39.00/10.19	YES
39.26/10.23	
39.26/10.23	
39.26/10.23	The dependency pairs transformation was applied.
39.26/10.23	
39.26/10.23	Remains to prove termination of the 29-rule system
39.26/10.23	{ (r1,true) (a,false) -> (a,true) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) ,
39.26/10.23	  (r1,true) (b,false) -> (b,true) ,
39.26/10.23	  (r2,true) (b,false) -> (a,true) (b,false) ,
39.26/10.23	  (r2,true) (b,false) -> (b,true) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l1,false) -> (r2,true) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (b,true) (l2,false) -> (r1,true) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 2:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 27-rule system
39.26/10.23	{ (r1,true) (a,false) -> (a,true) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) ,
39.26/10.23	  (r2,true) (b,false) -> (a,true) (b,false) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l1,false) -> (r2,true) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (b,true) (l2,false) -> (r1,true) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 2:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 25-rule system
39.26/10.23	{ (r1,true) (a,false) -> (a,true) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (a,false) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (a,true) (r1,false) ,
39.26/10.23	  (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) ,
39.26/10.23	  (r2,true) (b,false) -> (a,true) (b,false) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 2:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 22-rule system
39.26/10.23	{ (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (a,false) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (a,true) (r2,false) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) ,
39.26/10.23	  (r2,true) (b,false) -> (a,true) (b,false) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 2:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 18-rule system
39.26/10.23	{ (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (l1,false) -> (a,true) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) (a,false) ,
39.26/10.23	  (a,true) (a,false) (l2,false) -> (a,true) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 2:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 1 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /   \
39.26/10.23	| 1 0 |
39.26/10.23	| 0 1 |
39.26/10.23	 \   /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 13-rule system
39.26/10.23	{ (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (r2,true) (a,false) -> (r2,true) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 3:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 1 1 |
39.26/10.23	 \     /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 3 |
39.26/10.23	 \     /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 1 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 3 |
39.26/10.23	 \     /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 12-rule system
39.26/10.23	{ (r1,true) (a,false) -> (r1,true) ,
39.26/10.23	  (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 3:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 1 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 1 1 |
39.26/10.23	 \     /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 3 |
39.26/10.23	 \     /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 3 |
39.26/10.23	 \     /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 11-rule system
39.26/10.23	{ (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (b,true) (l2,false) -> (b,true) (r1,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 6:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 1 0 0 |
39.26/10.23	| 0 0 1 0 0 0 |
39.26/10.23	| 0 0 0 0 0 1 |
39.26/10.23	| 0 0 0 0 1 0 |
39.26/10.23	 \           /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 1 0 |
39.26/10.23	| 0 0 0 0 0 1 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 1 0 |
39.26/10.23	| 0 0 0 0 0 1 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 1 0 |
39.26/10.23	| 0 0 0 0 0 1 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 1 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /           \
39.26/10.23	| 1 0 1 0 0 0 |
39.26/10.23	| 0 1 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	| 0 0 0 0 0 0 |
39.26/10.23	 \           /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 10-rule system
39.26/10.23	{ (b,true) (l1,false) -> (b,true) (r2,false) ,
39.26/10.23	  (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system was filtered by the following matrix interpretation
39.26/10.23	of type E_J with J = {1,...,2} and dimension 3:
39.26/10.23	
39.26/10.23	(r1,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(a,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 1 |
39.26/10.23	 \     /
39.26/10.23	(a,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	 \     /
39.26/10.23	(r2,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(r2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(l1,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	 \     /
39.26/10.23	(l2,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,false) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 0 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	(b,true) is interpreted by
39.26/10.23	 /     \
39.26/10.23	| 1 0 1 |
39.26/10.23	| 0 1 0 |
39.26/10.23	| 0 0 0 |
39.26/10.23	 \     /
39.26/10.23	
39.26/10.23	Remains to prove termination of the 9-rule system
39.26/10.23	{ (r1,false) (a,false) ->= (a,false) (a,false) (a,false) (r1,false) ,
39.26/10.23	  (r2,false) (a,false) ->= (a,false) (a,false) (a,false) (r2,false) ,
39.26/10.23	  (a,false) (l1,false) ->= (l1,false) (a,false) (a,false) (a,false) ,
39.26/10.23	  (a,false) (a,false) (l2,false) ->= (l2,false) (a,false) (a,false) ,
39.26/10.23	  (r1,false) (b,false) ->= (l1,false) (b,false) ,
39.26/10.23	  (r2,false) (b,false) ->= (l2,false) (a,false) (b,false) ,
39.26/10.23	  (b,false) (l1,false) ->= (b,false) (r2,false) ,
39.26/10.23	  (b,false) (l2,false) ->= (b,false) (r1,false) ,
39.26/10.23	  (a,false) (a,false) ->= }
39.26/10.23	
39.26/10.23	
39.26/10.23	The system is trivially terminating.
39.48/10.36	EOF