1.58/0.59	YES
1.58/0.60	
1.58/0.60	
1.58/0.60	The dependency pairs transformation was applied.
1.58/0.60	
1.58/0.60	Remains to prove termination of the 9-rule system
1.58/0.60	{ (a,true) (b,false) -> (b,true) (c,false) (a,false) ,
1.58/0.60	  (a,true) (b,false) -> (a,true) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) (b,false) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) ,
1.58/0.60	  (b,true) (a,false) -> (a,true) (c,false) (b,false) ,
1.58/0.60	  (b,true) (a,false) -> (b,true) ,
1.58/0.60	  (a,false) (b,false) ->= (b,false) (c,false) (a,false) ,
1.58/0.60	  (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	
1.58/0.60	
1.58/0.60	The system was filtered by the following matrix interpretation
1.58/0.60	of type E_J with J = {1,...,2} and dimension 2:
1.58/0.60	
1.58/0.60	(a,true) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 1 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(b,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(b,true) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(c,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(a,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 1 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	
1.58/0.60	Remains to prove termination of the 8-rule system
1.58/0.60	{ (a,true) (b,false) -> (b,true) (c,false) (a,false) ,
1.58/0.60	  (a,true) (b,false) -> (a,true) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) (b,false) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) ,
1.58/0.60	  (b,true) (a,false) -> (a,true) (c,false) (b,false) ,
1.58/0.60	  (a,false) (b,false) ->= (b,false) (c,false) (a,false) ,
1.58/0.60	  (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	The system was filtered by the following matrix interpretation
1.58/0.60	of type E_J with J = {1,...,2} and dimension 3:
1.58/0.60	
1.58/0.60	(a,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 1 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(b,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 1 1 |
1.58/0.60	 \     /
1.58/0.60	(b,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(c,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(a,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	 \     /
1.58/0.60	
1.58/0.60	Remains to prove termination of the 6-rule system
1.58/0.60	{ (b,true) (c,false) -> (b,true) (b,false) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) ,
1.58/0.60	  (b,true) (a,false) -> (a,true) (c,false) (b,false) ,
1.58/0.60	  (a,false) (b,false) ->= (b,false) (c,false) (a,false) ,
1.58/0.60	  (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	The system was filtered by the following matrix interpretation
1.58/0.60	of type E_J with J = {1,...,2} and dimension 2:
1.58/0.60	
1.58/0.60	(a,true) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(b,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(b,true) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 1 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(c,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	(a,false) is interpreted by
1.58/0.60	 /   \
1.58/0.60	| 1 0 |
1.58/0.60	| 0 1 |
1.58/0.60	 \   /
1.58/0.60	
1.58/0.60	Remains to prove termination of the 5-rule system
1.58/0.60	{ (b,true) (c,false) -> (b,true) (b,false) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) ,
1.58/0.60	  (a,false) (b,false) ->= (b,false) (c,false) (a,false) ,
1.58/0.60	  (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	The system was filtered by the following matrix interpretation
1.58/0.60	of type E_J with J = {1,...,2} and dimension 3:
1.58/0.60	
1.58/0.60	(a,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(b,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 1 1 |
1.58/0.60	 \     /
1.58/0.60	(b,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(c,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(a,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 1 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	 \     /
1.58/0.60	
1.58/0.60	Remains to prove termination of the 4-rule system
1.58/0.60	{ (b,true) (c,false) -> (b,true) (b,false) ,
1.58/0.60	  (b,true) (c,false) -> (b,true) ,
1.58/0.60	  (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	The system was filtered by the following matrix interpretation
1.58/0.60	of type E_J with J = {1,...,2} and dimension 3:
1.58/0.60	
1.58/0.60	(a,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(b,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 1 |
1.58/0.60	 \     /
1.58/0.60	(b,true) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 1 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	(c,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 1 1 |
1.58/0.60	 \     /
1.58/0.60	(a,false) is interpreted by
1.58/0.60	 /     \
1.58/0.60	| 1 0 0 |
1.58/0.60	| 0 1 0 |
1.58/0.60	| 0 0 0 |
1.58/0.60	 \     /
1.58/0.60	
1.58/0.60	Remains to prove termination of the 2-rule system
1.58/0.60	{ (b,false) (c,false) ->= (c,false) (b,false) (b,false) ,
1.58/0.60	  (b,false) (a,false) ->= (a,false) (c,false) (b,false) }
1.58/0.60	
1.58/0.60	
1.58/0.60	The system is trivially terminating.
1.69/0.62	EOF