/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 6 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 5 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 5 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ b b -> c d ,
  c c -> d d d ,
  d c -> b f ,
  d d d -> a c ,
  f f -> f b }


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 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

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


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 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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


The system was reversed.

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


The dependency pairs transformation was applied.

Remains to prove termination of the 8-rule system
{ (b,true) (b,false) -> (c,true) ,
  (c,true) (d,false) -> (f,true) (b,false) ,
  (c,true) (d,false) -> (b,true) ,
  (f,true) (f,false) -> (b,true) (f,false) ,
  (f,true) (f,false) -> (f,true) ,
  (b,false) (b,false) ->= (d,false) (c,false) ,
  (c,false) (d,false) ->= (f,false) (b,false) ,
  (f,false) (f,false) ->= (b,false) (f,false) }




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

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

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


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

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

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


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

(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(d,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(f,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(f,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
{ (b,false) (b,false) ->= (d,false) (c,false) ,
  (c,false) (d,false) ->= (f,false) (b,false) ,
  (f,false) (f,false) ->= (b,false) (f,false) }


The system is trivially terminating.