/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 19-rule system
{ (a,true) (d,false) -> (d,true) (b,false) ,
  (a,true) (d,false) -> (b,true) ,
  (a,true) -> (b,true) (b,false) (b,false) ,
  (a,true) -> (b,true) (b,false) ,
  (a,true) -> (b,true) ,
  (b,true) (d,false) (b,false) -> (a,true) (d,false) ,
  (b,true) (d,false) (b,false) -> (d,true) ,
  (b,true) (c,false) -> (d,true) (d,false) ,
  (b,true) (c,false) -> (d,true) ,
  (a,true) (c,false) -> (b,true) (b,false) (c,false) (d,false) ,
  (a,true) (c,false) -> (b,true) (c,false) (d,false) ,
  (a,true) (c,false) -> (d,true) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (a,false) ->= (b,false) (b,false) (b,false) ,
  (d,false) ->= ,
  (a,false) ->= ,
  (b,false) (d,false) (b,false) ->= (a,false) (d,false) ,
  (b,false) (c,false) ->= (c,false) (d,false) (d,false) ,
  (a,false) (c,false) ->= (b,false) (b,false) (c,false) (d,false) }




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

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

Remains to prove termination of the 16-rule system
{ (a,true) (d,false) -> (d,true) (b,false) ,
  (a,true) (d,false) -> (b,true) ,
  (a,true) -> (b,true) (b,false) (b,false) ,
  (a,true) -> (b,true) (b,false) ,
  (a,true) -> (b,true) ,
  (b,true) (d,false) (b,false) -> (a,true) (d,false) ,
  (b,true) (d,false) (b,false) -> (d,true) ,
  (a,true) (c,false) -> (b,true) (b,false) (c,false) (d,false) ,
  (a,true) (c,false) -> (b,true) (c,false) (d,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (a,false) ->= (b,false) (b,false) (b,false) ,
  (d,false) ->= ,
  (a,false) ->= ,
  (b,false) (d,false) (b,false) ->= (a,false) (d,false) ,
  (b,false) (c,false) ->= (c,false) (d,false) (d,false) ,
  (a,false) (c,false) ->= (b,false) (b,false) (c,false) (d,false) }


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

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

Remains to prove termination of the 14-rule system
{ (a,true) (d,false) -> (b,true) ,
  (a,true) -> (b,true) (b,false) (b,false) ,
  (a,true) -> (b,true) (b,false) ,
  (a,true) -> (b,true) ,
  (b,true) (d,false) (b,false) -> (a,true) (d,false) ,
  (a,true) (c,false) -> (b,true) (b,false) (c,false) (d,false) ,
  (a,true) (c,false) -> (b,true) (c,false) (d,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (a,false) ->= (b,false) (b,false) (b,false) ,
  (d,false) ->= ,
  (a,false) ->= ,
  (b,false) (d,false) (b,false) ->= (a,false) (d,false) ,
  (b,false) (c,false) ->= (c,false) (d,false) (d,false) ,
  (a,false) (c,false) ->= (b,false) (b,false) (c,false) (d,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 |
 \     /
(d,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
(d,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
(b,true) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(c,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(a,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /

Remains to prove termination of the 13-rule system
{ (a,true) -> (b,true) (b,false) (b,false) ,
  (a,true) -> (b,true) (b,false) ,
  (a,true) -> (b,true) ,
  (b,true) (d,false) (b,false) -> (a,true) (d,false) ,
  (a,true) (c,false) -> (b,true) (b,false) (c,false) (d,false) ,
  (a,true) (c,false) -> (b,true) (c,false) (d,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (a,false) ->= (b,false) (b,false) (b,false) ,
  (d,false) ->= ,
  (a,false) ->= ,
  (b,false) (d,false) (b,false) ->= (a,false) (d,false) ,
  (b,false) (c,false) ->= (c,false) (d,false) (d,false) ,
  (a,false) (c,false) ->= (b,false) (b,false) (c,false) (d,false) }


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

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

Remains to prove termination of the 12-rule system
{ (a,true) -> (b,true) (b,false) (b,false) ,
  (a,true) -> (b,true) (b,false) ,
  (a,true) -> (b,true) ,
  (a,true) (c,false) -> (b,true) (b,false) (c,false) (d,false) ,
  (a,true) (c,false) -> (b,true) (c,false) (d,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (a,false) ->= (b,false) (b,false) (b,false) ,
  (d,false) ->= ,
  (a,false) ->= ,
  (b,false) (d,false) (b,false) ->= (a,false) (d,false) ,
  (b,false) (c,false) ->= (c,false) (d,false) (d,false) ,
  (a,false) (c,false) ->= (b,false) (b,false) (c,false) (d,false) }


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

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

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


The system is trivially terminating.