1.40/0.53	YES
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was reversed.
1.47/0.56	
1.47/0.56	Remains to prove termination of the 4-rule system
1.47/0.56	{ s a -> a s ,
1.47/0.56	  s b a b -> a s b a ,
1.47/0.56	  b b a b -> b a b a ,
1.47/0.56	  a a b a -> a b a b }
1.47/0.56	
1.47/0.56	
1.47/0.56	The dependency pairs transformation was applied.
1.47/0.56	
1.47/0.56	Remains to prove termination of the 18-rule system
1.47/0.56	{ (s,true) (a,false) -> (a,true) (s,false) ,
1.47/0.56	  (s,true) (a,false) -> (s,true) ,
1.47/0.56	  (s,true) (b,false) (a,false) (b,false) -> (a,true) (s,false) (b,false) (a,false) ,
1.47/0.56	  (s,true) (b,false) (a,false) (b,false) -> (s,true) (b,false) (a,false) ,
1.47/0.56	  (s,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) ,
1.47/0.56	  (s,true) (b,false) (a,false) (b,false) -> (a,true) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) (b,false) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (a,true) (b,false) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (a,true) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (b,true) ,
1.47/0.56	  (s,false) (a,false) ->= (a,false) (s,false) ,
1.47/0.56	  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
1.47/0.56	  (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was filtered by the following matrix interpretation
1.47/0.56	of type E_J with J = {1,...,2} and dimension 2:
1.47/0.56	
1.47/0.56	(s,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 1 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(a,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(a,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(s,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(b,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(b,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	
1.47/0.56	Remains to prove termination of the 14-rule system
1.47/0.56	{ (s,true) (a,false) -> (s,true) ,
1.47/0.56	  (s,true) (b,false) (a,false) (b,false) -> (s,true) (b,false) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) (b,false) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (a,true) (b,false) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) ,
1.47/0.56	  (b,true) (b,false) (a,false) (b,false) -> (a,true) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (b,true) (a,false) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (b,true) ,
1.47/0.56	  (s,false) (a,false) ->= (a,false) (s,false) ,
1.47/0.56	  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
1.47/0.56	  (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was filtered by the following matrix interpretation
1.47/0.56	of type E_J with J = {1,...,2} and dimension 2:
1.47/0.56	
1.47/0.56	(s,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(a,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 1 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(a,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(s,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(b,false) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 1 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	(b,true) is interpreted by
1.47/0.56	 /   \
1.47/0.56	| 1 0 |
1.47/0.56	| 0 1 |
1.47/0.56	 \   /
1.47/0.56	
1.47/0.56	Remains to prove termination of the 6-rule system
1.47/0.56	{ (b,true) (b,false) (a,false) (b,false) -> (b,true) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
1.47/0.56	  (s,false) (a,false) ->= (a,false) (s,false) ,
1.47/0.56	  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
1.47/0.56	  (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was filtered by the following matrix interpretation
1.47/0.56	of type E_J with J = {1,...,2} and dimension 5:
1.47/0.56	
1.47/0.56	(s,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(a,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 1 1 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(a,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(s,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(b,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 1 1 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(b,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 1 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	
1.47/0.56	Remains to prove termination of the 5-rule system
1.47/0.56	{ (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
1.47/0.56	  (s,false) (a,false) ->= (a,false) (s,false) ,
1.47/0.56	  (s,false) (b,false) (a,false) (b,false) ->= (a,false) (s,false) (b,false) (a,false) ,
1.47/0.56	  (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was filtered by the following matrix interpretation
1.47/0.56	of type E_J with J = {1,...,2} and dimension 3:
1.47/0.56	
1.47/0.56	(s,true) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 0 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 0 0 |
1.47/0.56	 \     /
1.47/0.56	(a,false) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 0 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 1 1 |
1.47/0.56	 \     /
1.47/0.56	(a,true) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 0 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 0 0 |
1.47/0.56	 \     /
1.47/0.56	(s,false) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 1 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 0 1 |
1.47/0.56	 \     /
1.47/0.56	(b,false) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 0 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 1 1 |
1.47/0.56	 \     /
1.47/0.56	(b,true) is interpreted by
1.47/0.56	 /     \
1.47/0.56	| 1 0 0 |
1.47/0.56	| 0 1 0 |
1.47/0.56	| 0 0 0 |
1.47/0.56	 \     /
1.47/0.56	
1.47/0.56	Remains to prove termination of the 3-rule system
1.47/0.56	{ (a,true) (a,false) (b,false) (a,false) -> (a,true) (b,false) (a,false) (b,false) ,
1.47/0.56	  (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	The system was filtered by the following matrix interpretation
1.47/0.56	of type E_J with J = {1,...,2} and dimension 5:
1.47/0.56	
1.47/0.56	(s,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(a,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 1 1 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(a,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 1 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(s,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(b,false) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 1 1 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	(b,true) is interpreted by
1.47/0.56	 /         \
1.47/0.56	| 1 0 0 0 0 |
1.47/0.56	| 0 1 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	| 0 0 0 0 0 |
1.47/0.56	 \         /
1.47/0.56	
1.47/0.56	Remains to prove termination of the 2-rule system
1.47/0.56	{ (b,false) (b,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (a,false) ,
1.47/0.56	  (a,false) (a,false) (b,false) (a,false) ->= (a,false) (b,false) (a,false) (b,false) }
1.47/0.56	
1.47/0.56	
1.47/0.56	The system is trivially terminating.
1.47/0.58	EOF