1.55/0.60	YES
1.55/0.62	
1.55/0.62	
1.55/0.62	
1.55/0.62	
1.55/0.62	The system was filtered by the following matrix interpretation
1.55/0.62	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.62	
1.55/0.62	r is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 2 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	e is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	w is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	i is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 0 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	t is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 3 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	
1.55/0.62	Remains to prove termination of the 5-rule system
1.55/0.62	{ r e -> w r ,
1.55/0.62	  i t -> e r ,
1.55/0.62	  e w -> r i ,
1.55/0.62	  w r -> i t ,
1.55/0.62	  r i t e r -> e w r i t e }
1.55/0.62	
1.55/0.62	
1.55/0.62	The dependency pairs transformation was applied.
1.55/0.62	
1.55/0.62	Remains to prove termination of the 17-rule system
1.55/0.62	{ (r,true) (e,false) -> (w,true) (r,false) ,
1.55/0.62	  (r,true) (e,false) -> (r,true) ,
1.55/0.62	  (i,true) (t,false) -> (e,true) (r,false) ,
1.55/0.62	  (i,true) (t,false) -> (r,true) ,
1.55/0.62	  (e,true) (w,false) -> (r,true) (i,false) ,
1.55/0.62	  (e,true) (w,false) -> (i,true) ,
1.55/0.62	  (w,true) (r,false) -> (i,true) (t,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) (w,false) (r,false) (i,false) (t,false) (e,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (w,true) (r,false) (i,false) (t,false) (e,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (r,true) (i,false) (t,false) (e,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (i,true) (t,false) (e,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) ,
1.55/0.62	  (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.62	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.62	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.62	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.62	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.62	
1.55/0.62	
1.55/0.62	
1.55/0.62	
1.55/0.62	The system was filtered by the following matrix interpretation
1.55/0.62	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.62	
1.55/0.62	(r,true) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 2 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(e,false) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(w,true) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(r,false) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 2 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(i,true) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 0 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(t,false) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 3 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(e,true) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(w,false) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 1 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	(i,false) is interpreted by
1.55/0.62	 /   \
1.55/0.62	| 1 0 |
1.55/0.62	| 0 1 |
1.55/0.62	 \   /
1.55/0.62	
1.55/0.62	Remains to prove termination of the 10-rule system
1.55/0.62	{ (r,true) (e,false) -> (w,true) (r,false) ,
1.55/0.62	  (i,true) (t,false) -> (e,true) (r,false) ,
1.55/0.62	  (e,true) (w,false) -> (r,true) (i,false) ,
1.55/0.62	  (w,true) (r,false) -> (i,true) (t,false) ,
1.55/0.62	  (r,true) (i,false) (t,false) (e,false) (r,false) -> (e,true) (w,false) (r,false) (i,false) (t,false) (e,false) ,
1.55/0.62	  (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.62	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.62	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.62	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.62	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.62	
1.55/0.62	
1.55/0.62	The system was filtered by the following matrix interpretation
1.55/0.62	of type E_J with J = {1,...,2} and dimension 4:
1.55/0.63	
1.55/0.63	(r,true) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 1 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(e,false) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(w,true) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 1 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(r,false) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(i,true) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(t,false) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	 \       /
1.55/0.63	(e,true) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(w,false) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 1 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	(i,false) is interpreted by
1.55/0.63	 /       \
1.55/0.63	| 1 0 0 0 |
1.55/0.63	| 0 1 0 0 |
1.55/0.63	| 0 0 0 1 |
1.55/0.63	| 0 0 0 0 |
1.55/0.63	 \       /
1.55/0.63	
1.55/0.63	Remains to prove termination of the 8-rule system
1.55/0.63	{ (r,true) (e,false) -> (w,true) (r,false) ,
1.55/0.63	  (i,true) (t,false) -> (e,true) (r,false) ,
1.55/0.63	  (e,true) (w,false) -> (r,true) (i,false) ,
1.55/0.63	  (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.63	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.63	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.63	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.63	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.63	
1.55/0.63	
1.55/0.63	The system was filtered by the following matrix interpretation
1.55/0.63	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.63	
1.55/0.63	(r,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(r,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 1 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(t,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	
1.55/0.63	Remains to prove termination of the 7-rule system
1.55/0.63	{ (r,true) (e,false) -> (w,true) (r,false) ,
1.55/0.63	  (e,true) (w,false) -> (r,true) (i,false) ,
1.55/0.63	  (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.63	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.63	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.63	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.63	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.63	
1.55/0.63	
1.55/0.63	The system was filtered by the following matrix interpretation
1.55/0.63	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.63	
1.55/0.63	(r,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(r,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(t,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 1 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	
1.55/0.63	Remains to prove termination of the 6-rule system
1.55/0.63	{ (r,true) (e,false) -> (w,true) (r,false) ,
1.55/0.63	  (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.63	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.63	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.63	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.63	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.63	
1.55/0.63	
1.55/0.63	The system was filtered by the following matrix interpretation
1.55/0.63	of type E_J with J = {1,...,2} and dimension 2:
1.55/0.63	
1.55/0.63	(r,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 1 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(r,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(t,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(e,true) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(w,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	(i,false) is interpreted by
1.55/0.63	 /   \
1.55/0.63	| 1 0 |
1.55/0.63	| 0 1 |
1.55/0.63	 \   /
1.55/0.63	
1.55/0.63	Remains to prove termination of the 5-rule system
1.55/0.63	{ (r,false) (e,false) ->= (w,false) (r,false) ,
1.55/0.63	  (i,false) (t,false) ->= (e,false) (r,false) ,
1.55/0.63	  (e,false) (w,false) ->= (r,false) (i,false) ,
1.55/0.63	  (w,false) (r,false) ->= (i,false) (t,false) ,
1.55/0.63	  (r,false) (i,false) (t,false) (e,false) (r,false) ->= (e,false) (w,false) (r,false) (i,false) (t,false) (e,false) }
1.55/0.63	
1.55/0.63	
1.55/0.63	The system is trivially terminating.
1.72/0.66	EOF