2.27/0.85	YES
2.27/0.86	
2.27/0.86	
2.27/0.86	The system was reversed.
2.27/0.86	
2.27/0.86	Remains to prove termination of the 3-rule system
2.27/0.86	{ a a -> b b b a ,
2.27/0.86	  a b -> c b b ,
2.27/0.86	  c b b a -> b a a a }
2.27/0.86	
2.27/0.86	
2.27/0.86	The dependency pairs transformation was applied.
2.27/0.86	
2.27/0.86	Remains to prove termination of the 8-rule system
2.27/0.86	{ (a,true) (a,false) -> (a,true) ,
2.27/0.86	  (a,true) (b,false) -> (c,true) (b,false) (b,false) ,
2.27/0.86	  (c,true) (b,false) (b,false) (a,false) -> (a,true) (a,false) (a,false) ,
2.27/0.86	  (c,true) (b,false) (b,false) (a,false) -> (a,true) (a,false) ,
2.27/0.86	  (c,true) (b,false) (b,false) (a,false) -> (a,true) ,
2.27/0.86	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) (a,false) ,
2.27/0.86	  (a,false) (b,false) ->= (c,false) (b,false) (b,false) ,
2.27/0.86	  (c,false) (b,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (a,false) }
2.27/0.86	
2.27/0.86	
2.27/0.86	
2.27/0.86	
2.27/0.86	The system was filtered by the following matrix interpretation
2.27/0.86	of type E_J with J = {1,...,2} and dimension 5:
2.27/0.86	
2.27/0.86	(a,true) is interpreted by
2.27/0.86	 /         \
2.27/0.86	| 1 0 0 1 0 |
2.27/0.86	| 0 1 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	 \         /
2.27/0.86	(a,false) is interpreted by
2.27/0.86	 /         \
2.27/0.86	| 1 0 0 0 0 |
2.27/0.86	| 0 1 0 0 0 |
2.27/0.86	| 0 0 0 1 0 |
2.27/0.86	| 0 0 0 1 0 |
2.27/0.86	| 0 1 0 1 0 |
2.27/0.86	 \         /
2.27/0.86	(b,false) is interpreted by
2.27/0.86	 /         \
2.27/0.86	| 1 0 0 0 0 |
2.27/0.86	| 0 1 0 0 0 |
2.27/0.86	| 0 0 0 1 0 |
2.27/0.86	| 0 0 0 0 1 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	 \         /
2.27/0.86	(c,true) is interpreted by
2.27/0.86	 /         \
2.27/0.86	| 1 0 1 0 0 |
2.27/0.86	| 0 1 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	 \         /
2.27/0.86	(c,false) is interpreted by
2.27/0.86	 /         \
2.27/0.86	| 1 0 0 0 0 |
2.27/0.86	| 0 1 0 0 0 |
2.27/0.86	| 0 0 1 0 0 |
2.27/0.86	| 0 0 1 0 0 |
2.27/0.86	| 0 0 0 0 0 |
2.27/0.86	 \         /
2.27/0.86	
2.27/0.86	Remains to prove termination of the 5-rule system
2.27/0.86	{ (a,true) (a,false) -> (a,true) ,
2.27/0.86	  (a,true) (b,false) -> (c,true) (b,false) (b,false) ,
2.27/0.86	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) (a,false) ,
2.27/0.86	  (a,false) (b,false) ->= (c,false) (b,false) (b,false) ,
2.27/0.86	  (c,false) (b,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (a,false) }
2.27/0.86	
2.27/0.86	
2.27/0.86	The system was filtered by the following matrix interpretation
2.27/0.86	of type E_J with J = {1,...,2} and dimension 2:
2.27/0.86	
2.27/0.86	(a,true) is interpreted by
2.27/0.86	 /   \
2.27/0.86	| 1 1 |
2.27/0.86	| 0 1 |
2.27/0.86	 \   /
2.27/0.86	(a,false) is interpreted by
2.27/0.86	 /   \
2.27/0.86	| 1 0 |
2.27/0.86	| 0 1 |
2.27/0.86	 \   /
2.27/0.86	(b,false) is interpreted by
2.27/0.86	 /   \
2.27/0.86	| 1 0 |
2.27/0.86	| 0 1 |
2.27/0.86	 \   /
2.27/0.86	(c,true) is interpreted by
2.27/0.86	 /   \
2.27/0.86	| 1 0 |
2.27/0.86	| 0 1 |
2.27/0.86	 \   /
2.27/0.86	(c,false) is interpreted by
2.27/0.86	 /   \
2.27/0.86	| 1 0 |
2.27/0.86	| 0 1 |
2.27/0.86	 \   /
2.27/0.86	
2.27/0.86	Remains to prove termination of the 4-rule system
2.27/0.86	{ (a,true) (a,false) -> (a,true) ,
2.27/0.86	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) (a,false) ,
2.27/0.86	  (a,false) (b,false) ->= (c,false) (b,false) (b,false) ,
2.27/0.86	  (c,false) (b,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (a,false) }
2.27/0.86	
2.27/0.86	
2.27/0.86	The system was filtered by the following matrix interpretation
2.27/0.86	of type E_J with J = {1,...,2} and dimension 3:
2.27/0.86	
2.27/0.86	(a,true) is interpreted by
2.27/0.86	 /     \
2.27/0.86	| 1 0 1 |
2.27/0.86	| 0 1 0 |
2.27/0.86	| 0 0 0 |
2.27/0.86	 \     /
2.27/0.86	(a,false) is interpreted by
2.27/0.86	 /     \
2.27/0.86	| 1 0 0 |
2.27/0.86	| 0 1 0 |
2.27/0.86	| 0 1 1 |
2.27/0.86	 \     /
2.27/0.86	(b,false) is interpreted by
2.27/0.86	 /     \
2.27/0.86	| 1 0 0 |
2.27/0.86	| 0 1 0 |
2.27/0.86	| 0 0 0 |
2.27/0.86	 \     /
2.27/0.86	(c,true) is interpreted by
2.27/0.86	 /     \
2.27/0.86	| 1 0 0 |
2.27/0.86	| 0 1 0 |
2.27/0.86	| 0 0 0 |
2.27/0.86	 \     /
2.27/0.86	(c,false) is interpreted by
2.27/0.86	 /     \
2.27/0.86	| 1 0 0 |
2.27/0.86	| 0 1 0 |
2.27/0.86	| 0 0 0 |
2.27/0.86	 \     /
2.27/0.86	
2.27/0.86	Remains to prove termination of the 3-rule system
2.27/0.86	{ (a,false) (a,false) ->= (b,false) (b,false) (b,false) (a,false) ,
2.27/0.86	  (a,false) (b,false) ->= (c,false) (b,false) (b,false) ,
2.27/0.86	  (c,false) (b,false) (b,false) (a,false) ->= (b,false) (a,false) (a,false) (a,false) }
2.27/0.86	
2.27/0.86	
2.27/0.86	The system is trivially terminating.
2.67/0.89	EOF