0.00/0.56	YES
1.56/0.59	
1.56/0.59	
1.56/0.59	The system was inverted.
1.56/0.59	
1.56/0.59	Remains to prove termination of the 6-rule system
1.56/0.59	{ a a c -> a c c ,
1.56/0.59	  b b c -> a b b ,
1.56/0.59	  c c b ->= a c a ,
1.56/0.59	  b a c ->= c a c ,
1.56/0.59	  c b c ->= b b b ,
1.56/0.59	  b b a ->= b a c }
1.56/0.59	
1.56/0.59	
1.56/0.59	Applying context closure of depth 1 in the following form: System R over Sigma
1.56/0.59	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
1.56/0.59	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
1.56/0.59	
1.56/0.59	Remains to prove termination of the 54-rule system
1.56/0.59	{ [a, a] [a, c] [c, c] [c, a] -> [a, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, a] -> [a, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, a] [a, a] ->= [a, c] [c, c] [c, b] [b, a] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, a] ->= [a, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, a] ->= [a, b] [b, b] [b, a] [a, a] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, c] -> [a, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, c] -> [a, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [a, a] [a, c] [c, a] [a, c] ->= [a, c] [c, c] [c, b] [b, c] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, c] ->= [a, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, b] -> [a, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, b] -> [a, b] [b, b] [b, c] [c, b] ,
1.56/0.59	  [a, a] [a, c] [c, a] [a, b] ->= [a, c] [c, c] [c, b] [b, b] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, b] ->= [a, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, b] ->= [a, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, a] -> [c, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [c, a] [a, b] [b, b] [b, a] -> [c, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [c, a] [a, c] [c, a] [a, a] ->= [c, c] [c, c] [c, b] [b, a] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, a] ->= [c, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, a] ->= [c, b] [b, b] [b, a] [a, a] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, c] -> [c, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [c, a] [a, b] [b, b] [b, c] -> [c, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [c, a] [a, c] [c, a] [a, c] ->= [c, c] [c, c] [c, b] [b, c] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, c] ->= [c, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, c] ->= [c, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, b] -> [c, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [c, a] [a, b] [b, b] [b, b] -> [c, b] [b, b] [b, c] [c, b] ,
1.56/0.59	  [c, a] [a, c] [c, a] [a, b] ->= [c, c] [c, c] [c, b] [b, b] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, b] ->= [c, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, b] ->= [c, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, a] -> [b, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [b, a] [a, b] [b, b] [b, a] -> [b, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [b, a] [a, c] [c, a] [a, a] ->= [b, c] [c, c] [c, b] [b, a] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, a] ->= [b, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, a] ->= [b, b] [b, b] [b, a] [a, a] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, c] -> [b, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [b, a] [a, b] [b, b] [b, c] -> [b, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [b, a] [a, c] [c, a] [a, c] ->= [b, c] [c, c] [c, b] [b, c] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, c] ->= [b, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, b] -> [b, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [b, a] [a, b] [b, b] [b, b] -> [b, b] [b, b] [b, c] [c, b] ,
1.56/0.59	  [b, a] [a, c] [c, a] [a, b] ->= [b, c] [c, c] [c, b] [b, b] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, b] ->= [b, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.59	
1.56/0.59	
1.56/0.59	
1.56/0.59	The system was filtered by the following matrix interpretation
1.56/0.59	of type E_J with J = {1,...,2} and dimension 2:
1.56/0.59	
1.56/0.59	[a, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[a, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[a, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	
1.56/0.59	Remains to prove termination of the 37-rule system
1.56/0.59	{ [a, a] [a, c] [c, c] [c, a] -> [a, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, a] -> [a, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, a] [a, a] ->= [a, c] [c, c] [c, b] [b, a] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, a] ->= [a, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, c] -> [a, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, c] -> [a, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, c] ->= [a, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, b] -> [a, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, b] -> [a, b] [b, b] [b, c] [c, b] ,
1.56/0.59	  [a, c] [c, a] [a, c] [c, b] ->= [a, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, b] ->= [a, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, a] -> [c, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, a] ->= [c, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, c] -> [c, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, c] ->= [c, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, c] ->= [c, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, b] -> [c, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [c, c] [c, a] [a, c] [c, b] ->= [c, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, b] ->= [c, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, a] -> [b, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, a] ->= [b, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, c] -> [b, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, c] ->= [b, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, b] -> [b, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [b, b] [b, b] [b, b] [b, b] ->= [b, c] [c, b] [b, c] [c, b] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.59	
1.56/0.59	
1.56/0.59	The system was filtered by the following matrix interpretation
1.56/0.59	of type E_J with J = {1,...,2} and dimension 2:
1.56/0.59	
1.56/0.59	[a, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[a, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[a, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 1 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, a] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[b, c] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	[c, b] is interpreted by
1.56/0.59	 /   \
1.56/0.59	| 1 0 |
1.56/0.59	| 0 1 |
1.56/0.59	 \   /
1.56/0.59	
1.56/0.59	Remains to prove termination of the 24-rule system
1.56/0.59	{ [a, a] [a, c] [c, c] [c, a] -> [a, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, a] -> [a, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, c] -> [a, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, c] -> [a, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, b] -> [a, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, a] -> [c, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, c] -> [c, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, c] ->= [c, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, b] -> [c, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, a] -> [b, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, c] -> [b, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, b] -> [b, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.59	
1.56/0.59	
1.56/0.59	The system was filtered by the following matrix interpretation
1.56/0.59	of type E_J with J = {1,...,2} and dimension 5:
1.56/0.59	
1.56/0.59	[a, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[a, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[a, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 1 0 |
1.56/0.59	| 0 0 0 0 1 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 1 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	
1.56/0.59	Remains to prove termination of the 23-rule system
1.56/0.59	{ [a, a] [a, c] [c, c] [c, a] -> [a, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, a] -> [a, b] [b, b] [b, c] [c, a] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, c] -> [a, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [a, a] [a, b] [b, b] [b, c] -> [a, b] [b, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, b] -> [a, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, a] -> [c, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, c] -> [c, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [c, a] [a, c] [c, c] [c, b] -> [c, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, a] -> [b, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, c] -> [b, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.59	  [b, a] [a, c] [c, c] [c, b] -> [b, a] [a, a] [a, c] [c, b] ,
1.56/0.59	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.59	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.59	
1.56/0.59	
1.56/0.59	The system was filtered by the following matrix interpretation
1.56/0.59	of type E_J with J = {1,...,2} and dimension 5:
1.56/0.59	
1.56/0.59	[a, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 1 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 2 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[a, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[a, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 1 0 1 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 1 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, a] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[b, c] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	[c, b] is interpreted by
1.56/0.59	 /         \
1.56/0.59	| 1 0 0 0 0 |
1.56/0.59	| 0 1 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	| 0 0 0 0 0 |
1.56/0.59	 \         /
1.56/0.59	
1.56/0.59	Remains to prove termination of the 21-rule system
1.56/0.59	{ [a, a] [a, c] [c, c] [c, a] -> [a, a] [a, a] [a, c] [c, a] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.59	  [a, a] [a, c] [c, c] [c, c] -> [a, a] [a, a] [a, c] [c, c] ,
1.56/0.59	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.60	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [a, a] [a, c] [c, c] [c, b] -> [a, a] [a, a] [a, c] [c, b] ,
1.56/0.60	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.60	  [c, a] [a, c] [c, c] [c, a] -> [c, a] [a, a] [a, c] [c, a] ,
1.56/0.60	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.60	  [c, a] [a, c] [c, c] [c, c] -> [c, a] [a, a] [a, c] [c, c] ,
1.56/0.60	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [c, a] [a, c] [c, c] [c, b] -> [c, a] [a, a] [a, c] [c, b] ,
1.56/0.60	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.60	  [b, a] [a, c] [c, c] [c, a] -> [b, a] [a, a] [a, c] [c, a] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.60	  [b, a] [a, c] [c, c] [c, c] -> [b, a] [a, a] [a, c] [c, c] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.60	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [b, a] [a, c] [c, c] [c, b] -> [b, a] [a, a] [a, c] [c, b] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.60	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.60	
1.56/0.60	
1.56/0.60	The system was filtered by the following matrix interpretation
1.56/0.60	of type E_J with J = {1,...,2} and dimension 2:
1.56/0.60	
1.56/0.60	[a, a] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 0 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[a, c] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 1 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[c, c] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 1 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[c, a] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 1 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[a, b] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 0 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[b, b] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 1 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[b, a] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 0 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[b, c] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 0 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	[c, b] is interpreted by
1.56/0.60	 /   \
1.56/0.60	| 1 0 |
1.56/0.60	| 0 1 |
1.56/0.60	 \   /
1.56/0.60	
1.56/0.60	Remains to prove termination of the 12-rule system
1.56/0.60	{ [a, b] [b, b] [b, b] [b, a] ->= [a, c] [c, b] [b, c] [c, a] ,
1.56/0.60	  [a, b] [b, b] [b, b] [b, c] ->= [a, c] [c, b] [b, c] [c, c] ,
1.56/0.60	  [a, b] [b, a] [a, c] [c, c] ->= [a, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [a, b] [b, a] [a, c] [c, b] ->= [a, b] [b, b] [b, a] [a, b] ,
1.56/0.60	  [c, b] [b, b] [b, b] [b, a] ->= [c, c] [c, b] [b, c] [c, a] ,
1.56/0.60	  [c, b] [b, a] [a, c] [c, c] ->= [c, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [c, b] [b, a] [a, c] [c, b] ->= [c, b] [b, b] [b, a] [a, b] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, a] ->= [b, b] [b, a] [a, c] [c, a] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, c] ->= [b, b] [b, a] [a, c] [c, c] ,
1.56/0.60	  [b, b] [b, a] [a, c] [c, c] ->= [b, b] [b, b] [b, a] [a, c] ,
1.56/0.60	  [b, c] [c, a] [a, c] [c, b] ->= [b, b] [b, a] [a, c] [c, b] ,
1.56/0.60	  [b, b] [b, a] [a, c] [c, b] ->= [b, b] [b, b] [b, a] [a, b] }
1.56/0.60	
1.56/0.60	
1.56/0.60	The system is trivially terminating.
1.63/0.62	EOF