0.00/0.29	YES
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	R is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	r is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	p is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	P is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 5-rule system
0.00/0.30	{ r p -> p p r P ,
0.00/0.30	  r r -> ,
0.00/0.30	  r P P -> P P r ,
0.00/0.30	  p P -> ,
0.00/0.30	  P p -> }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	R is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	r is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	p is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	P is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 4-rule system
0.00/0.30	{ r p -> p p r P ,
0.00/0.30	  r P P -> P P r ,
0.00/0.30	  p P -> ,
0.00/0.30	  P p -> }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was reversed.
0.00/0.30	
0.00/0.30	Remains to prove termination of the 4-rule system
0.00/0.30	{ p r -> P r p p ,
0.00/0.30	  P P r -> r P P ,
0.00/0.30	  P p -> ,
0.00/0.30	  p P -> }
0.00/0.30	
0.00/0.30	
0.00/0.30	The dependency pairs transformation was applied.
0.00/0.30	
0.00/0.30	Remains to prove termination of the 9-rule system
0.00/0.30	{ (p,true) (r,false) -> (P,true) (r,false) (p,false) (p,false) ,
0.00/0.30	  (p,true) (r,false) -> (p,true) (p,false) ,
0.00/0.30	  (p,true) (r,false) -> (p,true) ,
0.00/0.30	  (P,true) (P,false) (r,false) -> (P,true) (P,false) ,
0.00/0.30	  (P,true) (P,false) (r,false) -> (P,true) ,
0.00/0.30	  (p,false) (r,false) ->= (P,false) (r,false) (p,false) (p,false) ,
0.00/0.30	  (P,false) (P,false) (r,false) ->= (r,false) (P,false) (P,false) ,
0.00/0.30	  (P,false) (p,false) ->= ,
0.00/0.30	  (p,false) (P,false) ->= }
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	(p,true) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(r,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(P,true) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(p,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(P,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 8-rule system
0.00/0.30	{ (p,true) (r,false) -> (p,true) (p,false) ,
0.00/0.30	  (p,true) (r,false) -> (p,true) ,
0.00/0.30	  (P,true) (P,false) (r,false) -> (P,true) (P,false) ,
0.00/0.30	  (P,true) (P,false) (r,false) -> (P,true) ,
0.00/0.30	  (p,false) (r,false) ->= (P,false) (r,false) (p,false) (p,false) ,
0.00/0.30	  (P,false) (P,false) (r,false) ->= (r,false) (P,false) (P,false) ,
0.00/0.30	  (P,false) (p,false) ->= ,
0.00/0.30	  (p,false) (P,false) ->= }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	(p,true) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(r,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(P,true) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(p,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	(P,false) is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 4-rule system
0.00/0.30	{ (p,false) (r,false) ->= (P,false) (r,false) (p,false) (p,false) ,
0.00/0.30	  (P,false) (P,false) (r,false) ->= (r,false) (P,false) (P,false) ,
0.00/0.30	  (P,false) (p,false) ->= ,
0.00/0.30	  (p,false) (P,false) ->= }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system is trivially terminating.
0.00/0.33	EOF