/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 18 |
|  0  1 |
 \     /
b is interpreted by
 /     \
|  1 12 |
|  0  1 |
 \     /
d is interpreted by
 /   \
| 1 5 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /
f is interpreted by
 /     \
|  1 18 |
|  0  1 |
 \     /

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


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

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


The dependency pairs transformation was applied.

Remains to prove termination of the 14-rule system
{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
  (a,true) (a,false) -> (b,true) (b,false) ,
  (a,true) (a,false) -> (b,true) ,
  (a,true) -> (c,true) (d,false) ,
  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
  (b,true) (b,false) (b,false) -> (f,true) ,
  (c,true) (d,false) (d,false) -> (f,true) ,
  (f,true) (f,false) -> (f,true) (a,false) ,
  (f,true) (f,false) -> (a,true) ,
  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
  (a,false) ->= (d,false) (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
  (c,false) (d,false) (d,false) ->= (f,false) ,
  (f,false) (f,false) ->= (f,false) (a,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 3 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(d,false) is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
(f,false) is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
(f,true) is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

Remains to prove termination of the 9-rule system
{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
  (c,true) (d,false) (d,false) -> (f,true) ,
  (f,true) (f,false) -> (f,true) (a,false) ,
  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
  (a,false) ->= (d,false) (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
  (c,false) (d,false) (d,false) ->= (f,false) ,
  (f,false) (f,false) ->= (f,false) (a,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(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,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(f,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) (a,false) -> (b,true) (b,false) (b,false) ,
  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
  (f,true) (f,false) -> (f,true) (a,false) ,
  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
  (a,false) ->= (d,false) (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
  (c,false) (d,false) (d,false) ->= (f,false) ,
  (f,false) (f,false) ->= (f,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,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 1 0 |
 \     /
(c,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 |
 \     /
(f,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(f,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(c,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 7-rule system
{ (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
  (f,true) (f,false) -> (f,true) (a,false) ,
  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
  (a,false) ->= (d,false) (c,false) (d,false) ,
  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
  (c,false) (d,false) (d,false) ->= (f,false) ,
  (f,false) (f,false) ->= (f,false) (a,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 1 |
| 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,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(f,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

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


The system is trivially terminating.