/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 5-rule system
{ 0 1 0 -> 2 1 1 ,
  1 0 0 -> 1 1 0 ,
  1 2 2 ->= 1 0 0 ,
  2 1 2 ->= 0 2 2 ,
  2 1 0 ->= 0 2 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, [0, 2]->3, [2, 1]->4, [1, 1]->5, [1, 2]->6, [2, 2]->7, [2, 0]->8 },
it remains to prove termination of the 45-rule system
{ 0 1 2 0 -> 3 4 5 2 ,
  1 2 0 0 -> 1 5 2 0 ,
  1 6 7 8 ->= 1 2 0 0 ,
  3 4 6 8 ->= 0 3 7 8 ,
  3 4 2 0 ->= 0 3 4 2 ,
  0 1 2 1 -> 3 4 5 5 ,
  1 2 0 1 -> 1 5 2 1 ,
  1 6 7 4 ->= 1 2 0 1 ,
  3 4 6 4 ->= 0 3 7 4 ,
  3 4 2 1 ->= 0 3 4 5 ,
  0 1 2 3 -> 3 4 5 6 ,
  1 2 0 3 -> 1 5 2 3 ,
  1 6 7 7 ->= 1 2 0 3 ,
  3 4 6 7 ->= 0 3 7 7 ,
  3 4 2 3 ->= 0 3 4 6 ,
  2 1 2 0 -> 6 4 5 2 ,
  5 2 0 0 -> 5 5 2 0 ,
  5 6 7 8 ->= 5 2 0 0 ,
  6 4 6 8 ->= 2 3 7 8 ,
  6 4 2 0 ->= 2 3 4 2 ,
  2 1 2 1 -> 6 4 5 5 ,
  5 2 0 1 -> 5 5 2 1 ,
  5 6 7 4 ->= 5 2 0 1 ,
  6 4 6 4 ->= 2 3 7 4 ,
  6 4 2 1 ->= 2 3 4 5 ,
  2 1 2 3 -> 6 4 5 6 ,
  5 2 0 3 -> 5 5 2 3 ,
  5 6 7 7 ->= 5 2 0 3 ,
  6 4 6 7 ->= 2 3 7 7 ,
  6 4 2 3 ->= 2 3 4 6 ,
  8 1 2 0 -> 7 4 5 2 ,
  4 2 0 0 -> 4 5 2 0 ,
  4 6 7 8 ->= 4 2 0 0 ,
  7 4 6 8 ->= 8 3 7 8 ,
  7 4 2 0 ->= 8 3 4 2 ,
  8 1 2 1 -> 7 4 5 5 ,
  4 2 0 1 -> 4 5 2 1 ,
  4 6 7 4 ->= 4 2 0 1 ,
  7 4 6 4 ->= 8 3 7 4 ,
  7 4 2 1 ->= 8 3 4 5 ,
  8 1 2 3 -> 7 4 5 6 ,
  4 2 0 3 -> 4 5 2 3 ,
  4 6 7 7 ->= 4 2 0 3 ,
  7 4 6 7 ->= 8 3 7 7 ,
  7 4 2 3 ->= 8 3 4 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 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 0 |
| 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 { 1->0, 6->1, 7->2, 8->3, 2->4, 0->5, 3->6, 4->7, 5->8 }, 
it remains to prove termination of the 24-rule system
{ 0 1 2 3 ->= 0 4 5 5 ,
  6 7 1 3 ->= 5 6 2 3 ,
  6 7 4 5 ->= 5 6 7 4 ,
  0 1 2 7 ->= 0 4 5 0 ,
  6 7 1 7 ->= 5 6 2 7 ,
  0 1 2 2 ->= 0 4 5 6 ,
  6 7 1 2 ->= 5 6 2 2 ,
  6 7 4 6 ->= 5 6 7 1 ,
  8 1 2 3 ->= 8 4 5 5 ,
  1 7 1 3 ->= 4 6 2 3 ,
  1 7 4 5 ->= 4 6 7 4 ,
  8 1 2 7 ->= 8 4 5 0 ,
  1 7 1 7 ->= 4 6 2 7 ,
  8 1 2 2 ->= 8 4 5 6 ,
  1 7 1 2 ->= 4 6 2 2 ,
  1 7 4 6 ->= 4 6 7 1 ,
  7 1 2 3 ->= 7 4 5 5 ,
  2 7 1 3 ->= 3 6 2 3 ,
  2 7 4 5 ->= 3 6 7 4 ,
  7 1 2 7 ->= 7 4 5 0 ,
  2 7 1 7 ->= 3 6 2 7 ,
  7 1 2 2 ->= 7 4 5 6 ,
  2 7 1 2 ->= 3 6 2 2 ,
  2 7 4 6 ->= 3 6 7 1 }

The system is trivially terminating.