2.23/0.77	YES
2.46/0.82	
2.46/0.82	
2.46/0.82	The system was reversed.
2.46/0.82	
2.46/0.82	Remains to prove termination of the 4-rule system
2.46/0.82	{ a d -> d b ,
2.46/0.82	  b -> a a a ,
2.46/0.82	  c d c -> d a ,
2.46/0.82	  d d b -> c d d c c }
2.46/0.82	
2.46/0.82	
2.46/0.82	The dependency pairs transformation was applied.
2.46/0.82	
2.46/0.82	Remains to prove termination of the 16-rule system
2.46/0.82	{ (a,true) (d,false) -> (d,true) (b,false) ,
2.46/0.82	  (a,true) (d,false) -> (b,true) ,
2.46/0.82	  (b,true) -> (a,true) (a,false) (a,false) ,
2.46/0.82	  (b,true) -> (a,true) (a,false) ,
2.46/0.82	  (b,true) -> (a,true) ,
2.46/0.82	  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
2.46/0.82	  (c,true) (d,false) (c,false) -> (a,true) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (d,true) (c,false) (c,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (c,true) (c,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (c,true) ,
2.46/0.82	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.82	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.82	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.82	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.82	
2.46/0.82	
2.46/0.82	
2.46/0.82	
2.46/0.82	The system was filtered by the following matrix interpretation
2.46/0.82	of type E_J with J = {1,...,2} and dimension 2:
2.46/0.82	
2.46/0.82	(a,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(d,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 1 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(d,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 1 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(b,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(b,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(a,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(c,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(c,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	
2.46/0.82	Remains to prove termination of the 11-rule system
2.46/0.82	{ (a,true) (d,false) -> (d,true) (b,false) ,
2.46/0.82	  (b,true) -> (a,true) (a,false) (a,false) ,
2.46/0.82	  (b,true) -> (a,true) (a,false) ,
2.46/0.82	  (b,true) -> (a,true) ,
2.46/0.82	  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.82	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.82	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.82	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.82	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.82	
2.46/0.82	
2.46/0.82	The system was filtered by the following matrix interpretation
2.46/0.82	of type E_J with J = {1,...,2} and dimension 2:
2.46/0.82	
2.46/0.82	(a,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(d,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(d,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(b,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(b,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 1 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(a,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(c,true) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	(c,false) is interpreted by
2.46/0.82	 /   \
2.46/0.82	| 1 0 |
2.46/0.82	| 0 1 |
2.46/0.82	 \   /
2.46/0.82	
2.46/0.82	Remains to prove termination of the 8-rule system
2.46/0.82	{ (a,true) (d,false) -> (d,true) (b,false) ,
2.46/0.82	  (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
2.46/0.82	  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
2.46/0.83	  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.83	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.83	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.83	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.83	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.83	
2.46/0.83	
2.46/0.83	The system was filtered by the following matrix interpretation
2.46/0.83	of type E_J with J = {1,...,2} and dimension 2:
2.46/0.83	
2.46/0.83	(a,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 1 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(d,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(d,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(b,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(b,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(a,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(c,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(c,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	
2.46/0.83	Remains to prove termination of the 7-rule system
2.46/0.83	{ (c,true) (d,false) (c,false) -> (d,true) (a,false) ,
2.46/0.83	  (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
2.46/0.83	  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.83	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.83	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.83	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.83	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.83	
2.46/0.83	
2.46/0.83	The system was filtered by the following matrix interpretation
2.46/0.83	of type E_J with J = {1,...,2} and dimension 6:
2.46/0.83	
2.46/0.83	(a,true) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(d,false) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 1 0 0 |
2.46/0.83	| 0 0 0 0 1 0 |
2.46/0.83	| 0 0 0 0 0 1 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(d,true) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(b,false) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(b,true) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(a,false) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(c,true) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 1 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	(c,false) is interpreted by
2.46/0.83	 /           \
2.46/0.83	| 1 0 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 1 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	| 0 0 0 0 0 0 |
2.46/0.83	 \           /
2.46/0.83	
2.46/0.83	Remains to prove termination of the 6-rule system
2.46/0.83	{ (d,true) (d,false) (b,false) -> (c,true) (d,false) (d,false) (c,false) (c,false) ,
2.46/0.83	  (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.83	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.83	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.83	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.83	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.83	
2.46/0.83	
2.46/0.83	The system was filtered by the following matrix interpretation
2.46/0.83	of type E_J with J = {1,...,2} and dimension 2:
2.46/0.83	
2.46/0.83	(a,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(d,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(d,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 1 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(b,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(b,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(a,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(c,true) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	(c,false) is interpreted by
2.46/0.83	 /   \
2.46/0.83	| 1 0 |
2.46/0.83	| 0 1 |
2.46/0.83	 \   /
2.46/0.83	
2.46/0.83	Remains to prove termination of the 5-rule system
2.46/0.83	{ (d,true) (d,false) (b,false) -> (d,true) (d,false) (c,false) (c,false) ,
2.46/0.83	  (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.83	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.83	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.83	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.83	
2.46/0.83	
2.46/0.83	The system was filtered by the following matrix interpretation
2.46/0.83	of type E_J with J = {1,...,2} and dimension 4:
2.46/0.83	
2.46/0.83	(a,true) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(d,false) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 1 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(d,true) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 1 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(b,false) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	 \       /
2.46/0.83	(b,true) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(a,false) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(c,true) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	(c,false) is interpreted by
2.46/0.83	 /       \
2.46/0.83	| 1 0 0 0 |
2.46/0.83	| 0 1 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	| 0 0 0 0 |
2.46/0.83	 \       /
2.46/0.83	
2.46/0.83	Remains to prove termination of the 4-rule system
2.46/0.83	{ (a,false) (d,false) ->= (d,false) (b,false) ,
2.46/0.83	  (b,false) ->= (a,false) (a,false) (a,false) ,
2.46/0.83	  (c,false) (d,false) (c,false) ->= (d,false) (a,false) ,
2.46/0.83	  (d,false) (d,false) (b,false) ->= (c,false) (d,false) (d,false) (c,false) (c,false) }
2.46/0.83	
2.46/0.83	
2.46/0.83	The system is trivially terminating.
2.73/0.90	EOF