/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


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})

Remains to prove termination of the 12-rule system
{ [b, b] [b, b] [b, b] -> [b, c] [c, c] [c, c] [c, c] [c, b] ,
  [b, c] [c, b] -> [b, b] ,
  [b, b] [b, c] [c, b] [b, b] -> [b, b] [b, b] [b, b] [b, b] ,
  [b, b] [b, b] [b, c] -> [b, c] [c, c] [c, c] [c, c] [c, c] ,
  [b, c] [c, c] -> [b, c] ,
  [b, b] [b, c] [c, b] [b, c] -> [b, b] [b, b] [b, b] [b, c] ,
  [c, b] [b, b] [b, b] -> [c, c] [c, c] [c, c] [c, c] [c, b] ,
  [c, c] [c, b] -> [c, b] ,
  [c, b] [b, c] [c, b] [b, b] -> [c, b] [b, b] [b, b] [b, b] ,
  [c, b] [b, b] [b, c] -> [c, c] [c, c] [c, c] [c, c] [c, c] ,
  [c, c] [c, c] -> [c, c] ,
  [c, b] [b, c] [c, b] [b, c] -> [c, b] [b, b] [b, b] [b, c] }



The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

[b, b] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[b, c] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[c, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ [b, b] [b, c] [c, b] [b, b] -> [b, b] [b, b] [b, b] [b, b] ,
  [b, c] [c, c] -> [b, c] ,
  [b, b] [b, c] [c, b] [b, c] -> [b, b] [b, b] [b, b] [b, c] ,
  [c, c] [c, b] -> [c, b] ,
  [c, b] [b, c] [c, b] [b, b] -> [c, b] [b, b] [b, b] [b, b] ,
  [c, c] [c, c] -> [c, c] ,
  [c, b] [b, c] [c, b] [b, c] -> [c, b] [b, b] [b, b] [b, c] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

[b, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, c] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[c, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ [b, c] [c, c] -> [b, c] ,
  [c, c] [c, b] -> [c, b] ,
  [c, c] [c, c] -> [c, c] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

[b, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, c] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[c, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 0-rule system
{ }


The system is trivially terminating.