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


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


YES


The system was reversed.

Remains to prove termination of the 4-rule system
{ a d -> d b ,
  b -> a a a ,
  c d c -> d a ,
  d d b -> c d d c c }


The dependency pairs transformation was applied.

Remains to prove termination of the 16-rule system
{ (a,true) (d,false) -> (d,true) (b,false) ,
  (a,true) (d,false) -> (b,true) ,
  (b,true) -> (a,true) (a,false) (a,false) ,
  (b,true) -> (a,true) (a,false) ,
  (b,true) -> (a,true) ,
  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
  (c,true) (d,false) (c,false) -> (a,true) ,
  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (d,true) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (c,true) (c,false) ,
  (d,true) (d,false) (b,false) -> (c,true) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (b,false) ->= (a,false) (a,false) (a,false) ,
  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,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 1 |
| 0 1 |
 \   /
(d,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ (a,true) (d,false) -> (d,true) (b,false) ,
  (b,true) -> (a,true) (a,false) (a,false) ,
  (b,true) -> (a,true) (a,false) ,
  (b,true) -> (a,true) ,
  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (b,false) ->= (a,false) (a,false) (a,false) ,
  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,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 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ (a,true) (d,false) -> (d,true) (b,false) ,
  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (b,false) ->= (a,false) (a,false) (a,false) ,
  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

Remains to prove termination of the 6-rule system
{ (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (b,false) ->= (a,false) (a,false) (a,false) ,
  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,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 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
  (a,false) (d,false) ->= (d,false) (b,false) ,
  (b,false) ->= (a,false) (a,false) (a,false) ,
  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,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 0 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 0 1 |
| 0 0 0 0 |
 \       /
(d,true) is interpreted by
 /       \
| 1 0 1 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 1 0 0 |
| 0 1 0 0 |
 \       /
(b,true) 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 0 0 |
| 0 0 0 0 |
 \       /
(c,true) is interpreted by
 /       \
| 1 0 0 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 |
 \       /

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


The system is trivially terminating.