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


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 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 { 0->0, 1->1, 4->2, 5->3, 2->4, 6->5, 7->6, 3->7, 8->8 }, 
it remains to prove termination of the 30-rule system
{ 0 1 2 3 -> 0 0 1 4 ,
  5 6 4 0 -> 5 3 5 3 ,
  0 5 6 4 -> 5 3 1 4 ,
  5 6 2 3 ->= 0 5 6 4 ,
  5 6 4 1 -> 5 3 5 6 ,
  0 5 6 7 -> 5 3 1 7 ,
  0 1 2 8 -> 0 0 1 2 ,
  5 6 4 5 -> 5 3 5 8 ,
  0 5 6 2 -> 5 3 1 2 ,
  5 6 2 8 ->= 0 5 6 2 ,
  4 1 2 3 -> 4 0 1 4 ,
  2 6 4 0 -> 2 3 5 3 ,
  4 5 6 4 -> 2 3 1 4 ,
  2 6 2 3 ->= 4 5 6 4 ,
  2 6 4 1 -> 2 3 5 6 ,
  4 5 6 7 -> 2 3 1 7 ,
  4 1 2 8 -> 4 0 1 2 ,
  2 6 4 5 -> 2 3 5 8 ,
  4 5 6 2 -> 2 3 1 2 ,
  2 6 2 8 ->= 4 5 6 2 ,
  3 1 2 3 -> 3 0 1 4 ,
  8 6 4 0 -> 8 3 5 3 ,
  3 5 6 4 -> 8 3 1 4 ,
  8 6 2 3 ->= 3 5 6 4 ,
  8 6 4 1 -> 8 3 5 6 ,
  3 5 6 7 -> 8 3 1 7 ,
  3 1 2 8 -> 3 0 1 2 ,
  8 6 4 5 -> 8 3 5 8 ,
  3 5 6 2 -> 8 3 1 2 ,
  8 6 2 8 ->= 3 5 6 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 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 0 |
| 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, 8->7 }, 
it remains to prove termination of the 15-rule system
{ 0 1 2 3 -> 0 0 1 4 ,
  5 6 2 3 ->= 0 5 6 4 ,
  5 6 4 1 -> 5 3 5 6 ,
  0 1 2 7 -> 0 0 1 2 ,
  5 6 2 7 ->= 0 5 6 2 ,
  4 1 2 3 -> 4 0 1 4 ,
  2 6 2 3 ->= 4 5 6 4 ,
  2 6 4 1 -> 2 3 5 6 ,
  4 1 2 7 -> 4 0 1 2 ,
  2 6 2 7 ->= 4 5 6 2 ,
  3 1 2 3 -> 3 0 1 4 ,
  7 6 2 3 ->= 3 5 6 4 ,
  7 6 4 1 -> 7 3 5 6 ,
  3 1 2 7 -> 3 0 1 2 ,
  7 6 2 7 ->= 3 5 6 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 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 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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

The system is trivially terminating.