/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


The system was reversed.

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


The dependency pairs transformation was applied.

Remains to prove termination of the 17-rule system
{ (b,true) (b,false) (a,false) (a,false) -> (c,true) (c,false) (b,false) (b,false) ,
  (b,true) (b,false) (a,false) (a,false) -> (c,true) (b,false) (b,false) ,
  (b,true) (b,false) (a,false) (a,false) -> (b,true) (b,false) ,
  (b,true) (b,false) (a,false) (a,false) -> (b,true) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (c,true) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (c,true) ,
  (c,true) (c,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (c,false) (c,false) ,
  (c,true) (c,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (c,false) (c,false) ,
  (c,true) (c,false) (a,false) (a,false) -> (c,true) (c,false) ,
  (c,true) (c,false) (a,false) (a,false) -> (c,true) ,
  (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (c,false) (c,false) (b,false) (b,false) ,
  (c,false) (c,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,false) (c,false) (a,false) (a,false) ->= (b,false) (b,false) (a,false) (a,false) (c,false) (c,false) }




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

(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (b,false) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (b,true) (c,false) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (c,true) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (c,true) ,
  (c,true) (c,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (c,false) (c,false) ,
  (c,true) (c,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (c,false) (c,false) ,
  (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (c,false) (c,false) (b,false) (b,false) ,
  (c,false) (c,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,false) (c,false) (a,false) (a,false) ->= (b,false) (b,false) (a,false) (a,false) (c,false) (c,false) }


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

(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ (c,true) (c,false) (b,false) (b,false) -> (c,true) (c,false) ,
  (c,true) (c,false) (b,false) (b,false) -> (c,true) ,
  (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (c,false) (c,false) (b,false) (b,false) ,
  (c,false) (c,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,false) (c,false) (a,false) (a,false) ->= (b,false) (b,false) (a,false) (a,false) (c,false) (c,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

(b,true) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
(b,false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 1 1 1 0 |
 \         /
(a,false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
(c,true) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
(c,false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 2 0 |
| 0 1 2 0 0 |
| 0 0 1 1 1 |
 \         /

Remains to prove termination of the 3-rule system
{ (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (c,false) (c,false) (b,false) (b,false) ,
  (c,false) (c,false) (b,false) (b,false) ->= (b,false) (b,false) (b,false) (b,false) (c,false) (c,false) ,
  (c,false) (c,false) (a,false) (a,false) ->= (b,false) (b,false) (a,false) (a,false) (c,false) (c,false) }


The system is trivially terminating.