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


The system was reversed.

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

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

The system is trivially terminating.