/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:

f is interpreted by
 /     \
|  1 14 |
|  0  1 |
 \     /
b is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ a f -> f a a ,
  b b -> c c a c ,
  d b -> d a b ,
  c c -> d d d ,
  b d -> d b ,
  c d d -> f }


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

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

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


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

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

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


The dependency pairs transformation was applied.

Remains to prove termination of the 10-rule system
{ (a,true) (f,false) -> (a,true) (a,false) ,
  (a,true) (f,false) -> (a,true) ,
  (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
  (d,true) (b,false) -> (a,true) (b,false) ,
  (d,true) (b,false) -> (b,true) ,
  (b,true) (d,false) -> (d,true) (b,false) ,
  (b,true) (d,false) -> (b,true) ,
  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
  (b,false) (d,false) ->= (d,false) (b,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 |
 \   /
(f,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,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 |
 \   /
(d,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

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

Remains to prove termination of the 4-rule system
{ (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
  (b,false) (d,false) ->= (d,false) (b,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 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(f,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 0 |
 \     /
(d,true) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(b,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
(b,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(d,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


The system is trivially terminating.