0.00/0.47	YES
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	q0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q2 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q3 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	b is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q4 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 15-rule system
0.00/0.49	{ q1 0 -> 0 q1 ,
0.00/0.49	  q1 1' -> 1' q1 ,
0.00/0.49	  0 q1 1 -> q2 0 1' ,
0.00/0.49	  0' q1 1 -> q2 0' 1' ,
0.00/0.49	  1' q1 1 -> q2 1' 1' ,
0.00/0.49	  0 q2 0 -> q2 0 0 ,
0.00/0.49	  0' q2 0 -> q2 0' 0 ,
0.00/0.49	  1' q2 0 -> q2 1' 0 ,
0.00/0.49	  0 q2 1' -> q2 0 1' ,
0.00/0.49	  0' q2 1' -> q2 0' 1' ,
0.00/0.49	  1' q2 1' -> q2 1' 1' ,
0.00/0.49	  q2 0' -> 0' q0 ,
0.00/0.49	  q0 1' -> 1' q3 ,
0.00/0.49	  q3 1' -> 1' q3 ,
0.00/0.49	  q3 b -> b q4 }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	q0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q2 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q3 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	b is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q4 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 12-rule system
0.00/0.49	{ q1 0 -> 0 q1 ,
0.00/0.49	  q1 1' -> 1' q1 ,
0.00/0.49	  0 q2 0 -> q2 0 0 ,
0.00/0.49	  0' q2 0 -> q2 0' 0 ,
0.00/0.49	  1' q2 0 -> q2 1' 0 ,
0.00/0.49	  0 q2 1' -> q2 0 1' ,
0.00/0.49	  0' q2 1' -> q2 0' 1' ,
0.00/0.49	  1' q2 1' -> q2 1' 1' ,
0.00/0.49	  q2 0' -> 0' q0 ,
0.00/0.49	  q0 1' -> 1' q3 ,
0.00/0.49	  q3 1' -> 1' q3 ,
0.00/0.49	  q3 b -> b q4 }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	q0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q2 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q3 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	b is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q4 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 11-rule system
0.00/0.49	{ q1 0 -> 0 q1 ,
0.00/0.49	  q1 1' -> 1' q1 ,
0.00/0.49	  0 q2 0 -> q2 0 0 ,
0.00/0.49	  0' q2 0 -> q2 0' 0 ,
0.00/0.49	  1' q2 0 -> q2 1' 0 ,
0.00/0.49	  0 q2 1' -> q2 0 1' ,
0.00/0.49	  0' q2 1' -> q2 0' 1' ,
0.00/0.49	  1' q2 1' -> q2 1' 1' ,
0.00/0.49	  q0 1' -> 1' q3 ,
0.00/0.49	  q3 1' -> 1' q3 ,
0.00/0.49	  q3 b -> b q4 }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	q0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q2 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q3 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	b is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q4 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 10-rule system
0.00/0.49	{ q1 0 -> 0 q1 ,
0.00/0.49	  q1 1' -> 1' q1 ,
0.00/0.49	  0 q2 0 -> q2 0 0 ,
0.00/0.49	  0' q2 0 -> q2 0' 0 ,
0.00/0.49	  1' q2 0 -> q2 1' 0 ,
0.00/0.49	  0 q2 1' -> q2 0 1' ,
0.00/0.49	  0' q2 1' -> q2 0' 1' ,
0.00/0.49	  1' q2 1' -> q2 1' 1' ,
0.00/0.49	  q3 1' -> 1' q3 ,
0.00/0.49	  q3 b -> b q4 }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	q0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	0' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1' is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	1 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q2 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q3 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	b is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	q4 is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 9-rule system
0.00/0.49	{ q1 0 -> 0 q1 ,
0.00/0.49	  q1 1' -> 1' q1 ,
0.00/0.49	  0 q2 0 -> q2 0 0 ,
0.00/0.49	  0' q2 0 -> q2 0' 0 ,
0.00/0.49	  1' q2 0 -> q2 1' 0 ,
0.00/0.49	  0 q2 1' -> q2 0 1' ,
0.00/0.49	  0' q2 1' -> q2 0' 1' ,
0.00/0.49	  1' q2 1' -> q2 1' 1' ,
0.00/0.49	  q3 1' -> 1' q3 }
0.00/0.49	
0.00/0.49	
0.00/0.49	The dependency pairs transformation was applied.
0.00/0.49	
0.00/0.49	Remains to prove termination of the 27-rule system
0.00/0.49	{ (q1,true) (0,false) -> (0,true) (q1,false) ,
0.00/0.49	  (q1,true) (0,false) -> (q1,true) ,
0.00/0.49	  (q1,true) (1',false) -> (1',true) (q1,false) ,
0.00/0.49	  (q1,true) (1',false) -> (q1,true) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (q3,true) (1',false) -> (1',true) (q3,false) ,
0.00/0.49	  (q3,true) (1',false) -> (q3,true) ,
0.00/0.49	  (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	(q1,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q1,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q2,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 25-rule system
0.00/0.49	{ (q1,true) (0,false) -> (q1,true) ,
0.00/0.49	  (q1,true) (1',false) -> (q1,true) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (0,true) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (q3,true) (1',false) -> (1',true) (q3,false) ,
0.00/0.49	  (q3,true) (1',false) -> (q3,true) ,
0.00/0.49	  (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	(q1,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q1,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q2,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 21-rule system
0.00/0.49	{ (q1,true) (1',false) -> (q1,true) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (q3,true) (1',false) -> (1',true) (q3,false) ,
0.00/0.49	  (q3,true) (1',false) -> (q3,true) ,
0.00/0.49	  (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	(q1,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q1,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q2,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 20-rule system
0.00/0.49	{ (q1,true) (1',false) -> (q1,true) ,
0.00/0.49	  (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) ,
0.00/0.49	  (q3,true) (1',false) -> (1',true) (q3,false) ,
0.00/0.49	  (q3,true) (1',false) -> (q3,true) ,
0.00/0.49	  (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	(q1,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q1,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q2,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 15-rule system
0.00/0.49	{ (0,true) (q2,false) (0,false) -> (0,true) (0,false) ,
0.00/0.49	  (0',true) (q2,false) (0,false) -> (0',true) (0,false) ,
0.00/0.49	  (1',true) (q2,false) (0,false) -> (1',true) (0,false) ,
0.00/0.49	  (0,true) (q2,false) (1',false) -> (0,true) (1',false) ,
0.00/0.49	  (0',true) (q2,false) (1',false) -> (0',true) (1',false) ,
0.00/0.49	  (1',true) (q2,false) (1',false) -> (1',true) (1',false) ,
0.00/0.49	  (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	(q1,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q1,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(1',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q2,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(q3,false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	(0',false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 9-rule system
0.00/0.49	{ (q1,false) (0,false) ->= (0,false) (q1,false) ,
0.00/0.49	  (q1,false) (1',false) ->= (1',false) (q1,false) ,
0.00/0.49	  (0,false) (q2,false) (0,false) ->= (q2,false) (0,false) (0,false) ,
0.00/0.49	  (0',false) (q2,false) (0,false) ->= (q2,false) (0',false) (0,false) ,
0.00/0.49	  (1',false) (q2,false) (0,false) ->= (q2,false) (1',false) (0,false) ,
0.00/0.49	  (0,false) (q2,false) (1',false) ->= (q2,false) (0,false) (1',false) ,
0.00/0.49	  (0',false) (q2,false) (1',false) ->= (q2,false) (0',false) (1',false) ,
0.00/0.49	  (1',false) (q2,false) (1',false) ->= (q2,false) (1',false) (1',false) ,
0.00/0.49	  (q3,false) (1',false) ->= (1',false) (q3,false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system is trivially terminating.
0.00/0.52	EOF