0.00/0.41	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 14 |
0.00/0.43	|  0  1 |
0.00/0.43	 \     /
0.00/0.43	b is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 9 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	a 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	c is interpreted by
0.00/0.43	 /   \
0.00/0.43	| 1 6 |
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 4 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	
0.00/0.43	Remains to prove termination of the 6-rule system
0.00/0.43	{ a f -> f a a ,
0.00/0.43	  b b -> c c a c ,
0.00/0.43	  d b -> d a b ,
0.00/0.43	  c c -> d d d ,
0.00/0.43	  b d -> d b ,
0.00/0.43	  c d d -> f }
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 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	b 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	a 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	c 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 5-rule system
0.00/0.43	{ a f -> f a a ,
0.00/0.43	  d b -> d a b ,
0.00/0.43	  c c -> d d d ,
0.00/0.43	  b d -> d b ,
0.00/0.43	  c d d -> f }
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 0 |
0.00/0.43	| 0 1 |
0.00/0.43	 \   /
0.00/0.43	b 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	a 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	c 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	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	{ a f -> f a a ,
0.00/0.43	  d b -> d a b ,
0.00/0.43	  b d -> d b }
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 10-rule system
0.00/0.43	{ (a,true) (f,false) -> (a,true) (a,false) ,
0.00/0.43	  (a,true) (f,false) -> (a,true) ,
0.00/0.43	  (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (a,true) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (b,true) ,
0.00/0.43	  (b,true) (d,false) -> (d,true) (b,false) ,
0.00/0.43	  (b,true) (d,false) -> (b,true) ,
0.00/0.43	  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
0.00/0.43	  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
0.00/0.43	  (b,false) (d,false) ->= (d,false) (b,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	(a,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	(f,false) 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	(a,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,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	(b,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	(b,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	(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	
0.00/0.43	Remains to prove termination of the 8-rule system
0.00/0.43	{ (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (a,true) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (b,true) ,
0.00/0.43	  (b,true) (d,false) -> (d,true) (b,false) ,
0.00/0.43	  (b,true) (d,false) -> (b,true) ,
0.00/0.43	  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
0.00/0.43	  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
0.00/0.43	  (b,false) (d,false) ->= (d,false) (b,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 2:
0.00/0.43	
0.00/0.43	(a,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	(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	(a,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,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	(b,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	(b,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	(d,false) 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	
0.00/0.43	Remains to prove termination of the 6-rule system
0.00/0.43	{ (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (a,true) (b,false) ,
0.00/0.43	  (d,true) (b,false) -> (b,true) ,
0.00/0.43	  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
0.00/0.43	  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
0.00/0.43	  (b,false) (d,false) ->= (d,false) (b,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 2:
0.00/0.43	
0.00/0.43	(a,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	(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	(a,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,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	(b,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	(b,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	(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	
0.00/0.43	Remains to prove termination of the 4-rule system
0.00/0.43	{ (d,true) (b,false) -> (d,true) (a,false) (b,false) ,
0.00/0.43	  (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
0.00/0.43	  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
0.00/0.43	  (b,false) (d,false) ->= (d,false) (b,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	(a,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	(a,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,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	(b,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 0 |
0.00/0.43	 \     /
0.00/0.43	(b,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	(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 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	{ (a,false) (f,false) ->= (f,false) (a,false) (a,false) ,
0.00/0.43	  (d,false) (b,false) ->= (d,false) (a,false) (b,false) ,
0.00/0.43	  (b,false) (d,false) ->= (d,false) (b,false) }
0.00/0.43	
0.00/0.43	
0.00/0.43	The system is trivially terminating.
0.00/0.46	EOF