0.00/0.46	YES
0.00/0.48	
0.00/0.48	
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	t is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	f is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	c is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	n is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	o is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	s is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 8-rule system
0.00/0.48	{ t f -> t c n ,
0.00/0.48	  n f -> f n ,
0.00/0.48	  o f -> f o ,
0.00/0.48	  n s -> f s ,
0.00/0.48	  c f -> f c ,
0.00/0.48	  c n -> n c ,
0.00/0.48	  c o -> o c ,
0.00/0.48	  c o -> o }
0.00/0.48	
0.00/0.48	
0.00/0.48	The dependency pairs transformation was applied.
0.00/0.48	
0.00/0.48	Remains to prove termination of the 19-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (t,true) (f,false) -> (c,true) (n,false) ,
0.00/0.48	  (t,true) (f,false) -> (n,true) ,
0.00/0.48	  (n,true) (f,false) -> (n,true) ,
0.00/0.48	  (o,true) (f,false) -> (o,true) ,
0.00/0.48	  (c,true) (f,false) -> (c,true) ,
0.00/0.48	  (c,true) (n,false) -> (n,true) (c,false) ,
0.00/0.48	  (c,true) (n,false) -> (c,true) ,
0.00/0.48	  (c,true) (o,false) -> (o,true) (c,false) ,
0.00/0.48	  (c,true) (o,false) -> (c,true) ,
0.00/0.48	  (c,true) (o,false) -> (o,true) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (n,false) (s,false) ->= (f,false) (s,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 17-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (n,true) (f,false) -> (n,true) ,
0.00/0.48	  (o,true) (f,false) -> (o,true) ,
0.00/0.48	  (c,true) (f,false) -> (c,true) ,
0.00/0.48	  (c,true) (n,false) -> (n,true) (c,false) ,
0.00/0.48	  (c,true) (n,false) -> (c,true) ,
0.00/0.48	  (c,true) (o,false) -> (o,true) (c,false) ,
0.00/0.48	  (c,true) (o,false) -> (c,true) ,
0.00/0.48	  (c,true) (o,false) -> (o,true) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (n,false) (s,false) ->= (f,false) (s,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 14-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (n,true) (f,false) -> (n,true) ,
0.00/0.48	  (o,true) (f,false) -> (o,true) ,
0.00/0.48	  (c,true) (f,false) -> (c,true) ,
0.00/0.48	  (c,true) (n,false) -> (c,true) ,
0.00/0.48	  (c,true) (o,false) -> (c,true) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (n,false) (s,false) ->= (f,false) (s,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 13-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (n,true) (f,false) -> (n,true) ,
0.00/0.48	  (o,true) (f,false) -> (o,true) ,
0.00/0.48	  (c,true) (f,false) -> (c,true) ,
0.00/0.48	  (c,true) (n,false) -> (c,true) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (n,false) (s,false) ->= (f,false) (s,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 9-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (n,false) (s,false) ->= (f,false) (s,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 1 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 1 0 |
0.00/0.48	| 0 0 1 0 |
0.00/0.48	 \       /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 1 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 1 0 |
0.00/0.48	| 0 0 1 0 |
0.00/0.48	 \       /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 1 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /       \
0.00/0.48	| 1 0 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 1 0 0 |
0.00/0.48	| 0 0 0 0 |
0.00/0.48	 \       /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 8-rule system
0.00/0.48	{ (t,true) (f,false) -> (t,true) (c,false) (n,false) ,
0.00/0.48	  (t,false) (f,false) ->= (t,false) (c,false) (n,false) ,
0.00/0.48	  (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system was filtered by the following matrix interpretation
0.00/0.48	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.48	
0.00/0.48	(t,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(f,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 1 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(c,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(n,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,true) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(o,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(t,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	(s,false) is interpreted by
0.00/0.48	 /   \
0.00/0.48	| 1 0 |
0.00/0.48	| 0 1 |
0.00/0.48	 \   /
0.00/0.48	
0.00/0.48	Remains to prove termination of the 6-rule system
0.00/0.48	{ (n,false) (f,false) ->= (f,false) (n,false) ,
0.00/0.48	  (o,false) (f,false) ->= (f,false) (o,false) ,
0.00/0.48	  (c,false) (f,false) ->= (f,false) (c,false) ,
0.00/0.48	  (c,false) (n,false) ->= (n,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) (c,false) ,
0.00/0.48	  (c,false) (o,false) ->= (o,false) }
0.00/0.48	
0.00/0.48	
0.00/0.48	The system is trivially terminating.
0.00/0.51	EOF