/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:

q0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
0' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 15-rule system
{ q1 0 -> 0 q1 ,
  q1 1' -> 1' q1 ,
  0 q1 1 -> q2 0 1' ,
  0' q1 1 -> q2 0' 1' ,
  1' q1 1 -> q2 1' 1' ,
  0 q2 0 -> q2 0 0 ,
  0' q2 0 -> q2 0' 0 ,
  1' q2 0 -> q2 1' 0 ,
  0 q2 1' -> q2 0 1' ,
  0' q2 1' -> q2 0' 1' ,
  1' q2 1' -> q2 1' 1' ,
  q2 0' -> 0' q0 ,
  q0 1' -> 1' q3 ,
  q3 1' -> 1' q3 ,
  q3 b -> b q4 }


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

q0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 12-rule system
{ q1 0 -> 0 q1 ,
  q1 1' -> 1' q1 ,
  0 q2 0 -> q2 0 0 ,
  0' q2 0 -> q2 0' 0 ,
  1' q2 0 -> q2 1' 0 ,
  0 q2 1' -> q2 0 1' ,
  0' q2 1' -> q2 0' 1' ,
  1' q2 1' -> q2 1' 1' ,
  q2 0' -> 0' q0 ,
  q0 1' -> 1' q3 ,
  q3 1' -> 1' q3 ,
  q3 b -> b q4 }


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

q0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ q1 0 -> 0 q1 ,
  q1 1' -> 1' q1 ,
  0 q2 0 -> q2 0 0 ,
  0' q2 0 -> q2 0' 0 ,
  1' q2 0 -> q2 1' 0 ,
  0 q2 1' -> q2 0 1' ,
  0' q2 1' -> q2 0' 1' ,
  1' q2 1' -> q2 1' 1' ,
  q0 1' -> 1' q3 ,
  q3 1' -> 1' q3 ,
  q3 b -> b q4 }


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

q0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ q1 0 -> 0 q1 ,
  q1 1' -> 1' q1 ,
  0 q2 0 -> q2 0 0 ,
  0' q2 0 -> q2 0' 0 ,
  1' q2 0 -> q2 1' 0 ,
  0 q2 1' -> q2 0 1' ,
  0' q2 1' -> q2 0' 1' ,
  1' q2 1' -> q2 1' 1' ,
  q3 1' -> 1' q3 ,
  q3 b -> b q4 }


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

q0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1' is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ q1 0 -> 0 q1 ,
  q1 1' -> 1' q1 ,
  0 q2 0 -> q2 0 0 ,
  0' q2 0 -> q2 0' 0 ,
  1' q2 0 -> q2 1' 0 ,
  0 q2 1' -> q2 0 1' ,
  0' q2 1' -> q2 0' 1' ,
  1' q2 1' -> q2 1' 1' ,
  q3 1' -> 1' q3 }


The dependency pairs transformation was applied.

Remains to prove termination of the 27-rule system
{ (q1,true) (0,false) -> (0,true) (q1,false) ,
  (q1,true) (0,false) -> (q1,true) ,
  (q1,true) (1',false) -> (1',true) (q1,false) ,
  (q1,true) (1',false) -> (q1,true) ,
  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
  (0,true) (q2,false) (0,false) -> (0,true) ,
  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
  (0',true) (q2,false) (0,false) -> (0,true) ,
  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
  (1',true) (q2,false) (0,false) -> (0,true) ,
  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
  (0,true) (q2,false) (1',false) -> (1',true) ,
  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (1',true) ,
  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
  (1',true) (q2,false) (1',false) -> (1',true) ,
  (q3,true) (1',false) -> (1',true) (q3,false) ,
  (q3,true) (1',false) -> (q3,true) ,
  (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }




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

(q1,true) is interpreted by
 /   \
| 1 1 |
| 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 |
 \   /
(1',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 25-rule system
{ (q1,true) (0,false) -> (q1,true) ,
  (q1,true) (1',false) -> (q1,true) ,
  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
  (0,true) (q2,false) (0,false) -> (0,true) ,
  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
  (0',true) (q2,false) (0,false) -> (0,true) ,
  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
  (1',true) (q2,false) (0,false) -> (0,true) ,
  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
  (0,true) (q2,false) (1',false) -> (1',true) ,
  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (1',true) ,
  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
  (1',true) (q2,false) (1',false) -> (1',true) ,
  (q3,true) (1',false) -> (1',true) (q3,false) ,
  (q3,true) (1',false) -> (q3,true) ,
  (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }


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

(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 |
 \   /
(1',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 21-rule system
{ (q1,true) (1',false) -> (q1,true) ,
  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
  (0,true) (q2,false) (1',false) -> (1',true) ,
  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (1',true) ,
  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
  (1',true) (q2,false) (1',false) -> (1',true) ,
  (q3,true) (1',false) -> (1',true) (q3,false) ,
  (q3,true) (1',false) -> (q3,true) ,
  (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }


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

(q1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 20-rule system
{ (q1,true) (1',false) -> (q1,true) ,
  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (1',true) ,
  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
  (1',true) (q2,false) (1',false) -> (1',true) ,
  (q3,true) (1',false) -> (1',true) (q3,false) ,
  (q3,true) (1',false) -> (q3,true) ,
  (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }


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

(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 |
 \   /
(1',false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(1',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 15-rule system
{ (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
  (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }


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

(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 |
 \   /
(1',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(0',true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0',false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ (q1,false) (0,false) ->= (0,false) (q1,false) ,
  (q1,false) (1',false) ->= (1',false) (q1,false) ,
  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
  (q3,false) (1',false) ->= (1',false) (q3,false) }


The system is trivially terminating.