17.18/4.69	YES
17.51/4.72	
17.51/4.72	
17.51/4.72	Applying context closure of depth 1 in the following form: System R over Sigma
17.51/4.72	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
17.51/4.72	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
17.51/4.72	
17.51/4.72	Remains to prove termination of the 4-rule system
17.51/4.72	{ [a, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
17.51/4.72	  [a, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, b] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] ,
17.51/4.72	  [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
17.51/4.72	  [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, b] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] }
17.51/4.72	
17.51/4.72	
17.51/4.72	
17.51/4.72	The system was filtered by the following matrix interpretation
17.51/4.72	of type E_J with J = {1,...,2} and dimension 9:
17.51/4.72	
17.51/4.72	[a, a] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 1 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 1 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 1 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 1 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 1 |
17.51/4.72	| 0 0 0 0 0 1 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[a, b] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 1 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[b, a] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 1 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 1 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[b, b] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	
17.51/4.72	Remains to prove termination of the 2-rule system
17.51/4.72	{ [a, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
17.51/4.72	  [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, a] [a, a] [a, b] [b, a] [a, a] [a, a] [a, b] [b, a] }
17.51/4.72	
17.51/4.72	
17.51/4.72	The system was filtered by the following matrix interpretation
17.51/4.72	of type E_J with J = {1,...,2} and dimension 9:
17.51/4.72	
17.51/4.72	[a, a] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 1 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 1 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 1 0 0 0 3 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 1 0 |
17.51/4.72	| 0 0 1 0 0 0 0 0 1 |
17.51/4.72	| 0 1 0 0 0 1 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[a, b] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 1 0 0 0 0 |
17.51/4.72	| 0 0 0 0 1 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[b, a] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 1 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 1 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	[b, b] is interpreted by
17.51/4.72	 /                 \
17.51/4.72	| 1 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 1 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	| 0 0 0 0 0 0 0 0 0 |
17.51/4.72	 \                 /
17.51/4.72	
17.51/4.72	Remains to prove termination of the 0-rule system
17.51/4.72	{ }
17.51/4.72	
17.51/4.72	
17.51/4.72	The system is trivially terminating.
17.72/4.81	EOF