0.00/0.54	YES
0.00/0.56	
0.00/0.56	
0.00/0.56	The dependency pairs transformation was applied.
0.00/0.56	
0.00/0.56	Remains to prove termination of the 7-rule system
0.00/0.56	{ (a,true) (b,false) (b,false) -> (c,true) ,
0.00/0.56	  (c,true) (c,false) -> (a,true) (b,false) (c,false) (a,false) ,
0.00/0.56	  (c,true) (c,false) -> (c,true) (a,false) ,
0.00/0.56	  (c,true) (c,false) -> (a,true) ,
0.00/0.56	  (a,false) ->= (b,false) ,
0.00/0.56	  (a,false) (b,false) (b,false) ->= (c,false) ,
0.00/0.56	  (c,false) (c,false) ->= (a,false) (b,false) (c,false) (a,false) }
0.00/0.56	
0.00/0.56	
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	(a,true) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(b,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(c,true) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 2 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(c,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 3 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(a,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 5-rule system
0.00/0.56	{ (a,true) (b,false) (b,false) -> (c,true) ,
0.00/0.56	  (c,true) (c,false) -> (a,true) (b,false) (c,false) (a,false) ,
0.00/0.56	  (a,false) ->= (b,false) ,
0.00/0.56	  (a,false) (b,false) (b,false) ->= (c,false) ,
0.00/0.56	  (c,false) (c,false) ->= (a,false) (b,false) (c,false) (a,false) }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 5:
0.00/0.56	
0.00/0.56	(a,true) is interpreted by
0.00/0.56	 /         \
0.00/0.56	| 1 0 0 1 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	 \         /
0.00/0.56	(b,false) is interpreted by
0.00/0.56	 /         \
0.00/0.56	| 1 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 1 |
0.00/0.56	| 0 0 1 0 0 |
0.00/0.56	 \         /
0.00/0.56	(c,true) is interpreted by
0.00/0.56	 /         \
0.00/0.56	| 1 0 1 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	 \         /
0.00/0.56	(c,false) is interpreted by
0.00/0.56	 /         \
0.00/0.56	| 1 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 0 1 0 0 |
0.00/0.56	| 0 0 0 0 0 |
0.00/0.56	 \         /
0.00/0.56	(a,false) is interpreted by
0.00/0.56	 /         \
0.00/0.56	| 1 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 1 0 0 0 |
0.00/0.56	| 0 0 0 1 1 |
0.00/0.56	| 0 0 1 0 0 |
0.00/0.56	 \         /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 4-rule system
0.00/0.56	{ (a,true) (b,false) (b,false) -> (c,true) ,
0.00/0.56	  (a,false) ->= (b,false) ,
0.00/0.56	  (a,false) (b,false) (b,false) ->= (c,false) ,
0.00/0.56	  (c,false) (c,false) ->= (a,false) (b,false) (c,false) (a,false) }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	(a,true) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(b,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(c,true) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(c,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	(a,false) is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 3-rule system
0.00/0.56	{ (a,false) ->= (b,false) ,
0.00/0.56	  (a,false) (b,false) (b,false) ->= (c,false) ,
0.00/0.56	  (c,false) (c,false) ->= (a,false) (b,false) (c,false) (a,false) }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system is trivially terminating.
0.00/0.59	EOF