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


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


YES


The system was reversed.

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


The dependency pairs transformation was applied.

Remains to prove termination of the 10-rule system
{ (b,true) (a,false) -> (c,true) (b,false) ,
  (b,true) (a,false) -> (b,true) ,
  (c,true) (b,false) -> (b,true) (b,false) (c,false) ,
  (c,true) (b,false) -> (b,true) (c,false) ,
  (c,true) (b,false) -> (c,true) ,
  (c,true) (a,false) -> (b,true) (a,false) (c,false) ,
  (c,true) (a,false) -> (c,true) ,
  (b,false) (a,false) ->= (a,false) (c,false) (b,false) ,
  (c,false) (b,false) ->= (b,false) (b,false) (c,false) ,
  (c,false) (a,false) ->= (b,false) (a,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (c,true) (b,false) -> (b,true) (b,false) (c,false) ,
  (c,true) (b,false) -> (b,true) (c,false) ,
  (c,true) (b,false) -> (c,true) ,
  (c,true) (a,false) -> (b,true) (a,false) (c,false) ,
  (b,false) (a,false) ->= (a,false) (c,false) (b,false) ,
  (c,false) (b,false) ->= (b,false) (b,false) (c,false) ,
  (c,false) (a,false) ->= (b,false) (a,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ (c,true) (b,false) -> (c,true) ,
  (b,false) (a,false) ->= (a,false) (c,false) (b,false) ,
  (c,false) (b,false) ->= (b,false) (b,false) (c,false) ,
  (c,false) (a,false) ->= (b,false) (a,false) (c,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


The system is trivially terminating.