/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES


The dependency pairs transformation was applied.

Remains to prove termination of the 6-rule system
{ (a,true) (a,false) (b,false) -> (a,true) (a,false) (a,false) ,
  (a,true) (a,false) (b,false) -> (a,true) (a,false) ,
  (a,true) (a,false) (b,false) -> (a,true) ,
  (a,true) (c,false) -> (a,true) ,
  (a,false) (a,false) (b,false) ->= (c,false) (b,false) (a,false) (a,false) (a,false) ,
  (a,false) (c,false) ->= (b,false) (a,false) }




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

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

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


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

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

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


The system is trivially terminating.