/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:

P is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
Q is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ p p -> q q ,
  p Q Q -> Q Q p ,
  Q p q -> q p Q ,
  q q p -> p q q ,
  q Q -> ,
  Q q -> }


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

P is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
Q is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ p p -> q q ,
  p Q Q -> Q Q p ,
  Q p q -> q p Q ,
  q q p -> p q q }


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

P is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
Q is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
q is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ p Q Q -> Q Q p ,
  Q p q -> q p Q ,
  q q p -> p q q }


The system was reversed.

Remains to prove termination of the 3-rule system
{ Q Q p -> p Q Q ,
  q p Q -> Q p q ,
  p q q -> q q p }


The dependency pairs transformation was applied.

Remains to prove termination of the 12-rule system
{ (Q,true) (Q,false) (p,false) -> (p,true) (Q,false) (Q,false) ,
  (Q,true) (Q,false) (p,false) -> (Q,true) (Q,false) ,
  (Q,true) (Q,false) (p,false) -> (Q,true) ,
  (q,true) (p,false) (Q,false) -> (Q,true) (p,false) (q,false) ,
  (q,true) (p,false) (Q,false) -> (p,true) (q,false) ,
  (q,true) (p,false) (Q,false) -> (q,true) ,
  (p,true) (q,false) (q,false) -> (q,true) (q,false) (p,false) ,
  (p,true) (q,false) (q,false) -> (q,true) (p,false) ,
  (p,true) (q,false) (q,false) -> (p,true) ,
  (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }




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

(Q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(Q,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(p,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ (Q,true) (Q,false) (p,false) -> (p,true) (Q,false) (Q,false) ,
  (q,true) (p,false) (Q,false) -> (Q,true) (p,false) (q,false) ,
  (q,true) (p,false) (Q,false) -> (p,true) (q,false) ,
  (p,true) (q,false) (q,false) -> (q,true) (q,false) (p,false) ,
  (p,true) (q,false) (q,false) -> (q,true) (p,false) ,
  (p,true) (q,false) (q,false) -> (p,true) ,
  (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }


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

(Q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(Q,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(p,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ (Q,true) (Q,false) (p,false) -> (p,true) (Q,false) (Q,false) ,
  (q,true) (p,false) (Q,false) -> (Q,true) (p,false) (q,false) ,
  (p,true) (q,false) (q,false) -> (q,true) (q,false) (p,false) ,
  (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }


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

(Q,true) is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(Q,false) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 1 0 |
 \       /
(p,false) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
(p,true) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(q,true) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(q,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 5-rule system
{ (q,true) (p,false) (Q,false) -> (Q,true) (p,false) (q,false) ,
  (p,true) (q,false) (q,false) -> (q,true) (q,false) (p,false) ,
  (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }


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

(Q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(Q,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ (p,true) (q,false) (q,false) -> (q,true) (q,false) (p,false) ,
  (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }


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

(Q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(Q,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ (Q,false) (Q,false) (p,false) ->= (p,false) (Q,false) (Q,false) ,
  (q,false) (p,false) (Q,false) ->= (Q,false) (p,false) (q,false) ,
  (p,false) (q,false) (q,false) ->= (q,false) (q,false) (p,false) }


The system is trivially terminating.