0.00/0.38	YES
0.00/0.39	
0.00/0.39	
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.39	
0.00/0.39	a is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 7 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	b is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 5 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	c is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 3 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	d is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 5-rule system
0.00/0.39	{ a a -> b c c c ,
0.00/0.39	  b c -> d d d d ,
0.00/0.39	  a -> d c d ,
0.00/0.39	  c c -> d d d ,
0.00/0.39	  c d d -> a }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.39	
0.00/0.39	a is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 4 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	b is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	c is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	d is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 1 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 4-rule system
0.00/0.39	{ a a -> b c c c ,
0.00/0.39	  b c -> d d d d ,
0.00/0.39	  a -> d c d ,
0.00/0.39	  c d d -> a }
0.00/0.39	
0.00/0.39	
0.00/0.39	The dependency pairs transformation was applied.
0.00/0.39	
0.00/0.39	Remains to prove termination of the 10-rule system
0.00/0.39	{ (a,true) (a,false) -> (b,true) (c,false) (c,false) (c,false) ,
0.00/0.39	  (a,true) (a,false) -> (c,true) (c,false) (c,false) ,
0.00/0.39	  (a,true) (a,false) -> (c,true) (c,false) ,
0.00/0.39	  (a,true) (a,false) -> (c,true) ,
0.00/0.39	  (a,true) -> (c,true) (d,false) ,
0.00/0.39	  (c,true) (d,false) (d,false) -> (a,true) ,
0.00/0.39	  (a,false) (a,false) ->= (b,false) (c,false) (c,false) (c,false) ,
0.00/0.39	  (b,false) (c,false) ->= (d,false) (d,false) (d,false) (d,false) ,
0.00/0.39	  (a,false) ->= (d,false) (c,false) (d,false) ,
0.00/0.39	  (c,false) (d,false) (d,false) ->= (a,false) }
0.00/0.39	
0.00/0.39	
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.39	
0.00/0.39	(a,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(a,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 4 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(d,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 1 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 2 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 6-rule system
0.00/0.39	{ (a,true) (a,false) -> (b,true) (c,false) (c,false) (c,false) ,
0.00/0.39	  (c,true) (d,false) (d,false) -> (a,true) ,
0.00/0.39	  (a,false) (a,false) ->= (b,false) (c,false) (c,false) (c,false) ,
0.00/0.39	  (b,false) (c,false) ->= (d,false) (d,false) (d,false) (d,false) ,
0.00/0.39	  (a,false) ->= (d,false) (c,false) (d,false) ,
0.00/0.39	  (c,false) (d,false) (d,false) ->= (a,false) }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.39	
0.00/0.39	(a,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(a,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 1 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(d,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 5-rule system
0.00/0.39	{ (a,true) (a,false) -> (b,true) (c,false) (c,false) (c,false) ,
0.00/0.39	  (a,false) (a,false) ->= (b,false) (c,false) (c,false) (c,false) ,
0.00/0.39	  (b,false) (c,false) ->= (d,false) (d,false) (d,false) (d,false) ,
0.00/0.39	  (a,false) ->= (d,false) (c,false) (d,false) ,
0.00/0.39	  (c,false) (d,false) (d,false) ->= (a,false) }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.39	
0.00/0.39	(a,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 1 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(a,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(c,true) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(d,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	(b,false) is interpreted by
0.00/0.39	 /   \
0.00/0.39	| 1 0 |
0.00/0.39	| 0 1 |
0.00/0.39	 \   /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 4-rule system
0.00/0.39	{ (a,false) (a,false) ->= (b,false) (c,false) (c,false) (c,false) ,
0.00/0.39	  (b,false) (c,false) ->= (d,false) (d,false) (d,false) (d,false) ,
0.00/0.39	  (a,false) ->= (d,false) (c,false) (d,false) ,
0.00/0.39	  (c,false) (d,false) (d,false) ->= (a,false) }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system is trivially terminating.
0.00/0.41	EOF