2.32/0.78	YES
2.48/0.81	
2.48/0.81	
2.48/0.81	Applying context closure of depth 1 in the following form: System R over Sigma
2.48/0.81	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
2.48/0.81	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
2.48/0.81	
2.48/0.81	Remains to prove termination of the 36-rule system
2.48/0.81	{ [a, a] [a, a] -> [a, a] ,
2.48/0.81	  [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [a, b] [b, a] -> [a, a] ,
2.48/0.81	  [a, c] [c, c] [c, a] -> [a, b] [b, a] [a, a] ,
2.48/0.81	  [a, a] [a, b] -> [a, b] ,
2.48/0.81	  [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [a, b] [b, b] -> [a, b] ,
2.48/0.81	  [a, c] [c, c] [c, b] -> [a, b] [b, a] [a, b] ,
2.48/0.81	  [a, a] [a, c] -> [a, c] ,
2.48/0.81	  [a, a] [a, b] [b, c] -> [a, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [a, b] [b, c] -> [a, c] ,
2.48/0.81	  [a, c] [c, c] [c, c] -> [a, b] [b, a] [a, c] ,
2.48/0.81	  [b, a] [a, a] -> [b, a] ,
2.48/0.81	  [b, a] [a, b] [b, a] -> [b, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [b, b] [b, a] -> [b, a] ,
2.48/0.81	  [b, c] [c, c] [c, a] -> [b, b] [b, a] [a, a] ,
2.48/0.81	  [b, a] [a, b] -> [b, b] ,
2.48/0.81	  [b, a] [a, b] [b, b] -> [b, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [b, b] [b, b] -> [b, b] ,
2.48/0.81	  [b, c] [c, c] [c, b] -> [b, b] [b, a] [a, b] ,
2.48/0.81	  [b, a] [a, c] -> [b, c] ,
2.48/0.81	  [b, a] [a, b] [b, c] -> [b, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [b, b] [b, c] -> [b, c] ,
2.48/0.81	  [b, c] [c, c] [c, c] -> [b, b] [b, a] [a, c] ,
2.48/0.81	  [c, a] [a, a] -> [c, a] ,
2.48/0.81	  [c, a] [a, b] [b, a] -> [c, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [c, b] [b, a] -> [c, a] ,
2.48/0.81	  [c, c] [c, c] [c, a] -> [c, b] [b, a] [a, a] ,
2.48/0.81	  [c, a] [a, b] -> [c, b] ,
2.48/0.81	  [c, a] [a, b] [b, b] -> [c, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [c, b] [b, b] -> [c, b] ,
2.48/0.81	  [c, c] [c, c] [c, b] -> [c, b] [b, a] [a, b] ,
2.48/0.81	  [c, a] [a, c] -> [c, c] ,
2.48/0.81	  [c, a] [a, b] [b, c] -> [c, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [c, b] [b, c] -> [c, c] ,
2.48/0.81	  [c, c] [c, c] [c, c] -> [c, b] [b, a] [a, c] }
2.48/0.81	
2.48/0.81	
2.48/0.81	
2.48/0.81	The system was filtered by the following matrix interpretation
2.48/0.81	of type E_J with J = {1,...,2} and dimension 2:
2.48/0.81	
2.48/0.81	[a, a] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[a, b] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[b, a] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[b, b] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[a, c] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[c, a] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[c, c] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[c, b] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	[b, c] is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	
2.48/0.81	Remains to prove termination of the 21-rule system
2.48/0.81	{ [a, a] [a, b] [b, a] -> [a, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [a, b] [b, a] -> [a, a] ,
2.48/0.81	  [a, c] [c, c] [c, a] -> [a, b] [b, a] [a, a] ,
2.48/0.81	  [a, a] [a, b] [b, b] -> [a, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [a, b] [b, b] -> [a, b] ,
2.48/0.81	  [a, c] [c, c] [c, b] -> [a, b] [b, a] [a, b] ,
2.48/0.81	  [a, a] [a, b] [b, c] -> [a, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [b, a] [a, b] [b, a] -> [b, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [b, b] [b, a] -> [b, a] ,
2.48/0.81	  [b, a] [a, b] [b, b] -> [b, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [b, b] [b, b] -> [b, b] ,
2.48/0.81	  [b, a] [a, c] -> [b, c] ,
2.48/0.81	  [b, a] [a, b] [b, c] -> [b, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [b, b] [b, c] -> [b, c] ,
2.48/0.81	  [c, a] [a, b] [b, a] -> [c, b] [b, b] [b, a] [a, c] [c, a] ,
2.48/0.81	  [c, b] [b, a] -> [c, a] ,
2.48/0.81	  [c, a] [a, b] [b, b] -> [c, b] [b, b] [b, a] [a, c] [c, b] ,
2.48/0.81	  [c, b] [b, b] -> [c, b] ,
2.48/0.81	  [c, a] [a, c] -> [c, c] ,
2.48/0.81	  [c, a] [a, b] [b, c] -> [c, b] [b, b] [b, a] [a, c] [c, c] ,
2.48/0.81	  [c, b] [b, c] -> [c, c] }
2.48/0.81	
2.48/0.81	
2.48/0.81	The system was reversed.
2.48/0.81	
2.48/0.81	Remains to prove termination of the 21-rule system
2.48/0.81	{ [b, a] [a, b] [a, a] -> [c, a] [a, c] [b, a] [b, b] [a, b] ,
2.48/0.81	  [b, a] [a, b] -> [a, a] ,
2.48/0.81	  [c, a] [c, c] [a, c] -> [a, a] [b, a] [a, b] ,
2.48/0.81	  [b, b] [a, b] [a, a] -> [c, b] [a, c] [b, a] [b, b] [a, b] ,
2.48/0.81	  [b, b] [a, b] -> [a, b] ,
2.48/0.81	  [c, b] [c, c] [a, c] -> [a, b] [b, a] [a, b] ,
2.48/0.81	  [b, c] [a, b] [a, a] -> [c, c] [a, c] [b, a] [b, b] [a, b] ,
2.48/0.81	  [b, a] [a, b] [b, a] -> [c, a] [a, c] [b, a] [b, b] [b, b] ,
2.48/0.81	  [b, a] [b, b] -> [b, a] ,
2.48/0.81	  [b, b] [a, b] [b, a] -> [c, b] [a, c] [b, a] [b, b] [b, b] ,
2.48/0.81	  [b, b] [b, b] -> [b, b] ,
2.48/0.81	  [a, c] [b, a] -> [b, c] ,
2.48/0.81	  [b, c] [a, b] [b, a] -> [c, c] [a, c] [b, a] [b, b] [b, b] ,
2.48/0.81	  [b, c] [b, b] -> [b, c] ,
2.48/0.81	  [b, a] [a, b] [c, a] -> [c, a] [a, c] [b, a] [b, b] [c, b] ,
2.48/0.81	  [b, a] [c, b] -> [c, a] ,
2.48/0.81	  [b, b] [a, b] [c, a] -> [c, b] [a, c] [b, a] [b, b] [c, b] ,
2.48/0.81	  [b, b] [c, b] -> [c, b] ,
2.48/0.81	  [a, c] [c, a] -> [c, c] ,
2.48/0.81	  [b, c] [a, b] [c, a] -> [c, c] [a, c] [b, a] [b, b] [c, b] ,
2.48/0.81	  [b, c] [c, b] -> [c, c] }
2.48/0.81	
2.48/0.81	
2.48/0.81	The dependency pairs transformation was applied.
2.48/0.81	
2.48/0.81	Remains to prove termination of the 68-rule system
2.48/0.81	{ ([b, a],true) ([a, b],false) ([a, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([a, a],false) -> ([b, b],true) ([a, b],false) ,
2.48/0.81	  ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([b, b],true) ([a, b],false) ,
2.48/0.81	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([a, a],false) -> ([b, b],true) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.48/0.81	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.48/0.81	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.81	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ([b, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.48/0.81	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([b, b],true) ([c, b],false) ,
2.48/0.81	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.48/0.81	  ([b, a],true) ([c, b],false) -> ([c, a],true) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([b, b],true) ([c, b],false) ,
2.48/0.81	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.48/0.81	  ([b, b],true) ([c, b],false) -> ([c, b],true) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([b, b],true) ([c, b],false) ,
2.48/0.81	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.81	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.81	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.81	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.81	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.81	
2.48/0.81	
2.48/0.81	
2.48/0.81	
2.48/0.81	The system was filtered by the following matrix interpretation
2.48/0.81	of type E_J with J = {1,...,2} and dimension 2:
2.48/0.81	
2.48/0.81	([b, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	
2.48/0.81	Remains to prove termination of the 27-rule system
2.48/0.81	{ ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.48/0.81	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.81	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.48/0.81	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.81	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.81	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.81	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.81	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.81	
2.48/0.81	
2.48/0.81	The system was filtered by the following matrix interpretation
2.48/0.81	of type E_J with J = {1,...,2} and dimension 2:
2.48/0.81	
2.48/0.81	([b, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	
2.48/0.81	Remains to prove termination of the 26-rule system
2.48/0.81	{ ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.48/0.81	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.81	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.48/0.81	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.81	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.81	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.81	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.81	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.81	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.81	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.81	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.81	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.81	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.81	
2.48/0.81	
2.48/0.81	The system was filtered by the following matrix interpretation
2.48/0.81	of type E_J with J = {1,...,2} and dimension 2:
2.48/0.81	
2.48/0.81	([b, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([a, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 1 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],true) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, a],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([c, b],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	([b, c],false) is interpreted by
2.48/0.81	 /   \
2.48/0.81	| 1 0 |
2.48/0.81	| 0 1 |
2.48/0.81	 \   /
2.48/0.81	
2.48/0.81	Remains to prove termination of the 25-rule system
2.48/0.81	{ ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([a, b],false) ,
2.48/0.81	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.48/0.81	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.82	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.82	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.82	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.82	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.82	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.82	
2.48/0.82	
2.48/0.82	The system was filtered by the following matrix interpretation
2.48/0.82	of type E_J with J = {1,...,2} and dimension 2:
2.48/0.82	
2.48/0.82	([b, a],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([a, b],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([a, a],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([c, a],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([a, c],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([b, a],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([b, b],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([a, c],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([b, b],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([c, c],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([c, b],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 1 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([b, c],true) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([c, a],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([c, b],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	([b, c],false) is interpreted by
2.48/0.82	 /   \
2.48/0.82	| 1 0 |
2.48/0.82	| 0 1 |
2.48/0.82	 \   /
2.48/0.82	
2.48/0.82	Remains to prove termination of the 24-rule system
2.48/0.82	{ ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.48/0.82	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.82	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.82	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.82	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.82	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.82	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.82	
2.48/0.82	
2.48/0.82	The system was filtered by the following matrix interpretation
2.48/0.82	of type E_J with J = {1,...,2} and dimension 3:
2.48/0.82	
2.48/0.82	([b, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 1 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 1 1 |
2.48/0.82	 \     /
2.48/0.82	([a, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	
2.48/0.82	Remains to prove termination of the 23-rule system
2.48/0.82	{ ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.48/0.82	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.82	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.82	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.82	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.82	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.82	
2.48/0.82	
2.48/0.82	The system was filtered by the following matrix interpretation
2.48/0.82	of type E_J with J = {1,...,2} and dimension 3:
2.48/0.82	
2.48/0.82	([b, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 1 1 |
2.48/0.82	 \     /
2.48/0.82	([a, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 1 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	
2.48/0.82	Remains to prove termination of the 22-rule system
2.48/0.82	{ ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.82	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.82	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.82	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.82	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.82	
2.48/0.82	
2.48/0.82	The system was filtered by the following matrix interpretation
2.48/0.82	of type E_J with J = {1,...,2} and dimension 3:
2.48/0.82	
2.48/0.82	([b, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([a, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 1 1 |
2.48/0.82	 \     /
2.48/0.82	([a, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],true) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 1 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, a],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([c, b],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	([b, c],false) is interpreted by
2.48/0.82	 /     \
2.48/0.82	| 1 0 0 |
2.48/0.82	| 0 1 0 |
2.48/0.82	| 0 0 0 |
2.48/0.82	 \     /
2.48/0.82	
2.48/0.82	Remains to prove termination of the 21-rule system
2.48/0.82	{ ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.48/0.82	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.48/0.82	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([a, b],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.48/0.82	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([b, b],false) ,
2.48/0.82	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.48/0.82	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.48/0.82	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.48/0.82	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.48/0.82	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ([c, b],false) ,
2.48/0.82	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.48/0.82	
2.48/0.82	
2.48/0.82	The system is trivially terminating.
2.51/0.87	EOF