12.01/3.40	YES
12.29/3.43	
12.29/3.43	
12.29/3.43	Applying context closure of depth 1 in the following form: System R over Sigma
12.29/3.43	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
12.29/3.43	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
12.29/3.43	
12.29/3.43	Remains to prove termination of the 4-rule system
12.29/3.43	{ [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, a] ,
12.29/3.43	  [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, b] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, b] ,
12.29/3.43	  [b, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, a] ,
12.29/3.43	  [b, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, b] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, b] }
12.29/3.43	
12.29/3.43	
12.29/3.43	
12.29/3.43	The system was filtered by the following matrix interpretation
12.29/3.43	of type E_J with J = {1,...,2} and dimension 11:
12.29/3.43	
12.29/3.43	[a, a] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 1 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 1 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 1 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 1 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 1 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 1 |
12.29/3.43	| 0 0 0 0 0 0 1 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[a, b] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 1 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[b, b] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 1 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[b, a] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 1 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 1 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	
12.29/3.43	Remains to prove termination of the 2-rule system
12.29/3.43	{ [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, a] ,
12.29/3.43	  [b, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] -> [b, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, a] [a, b] [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] [b, a] }
12.29/3.43	
12.29/3.43	
12.29/3.43	The system was filtered by the following matrix interpretation
12.29/3.43	of type E_J with J = {1,...,2} and dimension 11:
12.29/3.43	
12.29/3.43	[a, a] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 1 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 1 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 1 0 0 0 |
12.29/3.43	| 0 0 1 0 0 0 0 0 2 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 1 0 |
12.29/3.43	| 0 0 1 0 0 0 0 0 0 0 1 |
12.29/3.43	| 0 1 0 0 0 0 1 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[a, b] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 1 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 1 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 1 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[b, b] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 1 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	[b, a] is interpreted by
12.29/3.43	 /                     \
12.29/3.43	| 1 0 1 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 1 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 1 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	| 0 0 0 0 0 0 0 0 0 0 0 |
12.29/3.43	 \                     /
12.29/3.43	
12.29/3.43	Remains to prove termination of the 0-rule system
12.29/3.43	{ }
12.29/3.43	
12.29/3.43	
12.29/3.43	The system is trivially terminating.
12.47/3.52	EOF