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


The system was reversed.

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

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

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

The system is trivially terminating.