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


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


YES

After renaming modulo { b->0, c->1, a->2 }, 
it remains to prove termination of the 3-rule system
{ 0 0 0 -> ,
  1 1 1 -> 2 2 ,
  2 ->= 2 1 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, [2, 1]->7, [1, 2]->8 },
it remains to prove termination of the 27-rule system
{ 0 0 0 0 -> 0 ,
  1 2 2 3 -> 4 5 6 ,
  4 6 ->= 4 7 3 0 ,
  0 0 0 1 -> 1 ,
  1 2 2 2 -> 4 5 7 ,
  4 7 ->= 4 7 3 1 ,
  0 0 0 4 -> 4 ,
  1 2 2 8 -> 4 5 5 ,
  4 5 ->= 4 7 3 4 ,
  3 0 0 0 -> 3 ,
  2 2 2 3 -> 8 5 6 ,
  8 6 ->= 8 7 3 0 ,
  3 0 0 1 -> 2 ,
  2 2 2 2 -> 8 5 7 ,
  8 7 ->= 8 7 3 1 ,
  3 0 0 4 -> 8 ,
  2 2 2 8 -> 8 5 5 ,
  8 5 ->= 8 7 3 4 ,
  6 0 0 0 -> 6 ,
  7 2 2 3 -> 5 5 6 ,
  5 6 ->= 5 7 3 0 ,
  6 0 0 1 -> 7 ,
  7 2 2 2 -> 5 5 7 ,
  5 7 ->= 5 7 3 1 ,
  6 0 0 4 -> 5 ,
  7 2 2 8 -> 5 5 5 ,
  5 5 ->= 5 7 3 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 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.