0.00/0.52	YES
1.41/0.55	
1.41/0.55	
1.41/0.55	The dependency pairs transformation was applied.
1.41/0.55	
1.41/0.55	Remains to prove termination of the 17-rule system
1.41/0.55	{ (f,true) -> (n,true) (c,false) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (c,true) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (n,true) (a,false) ,
1.41/0.55	  (c,true) (f,false) -> (f,true) (n,false) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (n,true) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (c,true) ,
1.41/0.55	  (n,true) (a,false) -> (c,true) ,
1.41/0.55	  (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (n,true) (s,false) -> (f,true) (s,false) (s,false) ,
1.41/0.55	  (n,true) (f,false) -> (f,true) (n,false) ,
1.41/0.55	  (n,true) (f,false) -> (n,true) ,
1.41/0.55	  (f,false) ->= (n,false) (c,false) (n,false) (a,false) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (s,false) ->= (f,false) (s,false) (s,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 3:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 1 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 1 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 1 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	 \     /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 16-rule system
1.41/0.55	{ (f,true) -> (n,true) (c,false) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (c,true) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (n,true) (a,false) ,
1.41/0.55	  (c,true) (f,false) -> (f,true) (n,false) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (n,true) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (c,true) ,
1.41/0.55	  (n,true) (a,false) -> (c,true) ,
1.41/0.55	  (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (n,true) (f,false) -> (f,true) (n,false) ,
1.41/0.55	  (n,true) (f,false) -> (n,true) ,
1.41/0.55	  (f,false) ->= (n,false) (c,false) (n,false) (a,false) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (s,false) ->= (f,false) (s,false) (s,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 3:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 1 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 1 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 1 |
1.41/0.55	 \     /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 0 |
1.41/0.55	 \     /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 0 1 |
1.41/0.55	 \     /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /     \
1.41/0.55	| 1 0 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	| 0 1 0 |
1.41/0.55	 \     /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 15-rule system
1.41/0.55	{ (f,true) -> (n,true) (c,false) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (c,true) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (n,true) (a,false) ,
1.41/0.55	  (c,true) (f,false) -> (f,true) (n,false) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (n,true) (a,false) (c,false) ,
1.41/0.55	  (c,true) (f,false) -> (c,true) ,
1.41/0.55	  (n,true) (a,false) -> (c,true) ,
1.41/0.55	  (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (n,true) (f,false) -> (f,true) (n,false) ,
1.41/0.55	  (n,true) (f,false) -> (n,true) ,
1.41/0.55	  (f,false) ->= (n,false) (c,false) (n,false) (a,false) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 2:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 1 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 9-rule system
1.41/0.55	{ (f,true) -> (n,true) (c,false) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (c,true) (n,false) (a,false) ,
1.41/0.55	  (f,true) -> (n,true) (a,false) ,
1.41/0.55	  (n,true) (a,false) -> (c,true) ,
1.41/0.55	  (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 2:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 1 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 6-rule system
1.41/0.55	{ (n,true) (a,false) -> (c,true) ,
1.41/0.55	  (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 2:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 1 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /   \
1.41/0.55	| 1 0 |
1.41/0.55	| 0 1 |
1.41/0.55	 \   /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 5-rule system
1.41/0.55	{ (c,true) (c,false) -> (c,true) ,
1.41/0.55	  (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system was filtered by the following matrix interpretation
1.41/0.55	of type E_J with J = {1,...,2} and dimension 4:
1.41/0.55	
1.41/0.55	(f,true) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(n,true) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(c,false) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 1 1 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(n,false) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 1 0 1 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(a,false) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 1 0 |
1.41/0.55	 \       /
1.41/0.55	(c,true) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 1 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(f,false) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	(s,false) is interpreted by
1.41/0.55	 /       \
1.41/0.55	| 1 0 0 0 |
1.41/0.55	| 0 1 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	| 0 0 0 0 |
1.41/0.55	 \       /
1.41/0.55	
1.41/0.55	Remains to prove termination of the 4-rule system
1.41/0.55	{ (c,false) (f,false) ->= (f,false) (n,false) (a,false) (c,false) ,
1.41/0.55	  (n,false) (a,false) ->= (c,false) ,
1.41/0.55	  (c,false) (c,false) ->= (c,false) ,
1.41/0.55	  (n,false) (f,false) ->= (f,false) (n,false) }
1.41/0.55	
1.41/0.55	
1.41/0.55	The system is trivially terminating.
1.41/0.59	EOF