/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:

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

Remains to prove termination of the 3-rule system
{ c b b -> a ,
  c -> b ,
  a a -> c b a c }


The dependency pairs transformation was applied.

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




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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


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

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

Remains to prove termination of the 3-rule system
{ (c,false) (b,false) (b,false) ->= (a,false) ,
  (c,false) ->= (b,false) ,
  (a,false) (a,false) ->= (c,false) (b,false) (a,false) (c,false) }


The system is trivially terminating.