2.07/0.71	YES
2.23/0.74	
2.23/0.74	
2.23/0.74	Applying context closure of depth 1 in the following form: System R over Sigma
2.23/0.74	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
2.23/0.74	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
2.23/0.74	
2.23/0.74	Remains to prove termination of the 36-rule system
2.23/0.74	{ [a, a] [a, a] -> [a, a] ,
2.23/0.74	  [a, a] [a, b] [b, a] -> [a, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [a, b] [b, a] -> [a, a] ,
2.23/0.74	  [a, c] [c, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] ,
2.23/0.74	  [a, a] [a, b] -> [a, b] ,
2.23/0.74	  [a, a] [a, b] [b, b] -> [a, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [a, b] [b, b] -> [a, b] ,
2.23/0.74	  [a, c] [c, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] ,
2.23/0.74	  [a, a] [a, c] -> [a, c] ,
2.23/0.74	  [a, a] [a, b] [b, c] -> [a, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [a, b] [b, c] -> [a, c] ,
2.23/0.74	  [a, c] [c, c] [c, c] -> [a, b] [b, b] [b, a] [a, c] ,
2.23/0.74	  [b, a] [a, a] -> [b, a] ,
2.23/0.74	  [b, a] [a, b] [b, a] -> [b, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [b, b] [b, a] -> [b, a] ,
2.23/0.74	  [b, c] [c, c] [c, a] -> [b, b] [b, b] [b, a] [a, a] ,
2.23/0.74	  [b, a] [a, b] -> [b, b] ,
2.23/0.74	  [b, a] [a, b] [b, b] -> [b, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [b, b] [b, b] -> [b, b] ,
2.23/0.74	  [b, c] [c, c] [c, b] -> [b, b] [b, b] [b, a] [a, b] ,
2.23/0.74	  [b, a] [a, c] -> [b, c] ,
2.23/0.74	  [b, a] [a, b] [b, c] -> [b, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [b, b] [b, c] -> [b, c] ,
2.23/0.74	  [b, c] [c, c] [c, c] -> [b, b] [b, b] [b, a] [a, c] ,
2.23/0.74	  [c, a] [a, a] -> [c, a] ,
2.23/0.74	  [c, a] [a, b] [b, a] -> [c, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [c, b] [b, a] -> [c, a] ,
2.23/0.74	  [c, c] [c, c] [c, a] -> [c, b] [b, b] [b, a] [a, a] ,
2.23/0.74	  [c, a] [a, b] -> [c, b] ,
2.23/0.74	  [c, a] [a, b] [b, b] -> [c, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [c, b] [b, b] -> [c, b] ,
2.23/0.74	  [c, c] [c, c] [c, b] -> [c, b] [b, b] [b, a] [a, b] ,
2.23/0.74	  [c, a] [a, c] -> [c, c] ,
2.23/0.74	  [c, a] [a, b] [b, c] -> [c, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [c, b] [b, c] -> [c, c] ,
2.23/0.74	  [c, c] [c, c] [c, c] -> [c, b] [b, b] [b, a] [a, c] }
2.23/0.74	
2.23/0.74	
2.23/0.74	
2.23/0.74	The system was filtered by the following matrix interpretation
2.23/0.74	of type E_J with J = {1,...,2} and dimension 2:
2.23/0.74	
2.23/0.74	[a, a] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 1 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[a, b] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 1 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[b, a] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 0 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[a, c] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 0 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[c, a] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 1 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[c, c] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 1 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[b, b] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 0 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[c, b] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 1 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	[b, c] is interpreted by
2.23/0.74	 /   \
2.23/0.74	| 1 0 |
2.23/0.74	| 0 1 |
2.23/0.74	 \   /
2.23/0.74	
2.23/0.74	Remains to prove termination of the 21-rule system
2.23/0.74	{ [a, a] [a, b] [b, a] -> [a, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [a, b] [b, a] -> [a, a] ,
2.23/0.74	  [a, c] [c, c] [c, a] -> [a, b] [b, b] [b, a] [a, a] ,
2.23/0.74	  [a, a] [a, b] [b, b] -> [a, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [a, b] [b, b] -> [a, b] ,
2.23/0.74	  [a, c] [c, c] [c, b] -> [a, b] [b, b] [b, a] [a, b] ,
2.23/0.74	  [a, a] [a, b] [b, c] -> [a, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [b, a] [a, b] [b, a] -> [b, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [b, b] [b, a] -> [b, a] ,
2.23/0.74	  [b, a] [a, b] [b, b] -> [b, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [b, b] [b, b] -> [b, b] ,
2.23/0.74	  [b, a] [a, c] -> [b, c] ,
2.23/0.74	  [b, a] [a, b] [b, c] -> [b, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [b, b] [b, c] -> [b, c] ,
2.23/0.74	  [c, a] [a, b] [b, a] -> [c, b] [b, a] [a, c] [c, a] ,
2.23/0.74	  [c, b] [b, a] -> [c, a] ,
2.23/0.74	  [c, a] [a, b] [b, b] -> [c, b] [b, a] [a, c] [c, b] ,
2.23/0.74	  [c, b] [b, b] -> [c, b] ,
2.23/0.74	  [c, a] [a, c] -> [c, c] ,
2.23/0.74	  [c, a] [a, b] [b, c] -> [c, b] [b, a] [a, c] [c, c] ,
2.23/0.74	  [c, b] [b, c] -> [c, c] }
2.23/0.74	
2.23/0.74	
2.23/0.74	The system was reversed.
2.23/0.74	
2.23/0.74	Remains to prove termination of the 21-rule system
2.23/0.74	{ [b, a] [a, b] [a, a] -> [c, a] [a, c] [b, a] [a, b] ,
2.23/0.74	  [b, a] [a, b] -> [a, a] ,
2.23/0.74	  [c, a] [c, c] [a, c] -> [a, a] [b, a] [b, b] [a, b] ,
2.23/0.74	  [b, b] [a, b] [a, a] -> [c, b] [a, c] [b, a] [a, b] ,
2.23/0.74	  [b, b] [a, b] -> [a, b] ,
2.23/0.74	  [c, b] [c, c] [a, c] -> [a, b] [b, a] [b, b] [a, b] ,
2.23/0.74	  [b, c] [a, b] [a, a] -> [c, c] [a, c] [b, a] [a, b] ,
2.23/0.74	  [b, a] [a, b] [b, a] -> [c, a] [a, c] [b, a] [b, b] ,
2.23/0.74	  [b, a] [b, b] -> [b, a] ,
2.23/0.74	  [b, b] [a, b] [b, a] -> [c, b] [a, c] [b, a] [b, b] ,
2.23/0.74	  [b, b] [b, b] -> [b, b] ,
2.23/0.74	  [a, c] [b, a] -> [b, c] ,
2.23/0.74	  [b, c] [a, b] [b, a] -> [c, c] [a, c] [b, a] [b, b] ,
2.23/0.74	  [b, c] [b, b] -> [b, c] ,
2.23/0.74	  [b, a] [a, b] [c, a] -> [c, a] [a, c] [b, a] [c, b] ,
2.23/0.74	  [b, a] [c, b] -> [c, a] ,
2.23/0.74	  [b, b] [a, b] [c, a] -> [c, b] [a, c] [b, a] [c, b] ,
2.23/0.74	  [b, b] [c, b] -> [c, b] ,
2.23/0.74	  [a, c] [c, a] -> [c, c] ,
2.23/0.74	  [b, c] [a, b] [c, a] -> [c, c] [a, c] [b, a] [c, b] ,
2.23/0.74	  [b, c] [c, b] -> [c, c] }
2.23/0.74	
2.23/0.74	
2.23/0.74	The dependency pairs transformation was applied.
2.23/0.74	
2.23/0.74	Remains to prove termination of the 61-rule system
2.23/0.74	{ ([b, a],true) ([a, b],false) ([a, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([a, b],false) ,
2.23/0.74	  ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.74	  ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([a, b],false) ,
2.23/0.74	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.74	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([a, a],false) -> ([a, c],true) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([a, a],false) -> ([b, a],true) ([a, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.23/0.74	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.23/0.74	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.74	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([a, c],true) ([b, a],false) ([b, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, a],true) ([b, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([b, a],false) -> ([b, b],true) ,
2.23/0.74	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, a],true) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([c, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([c, b],false) ,
2.23/0.74	  ([b, a],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.23/0.74	  ([b, a],true) ([c, b],false) -> ([c, a],true) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([c, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([c, b],false) ,
2.23/0.74	  ([b, b],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.23/0.74	  ([b, b],true) ([c, b],false) -> ([c, b],true) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([a, c],true) ([b, a],false) ([c, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([b, a],true) ([c, b],false) ,
2.23/0.74	  ([b, c],true) ([a, b],false) ([c, a],false) -> ([c, b],true) ,
2.23/0.74	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.74	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.74	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.74	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.74	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 2:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 29-rule system
2.23/0.75	{ ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([c, a],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.75	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.75	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.23/0.75	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.75	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.23/0.75	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 2:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 27-rule system
2.23/0.75	{ ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.75	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.23/0.75	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.75	  ([a, c],true) ([b, a],false) -> ([b, c],true) ,
2.23/0.75	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 2:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 26-rule system
2.23/0.75	{ ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, a],true) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([c, b],true) ([c, c],false) ([a, c],false) -> ([b, b],true) ([a, b],false) ,
2.23/0.75	  ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.23/0.75	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.75	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 2:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 1 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /   \
2.23/0.75	| 1 0 |
2.23/0.75	| 0 1 |
2.23/0.75	 \   /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 24-rule system
2.23/0.75	{ ([b, a],true) ([b, b],false) -> ([b, a],true) ,
2.23/0.75	  ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.75	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 3:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 1 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 1 1 |
2.23/0.75	 \     /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 23-rule system
2.23/0.75	{ ([b, b],true) ([b, b],false) -> ([b, b],true) ,
2.23/0.75	  ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 3:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 1 1 |
2.23/0.75	 \     /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 1 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 22-rule system
2.23/0.75	{ ([b, c],true) ([b, b],false) -> ([b, c],true) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system was filtered by the following matrix interpretation
2.23/0.75	of type E_J with J = {1,...,2} and dimension 3:
2.23/0.75	
2.23/0.75	([b, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([a, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 1 1 |
2.23/0.75	 \     /
2.23/0.75	([b, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],true) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 1 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, a],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([c, b],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	([b, c],false) is interpreted by
2.23/0.75	 /     \
2.23/0.75	| 1 0 0 |
2.23/0.75	| 0 1 0 |
2.23/0.75	| 0 0 0 |
2.23/0.75	 \     /
2.23/0.75	
2.23/0.75	Remains to prove termination of the 21-rule system
2.23/0.75	{ ([b, a],false) ([a, b],false) ([a, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ->= ([a, a],false) ,
2.23/0.75	  ([c, a],false) ([c, c],false) ([a, c],false) ->= ([a, a],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ->= ([a, b],false) ,
2.23/0.75	  ([c, b],false) ([c, c],false) ([a, c],false) ->= ([a, b],false) ([b, a],false) ([b, b],false) ([a, b],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([a, b],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([b, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, a],false) ([b, b],false) ->= ([b, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([b, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, b],false) ([b, b],false) ->= ([b, b],false) ,
2.23/0.75	  ([a, c],false) ([b, a],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([b, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([b, b],false) ,
2.23/0.75	  ([b, c],false) ([b, b],false) ->= ([b, c],false) ,
2.23/0.75	  ([b, a],false) ([a, b],false) ([c, a],false) ->= ([c, a],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, a],false) ([c, b],false) ->= ([c, a],false) ,
2.23/0.75	  ([b, b],false) ([a, b],false) ([c, a],false) ->= ([c, b],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, b],false) ([c, b],false) ->= ([c, b],false) ,
2.23/0.75	  ([a, c],false) ([c, a],false) ->= ([c, c],false) ,
2.23/0.75	  ([b, c],false) ([a, b],false) ([c, a],false) ->= ([c, c],false) ([a, c],false) ([b, a],false) ([c, b],false) ,
2.23/0.75	  ([b, c],false) ([c, b],false) ->= ([c, c],false) }
2.23/0.75	
2.23/0.75	
2.23/0.75	The system is trivially terminating.
2.23/0.78	EOF