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


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


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


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 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, 8->5, 7->6, 6->7, 5->8 }, 
it remains to prove termination of the 30-rule system
{ 0 0 0 0 -> 1 2 3 4 ,
  0 0 1 4 ->= 1 4 0 0 ,
  1 5 5 4 ->= 1 4 0 0 ,
  0 0 0 1 -> 1 2 3 5 ,
  0 0 1 5 ->= 1 4 0 1 ,
  1 5 5 5 ->= 1 4 0 1 ,
  0 0 0 6 -> 1 2 3 2 ,
  0 0 1 2 ->= 1 4 0 6 ,
  1 5 5 2 ->= 1 4 0 6 ,
  4 0 0 0 -> 5 2 3 4 ,
  4 0 1 4 ->= 5 4 0 0 ,
  5 5 5 4 ->= 5 4 0 0 ,
  4 0 0 1 -> 5 2 3 5 ,
  4 0 1 5 ->= 5 4 0 1 ,
  5 5 5 5 ->= 5 4 0 1 ,
  4 0 0 6 -> 5 2 3 2 ,
  4 0 1 2 ->= 5 4 0 6 ,
  5 5 5 2 ->= 5 4 0 6 ,
  7 0 0 0 -> 3 2 3 4 ,
  3 2 8 7 -> 8 7 6 7 ,
  7 0 1 4 ->= 3 4 0 0 ,
  3 5 5 4 ->= 3 4 0 0 ,
  7 0 0 1 -> 3 2 3 5 ,
  3 2 8 3 -> 8 7 6 3 ,
  7 0 1 5 ->= 3 4 0 1 ,
  3 5 5 5 ->= 3 4 0 1 ,
  7 0 0 6 -> 3 2 3 2 ,
  3 2 8 8 -> 8 7 6 8 ,
  7 0 1 2 ->= 3 4 0 6 ,
  3 5 5 2 ->= 3 4 0 6 }


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

The system is trivially terminating.