1.64/0.62	YES
1.84/0.66	
1.84/0.66	
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	a is interpreted by
1.84/0.66	 /     \
1.84/0.66	|  1 18 |
1.84/0.66	|  0  1 |
1.84/0.66	 \     /
1.84/0.66	b is interpreted by
1.84/0.66	 /     \
1.84/0.66	|  1 12 |
1.84/0.66	|  0  1 |
1.84/0.66	 \     /
1.84/0.66	d is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 5 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	c is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 8 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	f is interpreted by
1.84/0.66	 /     \
1.84/0.66	|  1 18 |
1.84/0.66	|  0  1 |
1.84/0.66	 \     /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 6-rule system
1.84/0.66	{ a a -> b b b ,
1.84/0.66	  a -> d c d ,
1.84/0.66	  b b b -> a f ,
1.84/0.66	  b b -> c c c ,
1.84/0.66	  c d d -> f ,
1.84/0.66	  f f -> f a }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	a is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 3 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	b is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 2 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	d is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	c is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	f is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 3 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 5-rule system
1.84/0.66	{ a a -> b b b ,
1.84/0.66	  a -> d c d ,
1.84/0.66	  b b b -> a f ,
1.84/0.66	  c d d -> f ,
1.84/0.66	  f f -> f a }
1.84/0.66	
1.84/0.66	
1.84/0.66	The dependency pairs transformation was applied.
1.84/0.66	
1.84/0.66	Remains to prove termination of the 14-rule system
1.84/0.66	{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
1.84/0.66	  (a,true) (a,false) -> (b,true) (b,false) ,
1.84/0.66	  (a,true) (a,false) -> (b,true) ,
1.84/0.66	  (a,true) -> (c,true) (d,false) ,
1.84/0.66	  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
1.84/0.66	  (b,true) (b,false) (b,false) -> (f,true) ,
1.84/0.66	  (c,true) (d,false) (d,false) -> (f,true) ,
1.84/0.66	  (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (f,true) (f,false) -> (a,true) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 3 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 6 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 4 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 3 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 6 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 6 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 10-rule system
1.84/0.66	{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
1.84/0.66	  (a,true) -> (c,true) (d,false) ,
1.84/0.66	  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
1.84/0.66	  (c,true) (d,false) (d,false) -> (f,true) ,
1.84/0.66	  (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 9-rule system
1.84/0.66	{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
1.84/0.66	  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
1.84/0.66	  (c,true) (d,false) (d,false) -> (f,true) ,
1.84/0.66	  (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 8-rule system
1.84/0.66	{ (a,true) (a,false) -> (b,true) (b,false) (b,false) ,
1.84/0.66	  (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
1.84/0.66	  (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 3:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 1 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	 \     /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	 \     /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 7-rule system
1.84/0.66	{ (b,true) (b,false) (b,false) -> (a,true) (f,false) ,
1.84/0.66	  (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 2:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 1 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /   \
1.84/0.66	| 1 0 |
1.84/0.66	| 0 1 |
1.84/0.66	 \   /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 6-rule system
1.84/0.66	{ (f,true) (f,false) -> (f,true) (a,false) ,
1.84/0.66	  (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system was filtered by the following matrix interpretation
1.84/0.66	of type E_J with J = {1,...,2} and dimension 3:
1.84/0.66	
1.84/0.66	(a,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(a,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(b,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(b,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(c,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(d,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(f,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	 \     /
1.84/0.66	(f,true) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 1 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 0 0 |
1.84/0.66	 \     /
1.84/0.66	(c,false) is interpreted by
1.84/0.66	 /     \
1.84/0.66	| 1 0 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	| 0 1 0 |
1.84/0.66	 \     /
1.84/0.66	
1.84/0.66	Remains to prove termination of the 5-rule system
1.84/0.66	{ (a,false) (a,false) ->= (b,false) (b,false) (b,false) ,
1.84/0.66	  (a,false) ->= (d,false) (c,false) (d,false) ,
1.84/0.66	  (b,false) (b,false) (b,false) ->= (a,false) (f,false) ,
1.84/0.66	  (c,false) (d,false) (d,false) ->= (f,false) ,
1.84/0.66	  (f,false) (f,false) ->= (f,false) (a,false) }
1.84/0.66	
1.84/0.66	
1.84/0.66	The system is trivially terminating.
1.84/0.68	EOF