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


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


YES


The system was reversed.

Remains to prove termination of the 7-rule system
{ 1 q0 1 -> q1 1 0 ,
  0 q0 1 -> q1 0 0 ,
  1 q1 1 -> q1 1 1 ,
  0 q1 1 -> q1 0 1 ,
  q1 0 -> 1 q2 ,
  q2 1 -> 1 q2 ,
  q2 0 -> q0 0 }


The dependency pairs transformation was applied.

Remains to prove termination of the 24-rule system
{ (1,true) (q0,false) (1,false) -> (q1,true) (1,false) (0,false) ,
  (1,true) (q0,false) (1,false) -> (1,true) (0,false) ,
  (1,true) (q0,false) (1,false) -> (0,true) ,
  (0,true) (q0,false) (1,false) -> (q1,true) (0,false) (0,false) ,
  (0,true) (q0,false) (1,false) -> (0,true) (0,false) ,
  (0,true) (q0,false) (1,false) -> (0,true) ,
  (1,true) (q1,false) (1,false) -> (q1,true) (1,false) (1,false) ,
  (1,true) (q1,false) (1,false) -> (1,true) (1,false) ,
  (1,true) (q1,false) (1,false) -> (1,true) ,
  (0,true) (q1,false) (1,false) -> (q1,true) (0,false) (1,false) ,
  (0,true) (q1,false) (1,false) -> (0,true) (1,false) ,
  (0,true) (q1,false) (1,false) -> (1,true) ,
  (q1,true) (0,false) -> (1,true) (q2,false) ,
  (q1,true) (0,false) -> (q2,true) ,
  (q2,true) (1,false) -> (1,true) (q2,false) ,
  (q2,true) (1,false) -> (q2,true) ,
  (q2,true) (0,false) -> (0,true) ,
  (1,false) (q0,false) (1,false) ->= (q1,false) (1,false) (0,false) ,
  (0,false) (q0,false) (1,false) ->= (q1,false) (0,false) (0,false) ,
  (1,false) (q1,false) (1,false) ->= (q1,false) (1,false) (1,false) ,
  (0,false) (q1,false) (1,false) ->= (q1,false) (0,false) (1,false) ,
  (q1,false) (0,false) ->= (1,false) (q2,false) ,
  (q2,false) (1,false) ->= (1,false) (q2,false) ,
  (q2,false) (0,false) ->= (q0,false) (0,false) }




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

(1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 12-rule system
{ (1,true) (q0,false) (1,false) -> (q1,true) (1,false) (0,false) ,
  (1,true) (q1,false) (1,false) -> (q1,true) (1,false) (1,false) ,
  (q1,true) (0,false) -> (1,true) (q2,false) ,
  (q1,true) (0,false) -> (q2,true) ,
  (q2,true) (0,false) -> (0,true) ,
  (1,false) (q0,false) (1,false) ->= (q1,false) (1,false) (0,false) ,
  (0,false) (q0,false) (1,false) ->= (q1,false) (0,false) (0,false) ,
  (1,false) (q1,false) (1,false) ->= (q1,false) (1,false) (1,false) ,
  (0,false) (q1,false) (1,false) ->= (q1,false) (0,false) (1,false) ,
  (q1,false) (0,false) ->= (1,false) (q2,false) ,
  (q2,false) (1,false) ->= (1,false) (q2,false) ,
  (q2,false) (0,false) ->= (q0,false) (0,false) }


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

(1,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ (1,true) (q0,false) (1,false) -> (q1,true) (1,false) (0,false) ,
  (1,true) (q1,false) (1,false) -> (q1,true) (1,false) (1,false) ,
  (q1,true) (0,false) -> (1,true) (q2,false) ,
  (1,false) (q0,false) (1,false) ->= (q1,false) (1,false) (0,false) ,
  (0,false) (q0,false) (1,false) ->= (q1,false) (0,false) (0,false) ,
  (1,false) (q1,false) (1,false) ->= (q1,false) (1,false) (1,false) ,
  (0,false) (q1,false) (1,false) ->= (q1,false) (0,false) (1,false) ,
  (q1,false) (0,false) ->= (1,false) (q2,false) ,
  (q2,false) (1,false) ->= (1,false) (q2,false) ,
  (q2,false) (0,false) ->= (q0,false) (0,false) }


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

(1,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(q0,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(1,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(q1,true) is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
(0,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
(0,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(q1,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(q2,false) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
(q2,true) is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 9-rule system
{ (1,true) (q0,false) (1,false) -> (q1,true) (1,false) (0,false) ,
  (1,true) (q1,false) (1,false) -> (q1,true) (1,false) (1,false) ,
  (1,false) (q0,false) (1,false) ->= (q1,false) (1,false) (0,false) ,
  (0,false) (q0,false) (1,false) ->= (q1,false) (0,false) (0,false) ,
  (1,false) (q1,false) (1,false) ->= (q1,false) (1,false) (1,false) ,
  (0,false) (q1,false) (1,false) ->= (q1,false) (0,false) (1,false) ,
  (q1,false) (0,false) ->= (1,false) (q2,false) ,
  (q2,false) (1,false) ->= (1,false) (q2,false) ,
  (q2,false) (0,false) ->= (q0,false) (0,false) }


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

(1,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (1,false) (q0,false) (1,false) ->= (q1,false) (1,false) (0,false) ,
  (0,false) (q0,false) (1,false) ->= (q1,false) (0,false) (0,false) ,
  (1,false) (q1,false) (1,false) ->= (q1,false) (1,false) (1,false) ,
  (0,false) (q1,false) (1,false) ->= (q1,false) (0,false) (1,false) ,
  (q1,false) (0,false) ->= (1,false) (q2,false) ,
  (q2,false) (1,false) ->= (1,false) (q2,false) ,
  (q2,false) (0,false) ->= (q0,false) (0,false) }


The system is trivially terminating.