 4 5 7 ->= 5 6 4 1 ,
  1 3 6 7 ->= 1 2 1 8 ,
  0 5 7 8 ->= 5 4 1 8 ,
  0 1 2 5 -> 1 3 4 5 ,
  5 6 6 6 -> 0 0 0 5 ,
  0 1 2 5 -> 0 0 0 5 ,
  5 4 5 6 ->= 5 6 4 5 ,
  1 3 6 6 ->= 1 2 1 3 ,
  0 5 7 3 ->= 5 4 1 3 ,
  2 1 2 0 -> 8 3 4 0 ,
  3 6 6 4 -> 2 0 0 0 ,
  2 1 2 0 -> 2 0 0 0 ,
  3 4 5 4 ->= 3 6 4 0 ,
  8 3 6 4 ->= 8 2 1 2 ,
  2 5 7 2 ->= 3 4 1 2 ,
  2 1 2 1 -> 8 3 4 1 ,
  3 6 6 7 -> 2 0 0 1 ,
  2 1 2 1 -> 2 0 0 1 ,
  3 4 5 7 ->= 3 6 4 1 ,
  8 3 6 7 ->= 8 2 1 8 ,
  2 5 7 8 ->= 3 4 1 8 ,
  2 1 2 5 -> 8 3 4 5 ,
  3 6 6 6 -> 2 0 0 5 ,
  2 1 2 5 -> 2 0 0 5 ,
  3 4 5 6 ->= 3 6 4 5 ,
  8 3 6 6 ->= 8 2 1 3 ,
  2 5 7 3 ->= 3 4 1 3 ,
  4 1 2 0 -> 7 3 4 0 ,
  6 6 6 4 -> 4 0 0 0 ,
  4 1 2 0 -> 4 0 0 0 ,
  6 4 5 4 ->= 6 6 4 0 ,
  7 3 6 4 ->= 7 2 1 2 ,
  4 5 7 2 ->= 6 4 1 2 ,
  4 1 2 1 -> 7 3 4 1 ,
  6 6 6 7 -> 4 0 0 1 ,
  4 1 2 1 -> 4 0 0 1 ,
  6 4 5 7 ->= 6 6 4 1 ,
  7 3 6 7 ->= 7 2 1 8 ,
  4 5 7 8 ->= 6 4 1 8 ,
  4 1 2 5 -> 7 3 4 5 ,
  6 6 6 6 -> 4 0 0 5 ,
  4 1 2 5 -> 4 0 0 5 ,
  6 4 5 6 ->= 6 6 4 5 ,
  7 3 6 6 ->= 7 2 1 3 ,
  4 5 7 3 ->= 6 4 1 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 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 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 48-rule system
{ 0 1 2 0 -> 1 3 4 0 ,
  5 6 6 4 -> 0 0 0 0 ,
  0 1 2 0 -> 0 0 0 0 ,
  5 4 5 4 ->= 5 6 4 0 ,
  1 3 6 4 ->= 1 2 1 2 ,
  0 5 7 2 ->= 5 4 1 2 ,
  0 1 2 1 -> 1 3 4 1 ,
  5 6 6 7 -> 0 0 0 1 ,
  0 1 2 1 -> 0 0 0 1 ,
  5 4 5 7 ->= 5 6 4 1 ,
  0 5 7 8 ->= 5 4 1 8 ,
  0 1 2 5 -> 1 3 4 5 ,
  5 6 6 6 -> 0 0 0 5 ,
  0 1 2 5 -> 0 0 0 5 ,
  5 4 5 6 ->= 5 6 4 5 ,
  1 3 6 6 ->= 1 2 1 3 ,
  0 5 7 3 ->= 5 4 1 3 ,
  3 6 6 4 -> 2 0 0 0 ,
  2 1 2 0 -> 2 0 0 0 ,
  3 4 5 4 ->= 3 6 4 0 ,
  8 3 6 4 ->= 8 2 1 2 ,
  2 5 7 2 ->= 3 4 1 2 ,
  3 6 6 7 -> 2 0 0 1 ,
  2 1 2 1 -> 2 0 0 1 ,
  3 4 5 7 ->= 3 6 4 1 ,
  2 5 7 8 ->= 3 4 1 8 ,
  3 6 6 6 -> 2 0 0 5 ,
  2 1 2 5 -> 2 0 0 5 ,
  3 4 5 6 ->= 3 6 4 5 ,
  8 3 6 6 ->= 8 2 1 3 ,
  2 5 7 3 ->= 3 4 1 3 ,
  4 1 2 0 -> 7 3 4 0 ,
  6 6 6 4 -> 4 0 0 0 ,
  4 1 2 0 -> 4 0 0 0 ,
  6 4 5 4 ->= 6 6 4 0 ,
  7 3 6 4 ->= 7 2 1 2 ,
  4 5 7 2 ->= 6 4 1 2 ,
  4 1 2 1 -> 7 3 4 1 ,
  6 6 6 7 -> 4 0 0 1 ,
  4 1 2 1 -> 4 0 0 1 ,
  6 4 5 7 ->= 6 6 4 1 ,
  4 5 7 8 ->= 6 4 1 8 ,
  4 1 2 5 -> 7 3 4 5 ,
  6 6 6 6 -> 4 0 0 5 ,
  4 1 2 5 -> 4 0 0 5 ,
  6 4 5 6 ->= 6 6 4 5 ,
  7 3 6 6 ->= 7 2 1 3 ,
  4 5 7 3 ->= 6 4 1 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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 7 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 5 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.