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


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YES




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

R is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
r is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
P is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ r p -> p p r P ,
  r r -> ,
  r P P -> P P r ,
  p P -> ,
  P p -> }


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

R is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
r is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
P is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ r p -> p p r P ,
  r P P -> P P r ,
  p P -> ,
  P p -> }


The system was reversed.

Remains to prove termination of the 4-rule system
{ p r -> P r p p ,
  P P r -> r P P ,
  P p -> ,
  p P -> }


The dependency pairs transformation was applied.

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




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

(p,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(P,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(P,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ (p,true) (r,false) -> (p,true) (p,false) ,
  (p,true) (r,false) -> (p,true) ,
  (P,true) (P,false) (r,false) -> (P,true) (P,false) ,
  (P,true) (P,false) (r,false) -> (P,true) ,
  (p,false) (r,false) ->= (P,false) (r,false) (p,false) (p,false) ,
  (P,false) (P,false) (r,false) ->= (r,false) (P,false) (P,false) ,
  (P,false) (p,false) ->= ,
  (p,false) (P,false) ->= }


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

(p,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(P,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(P,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ (p,false) (r,false) ->= (P,false) (r,false) (p,false) (p,false) ,
  (P,false) (P,false) (r,false) ->= (r,false) (P,false) (P,false) ,
  (P,false) (p,false) ->= ,
  (p,false) (P,false) ->= }


The system is trivially terminating.