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


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


YES




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

c is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ c c c a -> d d ,
  d b -> c c ,
  b c -> b a c ,
  d -> b c }


The system was reversed.

Remains to prove termination of the 4-rule system
{ a c c c -> d d ,
  b d -> c c ,
  c b -> c a b ,
  d -> c b }


The dependency pairs transformation was applied.

Remains to prove termination of the 13-rule system
{ (a,true) (c,false) (c,false) (c,false) -> (d,true) (d,false) ,
  (a,true) (c,false) (c,false) (c,false) -> (d,true) ,
  (b,true) (d,false) -> (c,true) (c,false) ,
  (b,true) (d,false) -> (c,true) ,
  (c,true) (b,false) -> (c,true) (a,false) (b,false) ,
  (c,true) (b,false) -> (a,true) (b,false) ,
  (c,true) (b,false) -> (b,true) ,
  (d,true) -> (c,true) (b,false) ,
  (d,true) -> (b,true) ,
  (a,false) (c,false) (c,false) (c,false) ->= (d,false) (d,false) ,
  (b,false) (d,false) ->= (c,false) (c,false) ,
  (c,false) (b,false) ->= (c,false) (a,false) (b,false) ,
  (d,false) ->= (c,false) (b,false) }




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

(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
(d,true) is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
(d,false) is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

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

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


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

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

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


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

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

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


The system is trivially terminating.