/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 5-rule system
{ s a -> a s ,
  s b a b -> a s b a ,
  b b a b -> s c ,
  s c -> b a b a ,
  a a b a -> a b a b }


The dependency pairs transformation was applied.

Remains to prove termination of the 20-rule system
{ (s,true) (a,false) -> (a,true) (s,false) ,
  (s,true) (a,false) -> (s,true) ,
  (s,true) (b,false) (a,false) (b,false) -> (a,true) (s,false) (b,false) (a,false) ,
  (s,true) (b,false) (a,false) (b,false) -> (s,true) (b,false) (a,false) ,
  (s,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) ,
  (s,true) (b,false) (a,false) (b,false) -> (a,true) ,
  (b,true) (b,false) (a,false) (b,false) -> (s,true) (c,false) ,
  (s,true) (c,false) -> (b,true) (a,false) (b,false) (a,false) ,
  (s,true) (c,false) -> (a,true) (b,false) (a,false) ,
  (s,true) (c,false) -> (b,true) (a,false) ,
  (s,true) (c,false) -> (a,true) ,
  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (b,true) ,
  (s,false) (a,false) ->= (a,false) (s,false) ,
  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
  (b,false) (b,false) (a,false) (b,false) ->= (s,false) (c,false) ,
  (s,false) (c,false) ->= (b,false) (a,false) (b,false) (a,false) ,
  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }




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

(s,true) is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(s,false) is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ (s,true) (a,false) -> (a,true) (s,false) ,
  (s,true) (b,false) (a,false) (b,false) -> (a,true) (s,false) (b,false) (a,false) ,
  (b,true) (b,false) (a,false) (b,false) -> (s,true) (c,false) ,
  (s,true) (c,false) -> (b,true) (a,false) (b,false) (a,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
  (s,false) (a,false) ->= (a,false) (s,false) ,
  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
  (b,false) (b,false) (a,false) (b,false) ->= (s,false) (c,false) ,
  (s,false) (c,false) ->= (b,false) (a,false) (b,false) (a,false) ,
  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }


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

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

Remains to prove termination of the 8-rule system
{ (b,true) (b,false) (a,false) (b,false) -> (s,true) (c,false) ,
  (s,true) (c,false) -> (b,true) (a,false) (b,false) (a,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
  (s,false) (a,false) ->= (a,false) (s,false) ,
  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
  (b,false) (b,false) (a,false) (b,false) ->= (s,false) (c,false) ,
  (s,false) (c,false) ->= (b,false) (a,false) (b,false) (a,false) ,
  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

Remains to prove termination of the 7-rule system
{ (s,true) (c,false) -> (b,true) (a,false) (b,false) (a,false) ,
  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
  (s,false) (a,false) ->= (a,false) (s,false) ,
  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
  (b,false) (b,false) (a,false) (b,false) ->= (s,false) (c,false) ,
  (s,false) (c,false) ->= (b,false) (a,false) (b,false) (a,false) ,
  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }


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

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

Remains to prove termination of the 6-rule system
{ (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
  (s,false) (a,false) ->= (a,false) (s,false) ,
  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
  (b,false) (b,false) (a,false) (b,false) ->= (s,false) (c,false) ,
  (s,false) (c,false) ->= (b,false) (a,false) (b,false) (a,false) ,
  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

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


The system is trivially terminating.