0.00/0.47	YES
0.00/0.49	
0.00/0.49	
0.00/0.49	Applying context closure of depth 1 in the following form: System R over Sigma
0.00/0.49	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
0.00/0.49	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
0.00/0.49	
0.00/0.49	Remains to prove termination of the 12-rule system
0.00/0.49	{ [a, a] [a, a] -> [a, a] ,
0.00/0.49	  [a, a] [a, a] [a, a] -> [a, a] [a, b] [b, a] [a, b] [b, a] ,
0.00/0.49	  [a, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] ,
0.00/0.49	  [a, a] [a, b] -> [a, b] ,
0.00/0.49	  [a, a] [a, a] [a, b] -> [a, a] [a, b] [b, a] [a, b] [b, b] ,
0.00/0.49	  [a, b] [b, b] [b, b] [b, b] [b, b] -> [a, a] [a, b] ,
0.00/0.49	  [b, a] [a, a] -> [b, a] ,
0.00/0.49	  [b, a] [a, a] [a, a] -> [b, a] [a, b] [b, a] [a, b] [b, a] ,
0.00/0.49	  [b, b] [b, b] [b, b] [b, b] [b, a] -> [b, a] [a, a] ,
0.00/0.49	  [b, a] [a, b] -> [b, b] ,
0.00/0.49	  [b, a] [a, a] [a, b] -> [b, a] [a, b] [b, a] [a, b] [b, b] ,
0.00/0.49	  [b, b] [b, b] [b, b] [b, b] [b, b] -> [b, a] [a, b] }
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	[a, a] is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 2 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	[a, b] is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	[b, a] is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	[b, b] is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 4-rule system
0.00/0.49	{ [a, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] ,
0.00/0.49	  [a, a] [a, a] [a, b] -> [a, a] [a, b] [b, a] [a, b] [b, b] ,
0.00/0.49	  [b, a] [a, b] -> [b, b] ,
0.00/0.49	  [b, a] [a, a] [a, b] -> [b, a] [a, b] [b, a] [a, b] [b, b] }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was reversed.
0.00/0.49	
0.00/0.49	Remains to prove termination of the 4-rule system
0.00/0.49	{ [b, a] [b, b] [b, b] [b, b] [a, b] -> [a, a] [a, a] ,
0.00/0.49	  [a, b] [a, a] [a, a] -> [b, b] [a, b] [b, a] [a, b] [a, a] ,
0.00/0.49	  [a, b] [b, a] -> [b, b] ,
0.00/0.49	  [a, b] [a, a] [b, a] -> [b, b] [a, b] [b, a] [a, b] [b, a] }
0.00/0.49	
0.00/0.49	
0.00/0.49	The dependency pairs transformation was applied.
0.00/0.49	
0.00/0.49	Remains to prove termination of the 11-rule system
0.00/0.49	{ ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([a, a],false) -> ([b, a],true) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([b, a],true) ([a, b],false) ([b, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([b, a],true) ,
0.00/0.49	  ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	([a, b],true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([a, a],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([b, a],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([a, b],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([b, a],true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([b, b],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 8-rule system
0.00/0.49	{ ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ,
0.00/0.49	  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ,
0.00/0.49	  ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system was filtered by the following matrix interpretation
0.00/0.49	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.49	
0.00/0.49	([a, b],true) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([a, a],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 2 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([b, a],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([a, b],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 0 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	([b, b],false) is interpreted by
0.00/0.49	 /   \
0.00/0.49	| 1 1 |
0.00/0.49	| 0 1 |
0.00/0.49	 \   /
0.00/0.49	
0.00/0.49	Remains to prove termination of the 4-rule system
0.00/0.49	{ ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
0.00/0.49	  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
0.00/0.49	  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }
0.00/0.49	
0.00/0.49	
0.00/0.49	The system is trivially terminating.
0.00/0.52	EOF