5.03/1.49	YES
5.03/1.51	
5.03/1.51	
5.03/1.51	Applying context closure of depth 1 in the following form: System R over Sigma
5.03/1.51	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
5.03/1.51	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
5.03/1.51	
5.03/1.51	Remains to prove termination of the 4-rule system
5.03/1.51	{ [b, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, b] -> [b, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, b] ,
5.03/1.51	  [b, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] ,
5.03/1.51	  [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, b] -> [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, b] ,
5.03/1.51	  [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] }
5.03/1.51	
5.03/1.51	
5.03/1.51	
5.03/1.51	The system was filtered by the following matrix interpretation
5.03/1.51	of type E_J with J = {1,...,2} and dimension 2:
5.03/1.51	
5.03/1.51	[b, b] is interpreted by
5.03/1.51	 /   \
5.03/1.51	| 1 1 |
5.03/1.51	| 0 1 |
5.03/1.51	 \   /
5.03/1.51	[b, a] is interpreted by
5.03/1.51	 /   \
5.03/1.51	| 1 0 |
5.03/1.51	| 0 1 |
5.03/1.51	 \   /
5.03/1.51	[a, b] is interpreted by
5.03/1.51	 /   \
5.03/1.51	| 1 0 |
5.03/1.51	| 0 1 |
5.03/1.51	 \   /
5.03/1.51	[a, a] is interpreted by
5.03/1.51	 /   \
5.03/1.51	| 1 0 |
5.03/1.51	| 0 1 |
5.03/1.51	 \   /
5.03/1.51	
5.03/1.51	Remains to prove termination of the 2-rule system
5.03/1.51	{ [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, b] -> [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, b] ,
5.03/1.51	  [a, b] [b, a] [a, b] [b, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, b] [b, a] [a, b] [b, a] [a, b] [b, a] [a, a] }
5.03/1.51	
5.03/1.51	
5.03/1.51	The dependency pairs transformation was applied.
5.03/1.51	
5.03/1.51	Remains to prove termination of the 9-rule system
5.03/1.51	{ ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) -> ([a, b],true) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ,
5.03/1.51	  ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, a],false) ,
5.03/1.51	  ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ,
5.03/1.51	  ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ->= ([a, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) }
5.03/1.51	
5.03/1.51	
5.03/1.51	
5.03/1.51	
5.03/1.51	The system was filtered by the following matrix interpretation
5.03/1.51	of type E_J with J = {1,...,2} and dimension 8:
5.03/1.51	
5.03/1.51	([a, b],true) is interpreted by
5.03/1.51	 /               \
5.03/1.51	| 1 0 1 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	 \               /
5.03/1.51	([b, a],false) is interpreted by
5.03/1.51	 /               \
5.03/1.51	| 1 0 0 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 1 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 1 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	 \               /
5.03/1.51	([a, b],false) is interpreted by
5.03/1.51	 /               \
5.03/1.51	| 1 0 0 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 1 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 1 0 0 0 0 0 |
5.03/1.51	| 0 0 2 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 1 0 0 0 |
5.03/1.51	 \               /
5.03/1.51	([a, a],false) is interpreted by
5.03/1.51	 /               \
5.03/1.51	| 1 0 0 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	| 0 1 0 0 0 0 1 0 |
5.03/1.51	| 0 0 0 1 0 1 0 1 |
5.03/1.51	| 0 0 0 0 0 0 0 0 |
5.03/1.51	 \               /
5.03/1.51	
5.03/1.51	Remains to prove termination of the 2-rule system
5.03/1.51	{ ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ,
5.03/1.51	  ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) ([a, a],false) ([a, a],false) ->= ([a, a],false) ([a, a],false) ([a, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) ([a, a],false) }
5.03/1.51	
5.03/1.51	
5.03/1.51	The system is trivially terminating.
5.13/1.55	EOF