/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:

q0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
x is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
y is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
bl 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 a -> a q1 ,
  q1 y -> y q1 ,
  a q1 b -> q2 a y ,
  a q2 a -> q2 a a ,
  a q2 y -> q2 a y ,
  y q1 b -> q2 y y ,
  y q2 a -> q2 y a ,
  y q2 y -> q2 y y ,
  q2 x -> x q0 ,
  q0 y -> y q3 ,
  q3 y -> y q3 ,
  q3 bl -> bl 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 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
x is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
y is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
bl 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 a -> a q1 ,
  q1 y -> y q1 ,
  a q2 a -> q2 a a ,
  a q2 y -> q2 a y ,
  y q2 a -> q2 y a ,
  y q2 y -> q2 y y ,
  q2 x -> x q0 ,
  q0 y -> y q3 ,
  q3 y -> y q3 ,
  q3 bl -> bl 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 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
x is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
y is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
bl 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 a -> a q1 ,
  q1 y -> y q1 ,
  a q2 a -> q2 a a ,
  a q2 y -> q2 a y ,
  y q2 a -> q2 y a ,
  y q2 y -> q2 y y ,
  q0 y -> y q3 ,
  q3 y -> y q3 ,
  q3 bl -> bl 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 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
x is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
y is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
bl is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ q1 a -> a q1 ,
  q1 y -> y q1 ,
  a q2 a -> q2 a a ,
  a q2 y -> q2 a y ,
  y q2 a -> q2 y a ,
  y q2 y -> q2 y y ,
  q3 y -> y q3 ,
  q3 bl -> bl 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 |
 \   /
a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
x is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
y is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
bl is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
q4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ q1 a -> a q1 ,
  q1 y -> y q1 ,
  a q2 a -> q2 a a ,
  a q2 y -> q2 a y ,
  y q2 a -> q2 y a ,
  y q2 y -> q2 y y ,
  q3 y -> y q3 }


The dependency pairs transformation was applied.

Remains to prove termination of the 21-rule system
{ (q1,true) (a,false) -> (a,true) (q1,false) ,
  (q1,true) (a,false) -> (q1,true) ,
  (q1,true) (y,false) -> (y,true) (q1,false) ,
  (q1,true) (y,false) -> (q1,true) ,
  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
  (a,true) (q2,false) (a,false) -> (a,true) ,
  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
  (a,true) (q2,false) (y,false) -> (y,true) ,
  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
  (y,true) (q2,false) (a,false) -> (a,true) ,
  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) ,
  (q3,true) (y,false) -> (y,true) (q3,false) ,
  (q3,true) (y,false) -> (q3,true) ,
  (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) 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 |
 \   /

Remains to prove termination of the 19-rule system
{ (q1,true) (a,false) -> (q1,true) ,
  (q1,true) (y,false) -> (q1,true) ,
  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
  (a,true) (q2,false) (a,false) -> (a,true) ,
  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
  (a,true) (q2,false) (y,false) -> (y,true) ,
  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
  (y,true) (q2,false) (a,false) -> (a,true) ,
  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) ,
  (q3,true) (y,false) -> (y,true) (q3,false) ,
  (q3,true) (y,false) -> (q3,true) ,
  (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) 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 |
 \   /

Remains to prove termination of the 16-rule system
{ (q1,true) (y,false) -> (q1,true) ,
  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
  (a,true) (q2,false) (y,false) -> (y,true) ,
  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) ,
  (q3,true) (y,false) -> (y,true) (q3,false) ,
  (q3,true) (y,false) -> (q3,true) ,
  (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) 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 |
 \   /

Remains to prove termination of the 15-rule system
{ (q1,true) (y,false) -> (q1,true) ,
  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) ,
  (q3,true) (y,false) -> (y,true) (q3,false) ,
  (q3,true) (y,false) -> (q3,true) ,
  (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(y,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) 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 |
 \   /

Remains to prove termination of the 11-rule system
{ (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
  (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,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 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(y,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q2,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(q3,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(q3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (q1,false) (a,false) ->= (a,false) (q1,false) ,
  (q1,false) (y,false) ->= (y,false) (q1,false) ,
  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
  (q3,false) (y,false) ->= (y,false) (q3,false) }


The system is trivially terminating.