0.00/0.49	YES
0.00/0.51	
0.00/0.51	
0.00/0.51	Applying context closure of depth 1 in the following form: System R over Sigma
0.00/0.51	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
0.00/0.51	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
0.00/0.51	
0.00/0.51	Remains to prove termination of the 54-rule system
0.00/0.51	{ [a, a] [a, a] [a, c] [c, a] -> [a, b] [b, b] [b, c] [c, a] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
0.00/0.51	  [a, a] [a, c] [c, a] [a, a] ->= [a, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, a] ->= [a, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [a, c] [c, a] [a, a] [a, a] ->= [a, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, c] -> [a, b] [b, b] [b, c] [c, c] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, c] -> [a, a] [a, a] [a, b] [b, c] ,
0.00/0.51	  [a, a] [a, c] [c, a] [a, c] ->= [a, a] [a, b] [b, b] [b, c] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, c] ->= [a, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [a, c] [c, a] [a, a] [a, c] ->= [a, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, b] -> [a, b] [b, b] [b, c] [c, b] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [a, a] [a, c] [c, a] [a, b] ->= [a, a] [a, b] [b, b] [b, b] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, b] ->= [a, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [a, b] [b, a] [a, c] [c, b] ->= [a, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [a, c] [c, a] [a, a] [a, b] ->= [a, a] [a, a] [a, a] [a, b] ,
0.00/0.51	  [c, a] [a, a] [a, c] [c, a] -> [c, b] [b, b] [b, c] [c, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
0.00/0.51	  [c, a] [a, c] [c, a] [a, a] ->= [c, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, a] ->= [c, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [c, a] [a, a] [a, c] [c, c] -> [c, b] [b, b] [b, c] [c, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] ,
0.00/0.51	  [c, a] [a, c] [c, a] [a, c] ->= [c, a] [a, b] [b, b] [b, c] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, c] ->= [c, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] ->= [c, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [c, a] [a, a] [a, c] [c, b] -> [c, b] [b, b] [b, c] [c, b] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [c, a] [a, c] [c, a] [a, b] ->= [c, a] [a, b] [b, b] [b, b] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, b] ->= [c, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] ->= [c, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] ,
0.00/0.51	  [b, a] [a, a] [a, c] [c, a] -> [b, b] [b, b] [b, c] [c, a] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
0.00/0.51	  [b, a] [a, c] [c, a] [a, a] ->= [b, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, a] ->= [b, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, a] ->= [b, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [b, a] [a, a] [a, c] [c, c] -> [b, b] [b, b] [b, c] [c, c] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
0.00/0.51	  [b, a] [a, c] [c, a] [a, c] ->= [b, a] [a, b] [b, b] [b, c] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, c] ->= [b, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, c] ->= [b, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [b, a] [a, a] [a, c] [c, b] -> [b, b] [b, b] [b, c] [c, b] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [b, a] [a, c] [c, a] [a, b] ->= [b, a] [a, b] [b, b] [b, b] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, b] ->= [b, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, b] ->= [b, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] }
0.00/0.51	
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.51	
0.00/0.51	[a, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 33-rule system
0.00/0.51	{ [a, a] [a, a] [a, c] [c, a] -> [a, b] [b, b] [b, c] [c, a] ,
0.00/0.51	  [a, a] [a, c] [c, a] [a, a] ->= [a, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, c] -> [a, b] [b, b] [b, c] [c, c] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, b] -> [a, b] [b, b] [b, c] [c, b] ,
0.00/0.51	  [a, b] [b, b] [b, b] [b, b] ->= [a, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
0.00/0.51	  [c, a] [a, c] [c, a] [a, a] ->= [c, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, a] ->= [c, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, c] ->= [c, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] ->= [c, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [c, b] [b, b] [b, b] [b, b] ->= [c, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] ->= [c, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
0.00/0.51	  [b, a] [a, c] [c, a] [a, a] ->= [b, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, a] ->= [b, c] [c, c] [c, b] [b, a] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, a] ->= [b, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, c] ->= [b, c] [c, c] [c, b] [b, c] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, c] ->= [b, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [b, b] [b, b] [b, b] [b, b] ->= [b, c] [c, c] [c, b] [b, b] ,
0.00/0.51	  [b, b] [b, a] [a, c] [c, b] ->= [b, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.51	
0.00/0.51	[a, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 16-rule system
0.00/0.51	{ [a, a] [a, a] [a, c] [c, a] -> [a, b] [b, b] [b, c] [c, a] ,
0.00/0.51	  [a, a] [a, c] [c, a] [a, a] ->= [a, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, c] -> [a, b] [b, b] [b, c] [c, c] ,
0.00/0.51	  [a, a] [a, a] [a, c] [c, b] -> [a, b] [b, b] [b, c] [c, b] ,
0.00/0.51	  [c, a] [a, c] [c, a] [a, a] ->= [c, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, a] ->= [c, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] ->= [c, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] ->= [c, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] ,
0.00/0.51	  [b, a] [a, c] [c, a] [a, a] ->= [b, a] [a, b] [b, b] [b, a] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system was filtered by the following matrix interpretation
0.00/0.51	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.51	
0.00/0.51	[a, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 1 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[a, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[b, a] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, c] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	[c, b] is interpreted by
0.00/0.51	 /   \
0.00/0.51	| 1 0 |
0.00/0.51	| 0 1 |
0.00/0.51	 \   /
0.00/0.51	
0.00/0.51	Remains to prove termination of the 9-rule system
0.00/0.51	{ [c, b] [b, a] [a, c] [c, a] ->= [c, a] [a, a] [a, c] [c, a] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, a] ->= [c, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, c] ->= [c, a] [a, a] [a, c] [c, c] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, c] ->= [c, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [c, b] [b, a] [a, c] [c, b] ->= [c, a] [a, a] [a, c] [c, b] ,
0.00/0.51	  [c, c] [c, a] [a, a] [a, b] ->= [c, a] [a, a] [a, a] [a, b] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, a] ->= [b, a] [a, a] [a, a] [a, a] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, c] ->= [b, a] [a, a] [a, a] [a, c] ,
0.00/0.51	  [b, c] [c, a] [a, a] [a, b] ->= [b, a] [a, a] [a, a] [a, b] }
0.00/0.51	
0.00/0.51	
0.00/0.51	The system is trivially terminating.
1.75/0.69	EOF