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


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


YES




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

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

Remains to prove termination of the 6-rule system
{ b d b -> c d b ,
  a d -> d c ,
  b b b -> a b c ,
  d c -> b d ,
  d c -> d b d ,
  d a c -> b b }


The system was reversed.

Remains to prove termination of the 6-rule system
{ b d b -> b d c ,
  d a -> c d ,
  b b b -> c b a ,
  c d -> d b ,
  c d -> d b d ,
  c a d -> b b }


The dependency pairs transformation was applied.

Remains to prove termination of the 20-rule system
{ (b,true) (d,false) (b,false) -> (b,true) (d,false) (c,false) ,
  (b,true) (d,false) (b,false) -> (d,true) (c,false) ,
  (b,true) (d,false) (b,false) -> (c,true) ,
  (d,true) (a,false) -> (c,true) (d,false) ,
  (d,true) (a,false) -> (d,true) ,
  (b,true) (b,false) (b,false) -> (c,true) (b,false) (a,false) ,
  (b,true) (b,false) (b,false) -> (b,true) (a,false) ,
  (c,true) (d,false) -> (d,true) (b,false) ,
  (c,true) (d,false) -> (b,true) ,
  (c,true) (d,false) -> (d,true) (b,false) (d,false) ,
  (c,true) (d,false) -> (b,true) (d,false) ,
  (c,true) (d,false) -> (d,true) ,
  (c,true) (a,false) (d,false) -> (b,true) (b,false) ,
  (c,true) (a,false) (d,false) -> (b,true) ,
  (b,false) (d,false) (b,false) ->= (b,false) (d,false) (c,false) ,
  (d,false) (a,false) ->= (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (c,false) (b,false) (a,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) (d,false) ,
  (c,false) (a,false) (d,false) ->= (b,false) (b,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 1 |
| 0 1 |
 \   /
(d,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(d,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 14-rule system
{ (b,true) (d,false) (b,false) -> (b,true) (d,false) (c,false) ,
  (d,true) (a,false) -> (c,true) (d,false) ,
  (b,true) (b,false) (b,false) -> (c,true) (b,false) (a,false) ,
  (c,true) (d,false) -> (d,true) (b,false) ,
  (c,true) (d,false) -> (b,true) ,
  (c,true) (d,false) -> (d,true) (b,false) (d,false) ,
  (c,true) (d,false) -> (b,true) (d,false) ,
  (c,true) (a,false) (d,false) -> (b,true) (b,false) ,
  (b,false) (d,false) (b,false) ->= (b,false) (d,false) (c,false) ,
  (d,false) (a,false) ->= (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (c,false) (b,false) (a,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) (d,false) ,
  (c,false) (a,false) (d,false) ->= (b,false) (b,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 |
 \     /
(d,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) 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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(c,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 1 0 |
 \     /

Remains to prove termination of the 13-rule system
{ (b,true) (d,false) (b,false) -> (b,true) (d,false) (c,false) ,
  (b,true) (b,false) (b,false) -> (c,true) (b,false) (a,false) ,
  (c,true) (d,false) -> (d,true) (b,false) ,
  (c,true) (d,false) -> (b,true) ,
  (c,true) (d,false) -> (d,true) (b,false) (d,false) ,
  (c,true) (d,false) -> (b,true) (d,false) ,
  (c,true) (a,false) (d,false) -> (b,true) (b,false) ,
  (b,false) (d,false) (b,false) ->= (b,false) (d,false) (c,false) ,
  (d,false) (a,false) ->= (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (c,false) (b,false) (a,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) (d,false) ,
  (c,false) (a,false) (d,false) ->= (b,false) (b,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 1 |
| 0 1 |
 \   /
(d,false) 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 |
 \   /
(d,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ (b,true) (d,false) (b,false) -> (b,true) (d,false) (c,false) ,
  (b,true) (b,false) (b,false) -> (c,true) (b,false) (a,false) ,
  (c,true) (d,false) -> (b,true) ,
  (c,true) (d,false) -> (b,true) (d,false) ,
  (c,true) (a,false) (d,false) -> (b,true) (b,false) ,
  (b,false) (d,false) (b,false) ->= (b,false) (d,false) (c,false) ,
  (d,false) (a,false) ->= (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (c,false) (b,false) (a,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) ,
  (c,false) (d,false) ->= (d,false) (b,false) (d,false) ,
  (c,false) (a,false) (d,false) ->= (b,false) (b,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 |
 \     /
(d,false) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) 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 |
 \     /
(c,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 1 1 |
 \     /

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


The system is trivially terminating.