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


The length-preserving system was inverted.

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

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

The system is trivially terminating.