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


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


YES




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

r is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
e is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
w is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
i is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
t is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ r e -> w r ,
  i t -> e r ,
  e w -> r i ,
  w r -> i t ,
  r i t e r -> e w r i t e }


The dependency pairs transformation was applied.

Remains to prove termination of the 17-rule system
{ (r,true) (e,false) -> (w,true) (r,false) ,
  (r,true) (e,false) -> (r,true) ,
  (i,true) (t,false) -> (e,true) (r,false) ,
  (i,true) (t,false) -> (r,true) ,
  (e,true) (w,false) -> (r,true) (i,false) ,
  (e,true) (w,false) -> (i,true) ,
  (w,true) (r,false) -> (i,true) (t,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) (w,false) (r,false) (i,false) (t,false) (e,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (w,true) (r,false) (i,false) (t,false) (e,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (r,true) (i,false) (t,false) (e,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (i,true) (t,false) (e,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) ,
  (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }




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

(r,true) is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
(e,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(w,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
(i,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
(e,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(w,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(i,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ (r,true) (e,false) -> (w,true) (r,false) ,
  (i,true) (t,false) -> (e,true) (r,false) ,
  (e,true) (w,false) -> (r,true) (i,false) ,
  (w,true) (r,false) -> (i,true) (t,false) ,
  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) (w,false) (r,false) (i,false) (t,false) (e,false) ,
  (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }


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

(r,true) is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(e,false) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
(w,true) is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(r,false) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
(i,true) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(t,false) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
(e,true) is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
(w,false) is interpreted by
 /       \
| 1 0 0 1 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
(i,false) 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 8-rule system
{ (r,true) (e,false) -> (w,true) (r,false) ,
  (i,true) (t,false) -> (e,true) (r,false) ,
  (e,true) (w,false) -> (r,true) (i,false) ,
  (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }


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

(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(e,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(w,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(e,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(w,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (r,true) (e,false) -> (w,true) (r,false) ,
  (e,true) (w,false) -> (r,true) (i,false) ,
  (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }


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

(r,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(e,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(w,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(e,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(w,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ (r,true) (e,false) -> (w,true) (r,false) ,
  (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }


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

(r,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(e,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(w,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(r,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(t,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(e,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(w,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(i,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ (r,false) (e,false) ->= (w,false) (r,false) ,
  (i,false) (t,false) ->= (e,false) (r,false) ,
  (e,false) (w,false) ->= (r,false) (i,false) ,
  (w,false) (r,false) ->= (i,false) (t,false) ,
  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }


The system is trivially terminating.