/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

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


The length-preserving system was inverted.

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


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 4 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /

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

The system is trivially terminating.