0.00/0.42	YES
0.00/0.43	
0.00/0.43	
0.00/0.43	
0.00/0.43	
0.00/0.43	The system was filtered by the following matrix interpretation
0.00/0.43	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.43	
0.00/0.43	f is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 1 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	0 is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	s is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	d is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	
0.00/0.43	Remains to prove termination of the 3-rule system
0.00/0.43	{ d 0 -> 0 ,
0.00/0.43	  d s -> s s d ,
0.00/0.43	  f s -> d f }
0.00/0.43	
0.00/0.43	
0.00/0.43	The dependency pairs transformation was applied.
0.00/0.43	
0.00/0.43	Remains to prove termination of the 6-rule system
0.00/0.43	{ (d,true) (s,false) -> (d,true) ,
0.00/0.43	  (f,true) (s,false) -> (d,true) (f,false) ,
0.00/0.43	  (f,true) (s,false) -> (f,true) ,
0.00/0.43	  (d,false) (0,false) ->= (0,false) ,
0.00/0.43	  (d,false) (s,false) ->= (s,false) (s,false) (d,false) ,
0.00/0.43	  (f,false) (s,false) ->= (d,false) (f,false) }
0.00/0.43	
0.00/0.43	
0.00/0.43	
0.00/0.43	
0.00/0.43	The system was filtered by the following matrix interpretation
0.00/0.43	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.43	
0.00/0.43	(d,true) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	(s,false) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	(f,true) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 1 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	(f,false) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	(d,false) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	(0,false) is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	
0.00/0.43	Remains to prove termination of the 5-rule system
0.00/0.43	{ (d,true) (s,false) -> (d,true) ,
0.00/0.43	  (f,true) (s,false) -> (f,true) ,
0.00/0.43	  (d,false) (0,false) ->= (0,false) ,
0.00/0.43	  (d,false) (s,false) ->= (s,false) (s,false) (d,false) ,
0.00/0.43	  (f,false) (s,false) ->= (d,false) (f,false) }
0.00/0.43	
0.00/0.43	
0.00/0.43	The system was filtered by the following matrix interpretation
0.00/0.43	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.43	
0.00/0.43	(d,true) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 1 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(s,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 1 1 |
0.00/0.43	 \     /
0.00/0.43	(f,true) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(f,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(d,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 2 |
0.00/0.43	 \     /
0.00/0.43	(0,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	
0.00/0.43	Remains to prove termination of the 4-rule system
0.00/0.43	{ (f,true) (s,false) -> (f,true) ,
0.00/0.43	  (d,false) (0,false) ->= (0,false) ,
0.00/0.43	  (d,false) (s,false) ->= (s,false) (s,false) (d,false) ,
0.00/0.43	  (f,false) (s,false) ->= (d,false) (f,false) }
0.00/0.43	
0.00/0.43	
0.00/0.43	The system was filtered by the following matrix interpretation
0.00/0.43	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.43	
0.00/0.43	(d,true) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(s,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 1 1 |
0.00/0.43	 \     /
0.00/0.43	(f,true) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 1 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(f,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	(d,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 2 |
0.00/0.43	 \     /
0.00/0.43	(0,false) is interpreted by
0.00/0.43	 /     \
0.00/0.43	| 1 0 0 |
0.00/0.43	| 0 1 0 |
0.00/0.43	| 0 0 0 |
0.00/0.43	 \     /
0.00/0.43	
0.00/0.43	Remains to prove termination of the 3-rule system
0.00/0.43	{ (d,false) (0,false) ->= (0,false) ,
0.00/0.43	  (d,false) (s,false) ->= (s,false) (s,false) (d,false) ,
0.00/0.43	  (f,false) (s,false) ->= (d,false) (f,false) }
0.00/0.43	
0.00/0.43	
0.00/0.43	The system is trivially terminating.
0.00/0.47	EOF