0.00/0.43	YES
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	q0 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	x is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q1 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	y is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q2 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q3 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	bl is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q4 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 12-rule system
0.00/0.45	{ q1 a -> a q1 ,
0.00/0.45	  q1 y -> y q1 ,
0.00/0.45	  a q1 b -> q2 a y ,
0.00/0.45	  a q2 a -> q2 a a ,
0.00/0.45	  a q2 y -> q2 a y ,
0.00/0.45	  y q1 b -> q2 y y ,
0.00/0.45	  y q2 a -> q2 y a ,
0.00/0.45	  y q2 y -> q2 y y ,
0.00/0.45	  q2 x -> x q0 ,
0.00/0.45	  q0 y -> y q3 ,
0.00/0.45	  q3 y -> y q3 ,
0.00/0.45	  q3 bl -> bl q4 }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	q0 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	x is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q1 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	y is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q2 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q3 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	bl is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q4 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 10-rule system
0.00/0.45	{ q1 a -> a q1 ,
0.00/0.45	  q1 y -> y q1 ,
0.00/0.45	  a q2 a -> q2 a a ,
0.00/0.45	  a q2 y -> q2 a y ,
0.00/0.45	  y q2 a -> q2 y a ,
0.00/0.45	  y q2 y -> q2 y y ,
0.00/0.45	  q2 x -> x q0 ,
0.00/0.45	  q0 y -> y q3 ,
0.00/0.45	  q3 y -> y q3 ,
0.00/0.45	  q3 bl -> bl q4 }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	q0 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	x is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q1 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	y is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q2 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q3 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	bl is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q4 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 9-rule system
0.00/0.45	{ q1 a -> a q1 ,
0.00/0.45	  q1 y -> y q1 ,
0.00/0.45	  a q2 a -> q2 a a ,
0.00/0.45	  a q2 y -> q2 a y ,
0.00/0.45	  y q2 a -> q2 y a ,
0.00/0.45	  y q2 y -> q2 y y ,
0.00/0.45	  q0 y -> y q3 ,
0.00/0.45	  q3 y -> y q3 ,
0.00/0.45	  q3 bl -> bl q4 }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	q0 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	x is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q1 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	y is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q2 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q3 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	bl is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q4 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 8-rule system
0.00/0.45	{ q1 a -> a q1 ,
0.00/0.45	  q1 y -> y q1 ,
0.00/0.45	  a q2 a -> q2 a a ,
0.00/0.45	  a q2 y -> q2 a y ,
0.00/0.45	  y q2 a -> q2 y a ,
0.00/0.45	  y q2 y -> q2 y y ,
0.00/0.45	  q3 y -> y q3 ,
0.00/0.45	  q3 bl -> bl q4 }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	q0 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	x is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q1 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	y is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q2 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q3 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	bl is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	q4 is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 7-rule system
0.00/0.45	{ q1 a -> a q1 ,
0.00/0.45	  q1 y -> y q1 ,
0.00/0.45	  a q2 a -> q2 a a ,
0.00/0.45	  a q2 y -> q2 a y ,
0.00/0.45	  y q2 a -> q2 y a ,
0.00/0.45	  y q2 y -> q2 y y ,
0.00/0.45	  q3 y -> y q3 }
0.00/0.45	
0.00/0.45	
0.00/0.45	The dependency pairs transformation was applied.
0.00/0.45	
0.00/0.45	Remains to prove termination of the 21-rule system
0.00/0.45	{ (q1,true) (a,false) -> (a,true) (q1,false) ,
0.00/0.45	  (q1,true) (a,false) -> (q1,true) ,
0.00/0.45	  (q1,true) (y,false) -> (y,true) (q1,false) ,
0.00/0.45	  (q1,true) (y,false) -> (q1,true) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (a,true) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (q3,true) (y,false) -> (y,true) (q3,false) ,
0.00/0.45	  (q3,true) (y,false) -> (q3,true) ,
0.00/0.45	  (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(q1,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q1,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q2,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 19-rule system
0.00/0.45	{ (q1,true) (a,false) -> (q1,true) ,
0.00/0.45	  (q1,true) (y,false) -> (q1,true) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (a,true) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (q3,true) (y,false) -> (y,true) (q3,false) ,
0.00/0.45	  (q3,true) (y,false) -> (q3,true) ,
0.00/0.45	  (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(q1,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q1,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q2,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 16-rule system
0.00/0.45	{ (q1,true) (y,false) -> (q1,true) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (q3,true) (y,false) -> (y,true) (q3,false) ,
0.00/0.45	  (q3,true) (y,false) -> (q3,true) ,
0.00/0.45	  (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(q1,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q1,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q2,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 15-rule system
0.00/0.45	{ (q1,true) (y,false) -> (q1,true) ,
0.00/0.45	  (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) ,
0.00/0.45	  (q3,true) (y,false) -> (y,true) (q3,false) ,
0.00/0.45	  (q3,true) (y,false) -> (q3,true) ,
0.00/0.45	  (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(q1,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q1,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q2,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 11-rule system
0.00/0.45	{ (a,true) (q2,false) (a,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,true) (q2,false) (y,false) -> (a,true) (y,false) ,
0.00/0.45	  (y,true) (q2,false) (a,false) -> (y,true) (a,false) ,
0.00/0.45	  (y,true) (q2,false) (y,false) -> (y,true) (y,false) ,
0.00/0.45	  (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(q1,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q1,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(y,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q2,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(q3,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 7-rule system
0.00/0.45	{ (q1,false) (a,false) ->= (a,false) (q1,false) ,
0.00/0.45	  (q1,false) (y,false) ->= (y,false) (q1,false) ,
0.00/0.45	  (a,false) (q2,false) (a,false) ->= (q2,false) (a,false) (a,false) ,
0.00/0.45	  (a,false) (q2,false) (y,false) ->= (q2,false) (a,false) (y,false) ,
0.00/0.45	  (y,false) (q2,false) (a,false) ->= (q2,false) (y,false) (a,false) ,
0.00/0.45	  (y,false) (q2,false) (y,false) ->= (q2,false) (y,false) (y,false) ,
0.00/0.45	  (q3,false) (y,false) ->= (y,false) (q3,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system is trivially terminating.
0.00/0.48	EOF