0.00/0.50	YES
0.00/0.52	
0.00/0.52	
0.00/0.52	Applying context closure of depth 1 in the following form: System R over Sigma
0.00/0.52	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
0.00/0.52	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
0.00/0.52	
0.00/0.52	Remains to prove termination of the 8-rule system
0.00/0.52	{ [a, a] [a, a] [a, a] -> [a, a] ,
0.00/0.52	  [a, a] [a, a] [a, a] ->= [a, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
0.00/0.52	  [a, a] [a, a] [a, b] -> [a, b] ,
0.00/0.52	  [a, a] [a, a] [a, b] ->= [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, a] -> [b, a] ,
0.00/0.52	  [b, a] [a, a] [a, a] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
0.00/0.52	  [b, a] [a, a] [a, b] -> [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, b] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] }
0.00/0.52	
0.00/0.52	
0.00/0.52	
0.00/0.52	The system was filtered by the following matrix interpretation
0.00/0.52	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.52	
0.00/0.52	[a, a] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 1 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 1 |
0.00/0.52	| 0 1 1 0 |
0.00/0.52	 \       /
0.00/0.52	[a, b] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	 \       /
0.00/0.52	[b, a] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	 \       /
0.00/0.52	[b, b] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	 \       /
0.00/0.52	
0.00/0.52	Remains to prove termination of the 6-rule system
0.00/0.52	{ [a, a] [a, a] [a, b] -> [a, b] ,
0.00/0.52	  [a, a] [a, a] [a, b] ->= [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, a] -> [b, a] ,
0.00/0.52	  [b, a] [a, a] [a, a] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, a] ,
0.00/0.52	  [b, a] [a, a] [a, b] -> [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, b] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, b] }
0.00/0.52	
0.00/0.52	
0.00/0.52	The system was filtered by the following matrix interpretation
0.00/0.52	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.52	
0.00/0.52	[a, a] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 1 |
0.00/0.52	| 0 0 1 0 |
0.00/0.52	 \       /
0.00/0.52	[a, b] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	 \       /
0.00/0.52	[b, a] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 1 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	 \       /
0.00/0.52	[b, b] is interpreted by
0.00/0.52	 /       \
0.00/0.52	| 1 0 0 0 |
0.00/0.52	| 0 1 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	| 0 0 0 0 |
0.00/0.52	 \       /
0.00/0.52	
0.00/0.52	Remains to prove termination of the 4-rule system
0.00/0.52	{ [a, a] [a, a] [a, b] -> [a, b] ,
0.00/0.52	  [a, a] [a, a] [a, b] ->= [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, a] -> [b, a] ,
0.00/0.52	  [b, a] [a, a] [a, a] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, a] }
0.00/0.52	
0.00/0.52	
0.00/0.52	The system was filtered by the following matrix interpretation
0.00/0.52	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.52	
0.00/0.52	[a, a] is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 1 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	[a, b] is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	[b, a] is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	[b, b] is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	
0.00/0.52	Remains to prove termination of the 2-rule system
0.00/0.52	{ [a, a] [a, a] [a, b] ->= [a, b] [b, a] [a, a] [a, a] [a, b] [b, b] ,
0.00/0.52	  [b, a] [a, a] [a, a] ->= [b, b] [b, a] [a, a] [a, a] [a, b] [b, a] }
0.00/0.52	
0.00/0.52	
0.00/0.52	The system is trivially terminating.
1.39/0.55	EOF