0.00/0.49	YES
0.00/0.51	
0.00/0.51	
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.51	
0.00/0.51	a is interpreted by
0.00/0.51	 /     \
0.00/0.51	| 1 0 0 |
0.00/0.51	| 0 1 0 |
0.00/0.51	| 0 0 0 |
0.00/0.51	 \     /
0.00/0.51	c is interpreted by
0.00/0.51	 /     \
0.00/0.51	| 1 0 0 |
0.00/0.51	| 0 1 0 |
0.00/0.51	| 0 0 0 |
0.00/0.51	 \     /
0.00/0.51	b is interpreted by
0.00/0.51	 /     \
0.00/0.51	| 1 0 0 |
0.00/0.51	| 0 1 0 |
0.00/0.51	| 0 0 0 |
0.00/0.51	 \     /
0.00/0.51	d is interpreted by
0.00/0.51	 /     \
0.00/0.51	| 1 0 1 |
0.00/0.51	| 0 1 0 |
0.00/0.51	| 0 1 0 |
0.00/0.51	 \     /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 6-rule system
0.00/0.51	{ a c a -> c a c ,
0.00/0.51	  a a b -> a d b ,
0.00/0.51	  a b -> b a a ,
0.00/0.51	  b b -> b c ,
0.00/0.51	  a d c -> c a ,
0.00/0.51	  b c -> a a a }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.51	
0.00/0.51	a is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	c is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	b is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	d is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 4-rule system
0.00/0.51	{ a c a -> c a c ,
0.00/0.51	  a a b -> a d b ,
0.00/0.51	  a b -> b a a ,
0.00/0.51	  a d c -> c a }
0.00/0.51	
0.00/0.51	
0.00/0.51	The dependency pairs transformation was applied.
0.00/0.51	
0.00/0.51	Remains to prove termination of the 9-rule system
0.00/0.51	{ (a,true) (c,false) (a,false) -> (a,true) (c,false) ,
0.00/0.51	  (a,true) (a,false) (b,false) -> (a,true) (d,false) (b,false) ,
0.00/0.51	  (a,true) (b,false) -> (a,true) (a,false) ,
0.00/0.51	  (a,true) (b,false) -> (a,true) ,
0.00/0.51	  (a,true) (d,false) (c,false) -> (a,true) ,
0.00/0.51	  (a,false) (c,false) (a,false) ->= (c,false) (a,false) (c,false) ,
0.00/0.51	  (a,false) (a,false) (b,false) ->= (a,false) (d,false) (b,false) ,
0.00/0.51	  (a,false) (b,false) ->= (b,false) (a,false) (a,false) ,
0.00/0.51	  (a,false) (d,false) (c,false) ->= (c,false) (a,false) }
0.00/0.51	
0.00/0.51	
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.51	
0.00/0.51	(a,true) is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	(c,false) is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	(a,false) is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	(b,false) is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	(d,false) is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 7-rule system
0.00/0.51	{ (a,true) (c,false) (a,false) -> (a,true) (c,false) ,
0.00/0.51	  (a,true) (a,false) (b,false) -> (a,true) (d,false) (b,false) ,
0.00/0.51	  (a,true) (d,false) (c,false) -> (a,true) ,
0.00/0.51	  (a,false) (c,false) (a,false) ->= (c,false) (a,false) (c,false) ,
0.00/0.51	  (a,false) (a,false) (b,false) ->= (a,false) (d,false) (b,false) ,
0.00/0.51	  (a,false) (b,false) ->= (b,false) (a,false) (a,false) ,
0.00/0.51	  (a,false) (d,false) (c,false) ->= (c,false) (a,false) }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.51	
0.00/0.51	(a,true) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 1 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(c,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 1 1 0 |
0.00/0.51	 \       /
0.00/0.51	(a,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	 \       /
0.00/0.51	(b,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(d,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 1 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 6-rule system
0.00/0.51	{ (a,true) (c,false) (a,false) -> (a,true) (c,false) ,
0.00/0.51	  (a,true) (a,false) (b,false) -> (a,true) (d,false) (b,false) ,
0.00/0.51	  (a,false) (c,false) (a,false) ->= (c,false) (a,false) (c,false) ,
0.00/0.51	  (a,false) (a,false) (b,false) ->= (a,false) (d,false) (b,false) ,
0.00/0.51	  (a,false) (b,false) ->= (b,false) (a,false) (a,false) ,
0.00/0.51	  (a,false) (d,false) (c,false) ->= (c,false) (a,false) }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.51	
0.00/0.51	(a,true) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 1 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(c,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(a,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 1 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	 \       /
0.00/0.51	(b,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	 \       /
0.00/0.51	(d,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 5-rule system
0.00/0.51	{ (a,true) (c,false) (a,false) -> (a,true) (c,false) ,
0.00/0.51	  (a,false) (c,false) (a,false) ->= (c,false) (a,false) (c,false) ,
0.00/0.51	  (a,false) (a,false) (b,false) ->= (a,false) (d,false) (b,false) ,
0.00/0.51	  (a,false) (b,false) ->= (b,false) (a,false) (a,false) ,
0.00/0.51	  (a,false) (d,false) (c,false) ->= (c,false) (a,false) }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.51	
0.00/0.51	(a,true) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 1 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(c,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 1 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(a,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 1 0 1 |
0.00/0.51	 \       /
0.00/0.51	(b,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	(d,false) is interpreted by
0.00/0.51	 /       \
0.00/0.51	| 1 0 0 0 |
0.00/0.51	| 0 1 1 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	| 0 0 0 0 |
0.00/0.51	 \       /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 4-rule system
0.00/0.51	{ (a,false) (c,false) (a,false) ->= (c,false) (a,false) (c,false) ,
0.00/0.51	  (a,false) (a,false) (b,false) ->= (a,false) (d,false) (b,false) ,
0.00/0.51	  (a,false) (b,false) ->= (b,false) (a,false) (a,false) ,
0.00/0.51	  (a,false) (d,false) (c,false) ->= (c,false) (a,false) }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system is trivially terminating.
0.00/0.53	EOF