1.46/0.55	YES
1.55/0.59	
1.55/0.59	
1.55/0.59	The dependency pairs transformation was applied.
1.55/0.59	
1.55/0.59	Remains to prove termination of the 12-rule system
1.55/0.59	{ (a,true) (a,false) (b,false) -> (b,true) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (a,true) (a,false) (b,false) -> (a,true) (b,false) (c,false) (a,false) ,
1.55/0.59	  (a,true) (a,false) (b,false) -> (b,true) (c,false) (a,false) ,
1.55/0.59	  (a,true) (a,false) (b,false) -> (a,true) ,
1.55/0.59	  (b,true) (a,false) -> (a,true) (b,false) (b,false) ,
1.55/0.59	  (b,true) (a,false) -> (b,true) (b,false) ,
1.55/0.59	  (b,true) (a,false) -> (b,true) ,
1.55/0.59	  (b,true) (c,false) (a,false) -> (a,true) (b,false) ,
1.55/0.59	  (b,true) (c,false) (a,false) -> (b,true) ,
1.55/0.59	  (a,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,false) (a,false) ->= (a,false) (b,false) (b,false) ,
1.55/0.59	  (b,false) (c,false) (a,false) ->= (c,false) (a,false) (b,false) }
1.55/0.59	
1.55/0.59	
1.55/0.59	
1.55/0.59	
1.55/0.59	The system was filtered by the following matrix interpretation
1.55/0.59	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.59	
1.55/0.59	(a,true) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 1 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(a,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 1 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(b,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(b,true) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(c,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	
1.55/0.59	Remains to prove termination of the 7-rule system
1.55/0.59	{ (a,true) (a,false) (b,false) -> (b,true) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (a,true) (a,false) (b,false) -> (a,true) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,true) (a,false) -> (a,true) (b,false) (b,false) ,
1.55/0.59	  (b,true) (c,false) (a,false) -> (a,true) (b,false) ,
1.55/0.59	  (a,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,false) (a,false) ->= (a,false) (b,false) (b,false) ,
1.55/0.59	  (b,false) (c,false) (a,false) ->= (c,false) (a,false) (b,false) }
1.55/0.59	
1.55/0.59	
1.55/0.59	The system was filtered by the following matrix interpretation
1.55/0.59	of type E_J with J = {1,...,2} and dimension 4:
1.55/0.59	
1.55/0.59	(a,true) is interpreted by
1.55/0.59	 /       \
1.55/0.59	| 1 0 0 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	 \       /
1.55/0.59	(a,false) is interpreted by
1.55/0.59	 /       \
1.55/0.59	| 1 0 0 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	 \       /
1.55/0.59	(b,false) is interpreted by
1.55/0.59	 /       \
1.55/0.59	| 1 0 0 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	| 0 0 1 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	 \       /
1.55/0.59	(b,true) is interpreted by
1.55/0.59	 /       \
1.55/0.59	| 1 0 1 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	 \       /
1.55/0.59	(c,false) is interpreted by
1.55/0.59	 /       \
1.55/0.59	| 1 0 0 0 |
1.55/0.59	| 0 1 0 0 |
1.55/0.59	| 0 0 0 1 |
1.55/0.59	| 0 0 0 0 |
1.55/0.59	 \       /
1.55/0.59	
1.55/0.59	Remains to prove termination of the 6-rule system
1.55/0.59	{ (a,true) (a,false) (b,false) -> (b,true) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (a,true) (a,false) (b,false) -> (a,true) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,true) (a,false) -> (a,true) (b,false) (b,false) ,
1.55/0.59	  (a,false) (a,false) (b,false) ->= (b,false) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,false) (a,false) ->= (a,false) (b,false) (b,false) ,
1.55/0.59	  (b,false) (c,false) (a,false) ->= (c,false) (a,false) (b,false) }
1.55/0.59	
1.55/0.59	
1.55/0.59	The system was filtered by the following matrix interpretation
1.55/0.59	of type E_J with J = {1,...,2} and dimension 3:
1.55/0.59	
1.55/0.59	(a,true) is interpreted by
1.55/0.59	 /     \
1.55/0.59	| 1 0 1 |
1.55/0.59	| 0 1 0 |
1.55/0.59	| 0 0 0 |
1.55/0.59	 \     /
1.55/0.59	(a,false) is interpreted by
1.55/0.59	 /     \
1.55/0.59	| 1 0 1 |
1.55/0.59	| 0 1 0 |
1.55/0.59	| 0 1 0 |
1.55/0.59	 \     /
1.55/0.59	(b,false) is interpreted by
1.55/0.59	 /     \
1.55/0.59	| 1 0 0 |
1.55/0.59	| 0 1 0 |
1.55/0.59	| 0 0 1 |
1.55/0.59	 \     /
1.55/0.59	(b,true) is interpreted by
1.55/0.59	 /     \
1.55/0.59	| 1 0 1 |
1.55/0.59	| 0 1 0 |
1.55/0.59	| 0 0 0 |
1.55/0.59	 \     /
1.55/0.59	(c,false) is interpreted by
1.55/0.59	 /     \
1.55/0.59	| 1 0 0 |
1.55/0.59	| 0 1 0 |
1.55/0.59	| 0 0 0 |
1.55/0.59	 \     /
1.55/0.59	
1.55/0.59	Remains to prove termination of the 3-rule system
1.55/0.59	{ (a,true) (a,false) (b,false) -> (b,true) (a,false) (b,false) (c,false) (a,false) ,
1.55/0.59	  (b,false) (a,false) ->= (a,false) (b,false) (b,false) ,
1.55/0.59	  (b,false) (c,false) (a,false) ->= (c,false) (a,false) (b,false) }
1.55/0.59	
1.55/0.59	
1.55/0.59	The system was filtered by the following matrix interpretation
1.55/0.59	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.59	
1.55/0.59	(a,true) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 1 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(a,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(b,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(b,true) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	(c,false) is interpreted by
1.55/0.59	 /   \
1.55/0.59	| 1 0 |
1.55/0.59	| 0 1 |
1.55/0.59	 \   /
1.55/0.59	
1.55/0.59	Remains to prove termination of the 2-rule system
1.55/0.59	{ (b,false) (a,false) ->= (a,false) (b,false) (b,false) ,
1.55/0.59	  (b,false) (c,false) (a,false) ->= (c,false) (a,false) (b,false) }
1.55/0.59	
1.55/0.59	
1.55/0.59	The system is trivially terminating.
1.55/0.62	EOF