3.83/1.16	YES
3.94/1.19	
3.94/1.19	
3.94/1.19	Applying context closure of depth 1 in the following form: System R over Sigma
3.94/1.19	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
3.94/1.19	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
3.94/1.19	
3.94/1.19	Remains to prove termination of the 63-rule system
3.94/1.19	{ [b, b] [b, b] [b, c] [c, b] -> [b, c] [c, a] [a, c] [c, b] ,
3.94/1.19	  [b, a] [a, c] [c, b] [b, b] -> [b, b] [b, c] [c, c] [c, b] ,
3.94/1.19	  [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, b] ->= [b, c] [c, c] [c, c] [c, b] ,
3.94/1.19	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.19	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, b] ->= [b, c] [c, c] [c, b] [b, b] ,
3.94/1.19	  [b, b] [b, b] [b, c] [c, c] -> [b, c] [c, a] [a, c] [c, c] ,
3.94/1.19	  [b, a] [a, c] [c, b] [b, c] -> [b, b] [b, c] [c, c] [c, c] ,
3.94/1.19	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, c] ->= [b, c] [c, c] [c, c] [c, c] ,
3.94/1.19	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.19	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, c] ->= [b, c] [c, c] [c, b] [b, c] ,
3.94/1.19	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.19	  [b, a] [a, c] [c, b] [b, a] -> [b, b] [b, c] [c, c] [c, a] ,
3.94/1.19	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, a] ->= [b, c] [c, c] [c, c] [c, a] ,
3.94/1.19	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.19	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.19	  [b, b] [b, a] [a, a] [a, a] ->= [b, c] [c, c] [c, b] [b, a] ,
3.94/1.19	  [c, b] [b, b] [b, c] [c, b] -> [c, c] [c, a] [a, c] [c, b] ,
3.94/1.19	  [c, a] [a, c] [c, b] [b, b] -> [c, b] [b, c] [c, c] [c, b] ,
3.94/1.19	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.19	  [c, b] [b, a] [a, a] [a, b] ->= [c, c] [c, c] [c, c] [c, b] ,
3.94/1.19	  [c, a] [a, a] [a, b] [b, b] ->= [c, b] [b, a] [a, a] [a, b] ,
3.94/1.19	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.19	  [c, b] [b, a] [a, a] [a, b] ->= [c, c] [c, c] [c, b] [b, b] ,
3.94/1.19	  [c, b] [b, b] [b, c] [c, c] -> [c, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [c, a] [a, c] [c, b] [b, c] -> [c, b] [b, c] [c, c] [c, c] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, b] [b, a] [a, a] [a, c] ->= [c, c] [c, c] [c, c] [c, c] ,
3.94/1.20	  [c, a] [a, a] [a, b] [b, c] ->= [c, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, a] [a, a] [a, c] ->= [c, c] [c, c] [c, b] [b, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, a] [a, c] [c, b] [b, a] -> [c, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, b] [b, a] [a, a] [a, a] ->= [c, c] [c, c] [c, c] [c, a] ,
3.94/1.20	  [c, a] [a, a] [a, b] [b, a] ->= [c, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, a] [a, a] [a, a] ->= [c, c] [c, c] [c, b] [b, a] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, b] -> [a, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, b] -> [a, b] [b, c] [c, c] [c, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, b] ->= [a, c] [c, c] [c, c] [c, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, b] ->= [a, c] [c, c] [c, b] [b, b] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, c] -> [a, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, c] -> [a, b] [b, c] [c, c] [c, c] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, c] ->= [a, c] [c, c] [c, c] [c, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, c] ->= [a, c] [c, c] [c, b] [b, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, a] ->= [a, c] [c, c] [c, c] [c, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, a] [a, a] [a, a] ->= [a, c] [c, c] [c, b] [b, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 2:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 2 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 2 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 35-rule system
3.94/1.20	{ [b, b] [b, b] [b, c] [c, b] -> [b, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, c] -> [b, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, a] [a, c] [c, b] [b, a] -> [b, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, b] -> [c, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, c] -> [c, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, b] -> [a, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, c] -> [a, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 5:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 1 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 1 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 1 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 34-rule system
3.94/1.20	{ [b, b] [b, b] [b, c] [c, b] -> [b, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, c] -> [b, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, b] -> [c, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, c] -> [c, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, b] -> [a, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, c] -> [a, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 5:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 1 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 1 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 32-rule system
3.94/1.20	{ [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, b] -> [c, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, c] -> [c, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, b] -> [a, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, c] -> [a, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 5:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 1 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 1 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 30-rule system
3.94/1.20	{ [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, b] -> [a, c] [c, a] [a, c] [c, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, c] -> [a, c] [c, a] [a, c] [c, c] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 5:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 1 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 1 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 28-rule system
3.94/1.20	{ [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, c] [c, b] [b, a] -> [a, b] [b, c] [c, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 5:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 1 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 1 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 1 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 0 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /         \
3.94/1.20	| 1 0 1 0 0 |
3.94/1.20	| 0 1 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	| 0 0 0 0 0 |
3.94/1.20	 \         /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 27-rule system
3.94/1.20	{ [b, b] [b, b] [b, b] [b, b] -> [b, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, c] -> [b, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, b] [b, b] [b, c] [c, a] -> [b, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [b, b] [b, b] [b, b] [b, a] -> [b, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, b] -> [c, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, b] ->= [c, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, c] -> [c, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, c] ->= [c, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [c, b] [b, b] [b, b] [b, a] -> [c, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [c, c] [c, a] [a, b] [b, a] ->= [c, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, b] -> [a, b] [b, c] [c, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, c] -> [a, b] [b, c] [c, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, b] [b, b] [b, c] [c, a] -> [a, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, b] [b, b] [b, b] [b, a] -> [a, b] [b, c] [c, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 2:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 2 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 3 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 2 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 13-rule system
3.94/1.20	{ [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, b] ->= [b, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, c] ->= [b, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, c] ->= [b, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [b, c] [c, a] [a, b] [b, a] ->= [b, b] [b, b] [b, a] [a, a] ,
3.94/1.20	  [c, b] [b, b] [b, c] [c, a] -> [c, c] [c, a] [a, c] [c, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, c] ->= [a, b] [b, a] [a, a] [a, c] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, c] ->= [a, b] [b, b] [b, a] [a, c] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system was filtered by the following matrix interpretation
3.94/1.20	of type E_J with J = {1,...,2} and dimension 2:
3.94/1.20	
3.94/1.20	[b, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 1 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[b, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[c, c] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, b] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	[a, a] is interpreted by
3.94/1.20	 /   \
3.94/1.20	| 1 0 |
3.94/1.20	| 0 1 |
3.94/1.20	 \   /
3.94/1.20	
3.94/1.20	Remains to prove termination of the 6-rule system
3.94/1.20	{ [b, a] [a, a] [a, b] [b, b] ->= [b, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [b, a] [a, a] [a, b] [b, a] ->= [b, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, b] ->= [a, b] [b, a] [a, a] [a, b] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, b] ->= [a, b] [b, b] [b, a] [a, b] ,
3.94/1.20	  [a, a] [a, a] [a, b] [b, a] ->= [a, b] [b, a] [a, a] [a, a] ,
3.94/1.20	  [a, c] [c, a] [a, b] [b, a] ->= [a, b] [b, b] [b, a] [a, a] }
3.94/1.20	
3.94/1.20	
3.94/1.20	The system is trivially terminating.
4.01/1.23	EOF