/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES




The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

g is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


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

g is interpreted by
 /       \
| 1 0 1 1 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
f is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 2-rule system
{ g g -> g f g ,
  f f g -> g f }


The dependency pairs transformation was applied.

Remains to prove termination of the 7-rule system
{ (g,true) (g,false) -> (g,true) (f,false) (g,false) ,
  (g,true) (g,false) -> (f,true) (g,false) ,
  (g,true) (g,false) -> (g,true) ,
  (f,true) (f,false) (g,false) -> (g,true) (f,false) ,
  (f,true) (f,false) (g,false) -> (f,true) ,
  (g,false) (g,false) ->= (g,false) (f,false) (g,false) ,
  (f,false) (f,false) (g,false) ->= (g,false) (f,false) }




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

(g,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(g,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(f,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(f,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

(g,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(g,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 |
 \   /

Remains to prove termination of the 3-rule system
{ (g,true) (g,false) -> (g,true) (f,false) (g,false) ,
  (g,false) (g,false) ->= (g,false) (f,false) (g,false) ,
  (f,false) (f,false) (g,false) ->= (g,false) (f,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

(g,true) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
(g,false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
(f,false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
 \         /
(f,true) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /

Remains to prove termination of the 2-rule system
{ (g,false) (g,false) ->= (g,false) (f,false) (g,false) ,
  (f,false) (f,false) (g,false) ->= (g,false) (f,false) }


The system is trivially terminating.