/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 7-rule system
{ 0 0 1 -> 1 2 1 ,
  2 1 0 -> 0 1 1 ,
  0 0 0 -> 0 1 2 ,
  0 2 2 ->= 1 1 1 ,
  2 2 0 ->= 0 2 2 ,
  1 2 0 ->= 0 0 2 ,
  0 2 2 ->= 1 1 0 }


The system was reversed.

After renaming modulo { 1->0, 0->1, 2->2 }, 
it remains to prove termination of the 7-rule system
{ 0 1 1 -> 0 2 0 ,
  1 0 2 -> 0 0 1 ,
  1 1 1 -> 2 0 1 ,
  2 2 1 ->= 0 0 0 ,
  1 2 2 ->= 2 2 1 ,
  1 2 0 ->= 2 1 1 ,
  2 2 1 ->= 1 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, 1]->2, [1, 0]->3, [0, 2]->4, [2, 0]->5, [2, 2]->6, [2, 1]->7, [1, 2]->8 },
it remains to prove termination of the 63-rule system
{ 0 1 2 3 -> 0 4 5 0 ,
  1 3 4 5 -> 0 0 1 3 ,
  1 2 2 3 -> 4 5 1 3 ,
  4 6 7 3 ->= 0 0 0 0 ,
  1 8 6 5 ->= 4 6 7 3 ,
  1 8 5 0 ->= 4 7 2 3 ,
  4 6 7 3 ->= 1 3 0 0 ,
  0 1 2 2 -> 0 4 5 1 ,
  1 3 4 7 -> 0 0 1 2 ,
  1 2 2 2 -> 4 5 1 2 ,
  4 6 7 2 ->= 0 0 0 1 ,
  1 8 6 7 ->= 4 6 7 2 ,
  1 8 5 1 ->= 4 7 2 2 ,
  4 6 7 2 ->= 1 3 0 1 ,
  0 1 2 8 -> 0 4 5 4 ,
  1 3 4 6 -> 0 0 1 8 ,
  1 2 2 8 -> 4 5 1 8 ,
  4 6 7 8 ->= 0 0 0 4 ,
  1 8 6 6 ->= 4 6 7 8 ,
  1 8 5 4 ->= 4 7 2 8 ,
  4 6 7 8 ->= 1 3 0 4 ,
  3 1 2 3 -> 3 4 5 0 ,
  2 3 4 5 -> 3 0 1 3 ,
  2 2 2 3 -> 8 5 1 3 ,
  8 6 7 3 ->= 3 0 0 0 ,
  2 8 6 5 ->= 8 6 7 3 ,
  2 8 5 0 ->= 8 7 2 3 ,
  8 6 7 3 ->= 2 3 0 0 ,
  3 1 2 2 -> 3 4 5 1 ,
  2 3 4 7 -> 3 0 1 2 ,
  2 2 2 2 -> 8 5 1 2 ,
  8 6 7 2 ->= 3 0 0 1 ,
  2 8 6 7 ->= 8 6 7 2 ,
  2 8 5 1 ->= 8 7 2 2 ,
  8 6 7 2 ->= 2 3 0 1 ,
  3 1 2 8 -> 3 4 5 4 ,
  2 3 4 6 -> 3 0 1 8 ,
  2 2 2 8 -> 8 5 1 8 ,
  8 6 7 8 ->= 3 0 0 4 ,
  2 8 6 6 ->= 8 6 7 8 ,
  2 8 5 4 ->= 8 7 2 8 ,
  8 6 7 8 ->= 2 3 0 4 ,
  5 1 2 3 -> 5 4 5 0 ,
  7 3 4 5 -> 5 0 1 3 ,
  7 2 2 3 -> 6 5 1 3 ,
  6 6 7 3 ->= 5 0 0 0 ,
  7 8 6 5 ->= 6 6 7 3 ,
  7 8 5 0 ->= 6 7 2 3 ,
  6 6 7 3 ->= 7 3 0 0 ,
  5 1 2 2 -> 5 4 5 1 ,
  7 3 4 7 -> 5 0 1 2 ,
  7 2 2 2 -> 6 5 1 2 ,
  6 6 7 2 ->= 5 0 0 1 ,
  7 8 6 7 ->= 6 6 7 2 ,
  7 8 5 1 ->= 6 7 2 2 ,
  6 6 7 2 ->= 7 3 0 1 ,
  5 1 2 8 -> 5 4 5 4 ,
  7 3 4 6 -> 5 0 1 8 ,
  7 2 2 8 -> 6 5 1 8 ,
  6 6 7 8 ->= 5 0 0 4 ,
  7 8 6 6 ->= 6 6 7 8 ,
  7 8 5 4 ->= 6 7 2 8 ,
  6 6 7 8 ->= 7 3 0 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 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 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 8->6, 7->7, 6->8 }, 
it remains to prove termination of the 35-rule system
{ 0 1 2 3 -> 0 4 5 0 ,
  1 2 2 3 -> 4 5 1 3 ,
  1 6 5 0 ->= 4 7 2 3 ,
  0 1 2 2 -> 0 4 5 1 ,
  1 2 2 2 -> 4 5 1 2 ,
  1 6 8 7 ->= 4 8 7 2 ,
  1 6 5 1 ->= 4 7 2 2 ,
  0 1 2 6 -> 0 4 5 4 ,
  1 2 2 6 -> 4 5 1 6 ,
  1 6 8 8 ->= 4 8 7 6 ,
  1 6 5 4 ->= 4 7 2 6 ,
  3 1 2 3 -> 3 4 5 0 ,
  2 2 2 3 -> 6 5 1 3 ,
  2 6 5 0 ->= 6 7 2 3 ,
  3 1 2 2 -> 3 4 5 1 ,
  2 2 2 2 -> 6 5 1 2 ,
  2 6 8 7 ->= 6 8 7 2 ,
  2 6 5 1 ->= 6 7 2 2 ,
  3 1 2 6 -> 3 4 5 4 ,
  2 2 2 6 -> 6 5 1 6 ,
  2 6 8 8 ->= 6 8 7 6 ,
  2 6 5 4 ->= 6 7 2 6 ,
  5 1 2 3 -> 5 4 5 0 ,
  7 2 2 3 -> 8 5 1 3 ,
  7 6 5 0 ->= 8 7 2 3 ,
  5 1 2 2 -> 5 4 5 1 ,
  7 3 4 7 -> 5 0 1 2 ,
  7 2 2 2 -> 8 5 1 2 ,
  7 6 8 7 ->= 8 8 7 2 ,
  7 6 5 1 ->= 8 7 2 2 ,
  5 1 2 6 -> 5 4 5 4 ,
  7 3 4 8 -> 5 0 1 6 ,
  7 2 2 6 -> 8 5 1 6 ,
  7 6 8 8 ->= 8 8 7 6 ,
  7 6 5 4 ->= 8 7 2 6 }


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 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 1 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 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 1 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
8 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 |
 \         /

After renaming modulo { 1->0, 2->1, 3->2, 4->3, 5->4, 6->5, 0->6, 7->7, 8->8 }, 
it remains to prove termination of the 31-rule system
{ 0 1 1 2 -> 3 4 0 2 ,
  0 5 4 6 ->= 3 7 1 2 ,
  6 0 1 1 -> 6 3 4 0 ,
  0 1 1 1 -> 3 4 0 1 ,
  0 5 8 7 ->= 3 8 7 1 ,
  0 5 4 0 ->= 3 7 1 1 ,
  6 0 1 5 -> 6 3 4 3 ,
  0 1 1 5 -> 3 4 0 5 ,
  0 5 8 8 ->= 3 8 7 5 ,
  0 5 4 3 ->= 3 7 1 5 ,
  1 1 1 2 -> 5 4 0 2 ,
  1 5 4 6 ->= 5 7 1 2 ,
  2 0 1 1 -> 2 3 4 0 ,
  1 1 1 1 -> 5 4 0 1 ,
  1 5 8 7 ->= 5 8 7 1 ,
  1 5 4 0 ->= 5 7 1 1 ,
  2 0 1 5 -> 2 3 4 3 ,
  1 1 1 5 -> 5 4 0 5 ,
  1 5 8 8 ->= 5 8 7 5 ,
  1 5 4 3 ->= 5 7 1 5 ,
  4 0 1 2 -> 4 3 4 6 ,
  7 1 1 2 -> 8 4 0 2 ,
  7 5 4 6 ->= 8 7 1 2 ,
  4 0 1 1 -> 4 3 4 0 ,
  7 1 1 1 -> 8 4 0 1 ,
  7 5 8 7 ->= 8 8 7 1 ,
  7 5 4 0 ->= 8 7 1 1 ,
  4 0 1 5 -> 4 3 4 3 ,
  7 1 1 5 -> 8 4 0 5 ,
  7 5 8 8 ->= 8 8 7 5 ,
  7 5 4 3 ->= 8 7 1 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 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 3 |
| 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 { 1->0, 5->1, 8->2, 7->3 }, 
it remains to prove termination of the 4-rule system
{ 0 1 2 3 ->= 1 2 3 0 ,
  0 1 2 2 ->= 1 2 3 1 ,
  3 1 2 3 ->= 2 2 3 0 ,
  3 1 2 2 ->= 2 2 3 1 }

The system is trivially terminating.