0.00/0.44	YES
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 2 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	d is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 3 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	c is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 2 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 4-rule system
0.00/0.45	{ a a -> d c ,
0.00/0.45	  b b -> a c c ,
0.00/0.45	  c c -> b ,
0.00/0.45	  c d -> a a }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	a is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	d is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	c is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 2 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	b is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 3 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 2-rule system
0.00/0.45	{ a a -> d c ,
0.00/0.45	  c d -> a a }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was reversed.
0.00/0.45	
0.00/0.45	Remains to prove termination of the 2-rule system
0.00/0.45	{ a a -> c d ,
0.00/0.45	  d c -> a a }
0.00/0.45	
0.00/0.45	
0.00/0.45	The dependency pairs transformation was applied.
0.00/0.45	
0.00/0.45	Remains to prove termination of the 5-rule system
0.00/0.45	{ (a,true) (a,false) -> (d,true) ,
0.00/0.45	  (d,true) (c,false) -> (a,true) (a,false) ,
0.00/0.45	  (d,true) (c,false) -> (a,true) ,
0.00/0.45	  (a,false) (a,false) ->= (c,false) (d,false) ,
0.00/0.45	  (d,false) (c,false) ->= (a,false) (a,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(d,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(c,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(d,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 3-rule system
0.00/0.45	{ (d,true) (c,false) -> (a,true) (a,false) ,
0.00/0.45	  (a,false) (a,false) ->= (c,false) (d,false) ,
0.00/0.45	  (d,false) (c,false) ->= (a,false) (a,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system was filtered by the following matrix interpretation
0.00/0.45	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.45	
0.00/0.45	(a,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(a,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(d,true) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 1 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(c,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	(d,false) is interpreted by
0.00/0.45	 /   \
0.00/0.45	| 1 0 |
0.00/0.45	| 0 1 |
0.00/0.45	 \   /
0.00/0.45	
0.00/0.45	Remains to prove termination of the 2-rule system
0.00/0.45	{ (a,false) (a,false) ->= (c,false) (d,false) ,
0.00/0.45	  (d,false) (c,false) ->= (a,false) (a,false) }
0.00/0.45	
0.00/0.45	
0.00/0.45	The system is trivially terminating.
0.00/0.48	EOF