/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 reversed.

Remains to prove termination of the 3-rule system
{ p a -> A a p ,
  A a -> a A ,
  A A p -> p a }


The dependency pairs transformation was applied.

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




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

(p,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 1 1 |
 \     /
(A,true) is interpreted by
 /     \
| 1 1 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(p,false) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 2 |
 \     /
(A,false) is interpreted by
 /     \
| 1 1 0 |
| 0 1 0 |
| 0 1 1 |
 \     /

Remains to prove termination of the 4-rule system
{ (p,true) (a,false) -> (A,true) (a,false) (p,false) ,
  (A,true) (a,false) -> (A,true) ,
  (p,false) (a,false) ->= (A,false) (a,false) (p,false) ,
  (A,false) (a,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:

(p,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(A,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(A,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ (A,true) (a,false) -> (A,true) ,
  (p,false) (a,false) ->= (A,false) (a,false) (p,false) ,
  (A,false) (a,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:

(p,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 |
 \   /
(p,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(A,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 2-rule system
{ (p,false) (a,false) ->= (A,false) (a,false) (p,false) ,
  (A,false) (a,false) ->= (a,false) (A,false) }


The system is trivially terminating.