/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 4-rule system
{ l a -> a l ,
  c a -> a c ,
  r a c -> a r ,
  a a r l -> r c c c l a a }


The dependency pairs transformation was applied.

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




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

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

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


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

(l,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(l,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 |
 \   /
(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ (r,true) (a,false) (c,false) -> (a,true) (r,false) ,
  (a,true) (a,false) (r,false) (l,false) -> (r,true) (c,false) (c,false) (c,false) (l,false) (a,false) (a,false) ,
  (a,true) (a,false) (r,false) (l,false) -> (c,true) (c,false) (c,false) (l,false) (a,false) (a,false) ,
  (a,true) (a,false) (r,false) (l,false) -> (c,true) (c,false) (l,false) (a,false) (a,false) ,
  (a,true) (a,false) (r,false) (l,false) -> (c,true) (l,false) (a,false) (a,false) ,
  (l,false) (a,false) ->= (a,false) (l,false) ,
  (c,false) (a,false) ->= (a,false) (c,false) ,
  (r,false) (a,false) (c,false) ->= (a,false) (r,false) ,
  (a,false) (a,false) (r,false) (l,false) ->= (r,false) (c,false) (c,false) (c,false) (l,false) (a,false) (a,false) }


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

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


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

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

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


The system is trivially terminating.