1.88/0.67	YES
1.88/0.70	
1.88/0.70	
1.88/0.70	Applying context closure of depth 1 in the following form: System R over Sigma
1.88/0.70	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
1.88/0.70	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
1.88/0.70	
1.88/0.70	Remains to prove termination of the 16-rule system
1.88/0.70	{ [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, b] [b, a] ,
1.88/0.70	  [a, b] [b, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] ,
1.88/0.70	  [a, a] [a, a] -> [a, a] ,
1.88/0.70	  [a, b] [b, a] -> [a, a] ,
1.88/0.70	  [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, b] [b, b] ,
1.88/0.70	  [a, b] [b, a] [a, b] -> [a, a] [a, a] [a, a] [a, b] ,
1.88/0.70	  [a, a] [a, b] -> [a, b] ,
1.88/0.70	  [a, b] [b, b] -> [a, b] ,
1.88/0.70	  [b, a] [a, b] [b, a] -> [b, b] [b, b] [b, b] [b, a] ,
1.88/0.70	  [b, b] [b, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] ,
1.88/0.70	  [b, a] [a, a] -> [b, a] ,
1.88/0.70	  [b, b] [b, a] -> [b, a] ,
1.88/0.70	  [b, a] [a, b] [b, b] -> [b, b] [b, b] [b, b] [b, b] ,
1.88/0.70	  [b, b] [b, a] [a, b] -> [b, a] [a, a] [a, a] [a, b] ,
1.88/0.70	  [b, a] [a, b] -> [b, b] ,
1.88/0.70	  [b, b] [b, b] -> [b, b] }
1.88/0.70	
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 2:
1.88/0.70	
1.88/0.70	[a, a] is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	[a, b] is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 1 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	[b, a] is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	[b, b] is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 10-rule system
1.88/0.70	{ [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, b] [b, a] ,
1.88/0.70	  [a, a] [a, a] -> [a, a] ,
1.88/0.70	  [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, b] [b, b] ,
1.88/0.70	  [a, a] [a, b] -> [a, b] ,
1.88/0.70	  [a, b] [b, b] -> [a, b] ,
1.88/0.70	  [b, b] [b, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] ,
1.88/0.70	  [b, a] [a, a] -> [b, a] ,
1.88/0.70	  [b, b] [b, a] -> [b, a] ,
1.88/0.70	  [b, b] [b, a] [a, b] -> [b, a] [a, a] [a, a] [a, b] ,
1.88/0.70	  [b, b] [b, b] -> [b, b] }
1.88/0.70	
1.88/0.70	
1.88/0.70	The dependency pairs transformation was applied.
1.88/0.70	
1.88/0.70	Remains to prove termination of the 32-rule system
1.88/0.70	{ ([a, a],true) ([a, b],false) ([b, a],false) -> ([a, b],true) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, a],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ,
1.88/0.70	  ([a, a],true) ([a, a],false) -> ([a, a],true) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, b],false) -> ([a, b],true) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) ([b, b],false) ,
1.88/0.70	  ([a, a],true) ([a, b],false) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],true) ([a, b],false) -> ([a, b],true) ,
1.88/0.70	  ([a, b],true) ([b, b],false) -> ([a, b],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ,
1.88/0.70	  ([b, a],true) ([a, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, b],true) ,
1.88/0.70	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 2:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 1 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 22-rule system
1.88/0.70	{ ([a, a],true) ([a, a],false) -> ([a, a],true) ,
1.88/0.70	  ([a, b],true) ([b, b],false) -> ([a, b],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ([a, a],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, a],false) -> ([a, a],true) ,
1.88/0.70	  ([b, a],true) ([a, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([b, a],true) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, a],false) ([a, b],false) -> ([a, a],true) ([a, b],false) ,
1.88/0.70	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 2:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 1 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /   \
1.88/0.70	| 1 0 |
1.88/0.70	| 0 1 |
1.88/0.70	 \   /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 14-rule system
1.88/0.70	{ ([a, a],true) ([a, a],false) -> ([a, a],true) ,
1.88/0.70	  ([a, b],true) ([b, b],false) -> ([a, b],true) ,
1.88/0.70	  ([b, a],true) ([a, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 3:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 1 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 1 1 |
1.88/0.70	 \     /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 13-rule system
1.88/0.70	{ ([a, b],true) ([b, b],false) -> ([a, b],true) ,
1.88/0.70	  ([b, a],true) ([a, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 3:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 1 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 1 1 |
1.88/0.70	 \     /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 12-rule system
1.88/0.70	{ ([b, a],true) ([a, a],false) -> ([b, a],true) ,
1.88/0.70	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 3:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 1 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 1 1 |
1.88/0.70	 \     /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 11-rule system
1.88/0.70	{ ([b, b],true) ([b, b],false) -> ([b, b],true) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system was filtered by the following matrix interpretation
1.88/0.70	of type E_J with J = {1,...,2} and dimension 3:
1.88/0.70	
1.88/0.70	([a, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, b],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 1 1 |
1.88/0.70	 \     /
1.88/0.70	([b, b],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 1 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([b, a],true) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	([a, a],false) is interpreted by
1.88/0.70	 /     \
1.88/0.70	| 1 0 0 |
1.88/0.70	| 0 1 0 |
1.88/0.70	| 0 0 0 |
1.88/0.70	 \     /
1.88/0.70	
1.88/0.70	Remains to prove termination of the 10-rule system
1.88/0.70	{ ([a, a],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, a],false) ,
1.88/0.70	  ([a, a],false) ([a, a],false) ->= ([a, a],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ([b, b],false) ->= ([a, b],false) ([b, b],false) ([b, b],false) ([b, b],false) ,
1.88/0.70	  ([a, a],false) ([a, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([a, b],false) ([b, b],false) ->= ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, a],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ,
1.88/0.70	  ([b, a],false) ([a, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ->= ([b, a],false) ,
1.88/0.70	  ([b, b],false) ([b, a],false) ([a, b],false) ->= ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ,
1.88/0.70	  ([b, b],false) ([b, b],false) ->= ([b, b],false) }
1.88/0.70	
1.88/0.70	
1.88/0.70	The system is trivially terminating.
2.06/0.74	EOF