33.14/8.66	YES
33.38/8.73	
33.38/8.73	
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 4:
33.38/8.73	
33.38/8.73	c is interpreted by
33.38/8.73	 /       \
33.38/8.73	| 1 0 1 0 |
33.38/8.73	| 0 1 0 0 |
33.38/8.73	| 0 0 0 1 |
33.38/8.73	| 0 1 0 0 |
33.38/8.73	 \       /
33.38/8.73	a is interpreted by
33.38/8.73	 /       \
33.38/8.73	| 1 0 0 0 |
33.38/8.73	| 0 1 0 0 |
33.38/8.73	| 0 0 0 0 |
33.38/8.73	| 0 0 0 0 |
33.38/8.73	 \       /
33.38/8.73	b is interpreted by
33.38/8.73	 /       \
33.38/8.73	| 1 0 0 0 |
33.38/8.73	| 0 1 0 0 |
33.38/8.73	| 0 0 0 0 |
33.38/8.73	| 0 0 0 0 |
33.38/8.73	 \       /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 4-rule system
33.38/8.73	{ c c a -> c c b ,
33.38/8.73	  b b c -> a a b ,
33.38/8.73	  b a b ->= a c b ,
33.38/8.73	  c a a ->= b a b }
33.38/8.73	
33.38/8.73	
33.38/8.73	Applying context closure of depth 1 in the following form: System R over Sigma
33.38/8.73	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
33.38/8.73	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
33.38/8.73	
33.38/8.73	Remains to prove termination of the 36-rule system
33.38/8.73	{ [c, c] [c, c] [c, a] [a, c] -> [c, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, c] [c, a] [a, a] [a, c] ->= [c, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, a] -> [c, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, a] [a, a] [a, a] ->= [c, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [c, c] [c, a] [a, a] [a, b] ->= [c, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, c] -> [a, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, c] -> [a, a] [a, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, a] -> [a, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, a] ->= [a, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, c] ->= [b, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, a] -> [b, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, a] ->= [b, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, a] ->= [b, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, b] ->= [b, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 2:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 30-rule system
33.38/8.73	{ [c, c] [c, c] [c, a] [a, c] -> [c, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, a] -> [c, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, c] -> [a, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, a] -> [a, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, a] ->= [a, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, c] ->= [b, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, a] -> [b, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, a] ->= [b, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, a] ->= [b, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, b] ->= [b, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 1 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 1 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 1 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 1 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 1 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 27-rule system
33.38/8.73	{ [c, c] [c, c] [c, a] [a, c] -> [c, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, a] -> [c, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, c] -> [a, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, a] -> [a, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, a] ->= [a, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, c] ->= [b, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, a] -> [b, c] [c, c] [c, b] [b, a] ,
33.38/8.73	  [b, b] [b, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, a] ->= [b, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, a] ->= [b, b] [b, a] [a, b] [b, a] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, b] [b, a] [a, b] [b, b] ->= [b, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 2:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 18-rule system
33.38/8.73	{ [c, c] [c, c] [c, a] [a, c] -> [c, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, c] -> [a, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 1 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 17-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, c] -> [a, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 1 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 16-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, c] [c, c] [c, a] [a, b] -> [c, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 1 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 15-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, c] [c, a] [a, b] -> [a, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 1 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 14-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, a] ->= [c, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 1 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 1 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 1 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 13-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, c] ->= [a, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, b] ->= [a, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, c] -> [b, c] [c, c] [c, b] [b, c] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, c] ->= [b, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [b, c] [c, c] [c, a] [a, b] -> [b, c] [c, c] [c, b] [b, b] ,
33.38/8.73	  [b, c] [c, a] [a, a] [a, b] ->= [b, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 5:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 1 0 1 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 1 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 1 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /         \
33.38/8.73	| 1 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 |
33.38/8.73	| 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 |
33.38/8.73	 \         /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 6-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, c] ->= [a, b] [b, a] [a, b] [b, c] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 8:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 1 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 1 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 1 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 1 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 1 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /               \
33.38/8.73	| 1 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 0 0 0 0 0 1 0 |
33.38/8.73	| 0 0 0 0 0 0 0 0 |
33.38/8.73	| 0 1 0 0 0 0 0 0 |
33.38/8.73	 \               /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 5-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system was filtered by the following matrix interpretation
33.38/8.73	of type E_J with J = {1,...,2} and dimension 2:
33.38/8.73	
33.38/8.73	[c, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[c, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, c] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 1 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[a, b] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	[b, a] is interpreted by
33.38/8.73	 /   \
33.38/8.73	| 1 0 |
33.38/8.73	| 0 1 |
33.38/8.73	 \   /
33.38/8.73	
33.38/8.73	Remains to prove termination of the 4-rule system
33.38/8.73	{ [c, b] [b, a] [a, b] [b, c] ->= [c, a] [a, c] [c, b] [b, c] ,
33.38/8.73	  [c, b] [b, a] [a, b] [b, b] ->= [c, a] [a, c] [c, b] [b, b] ,
33.38/8.73	  [a, b] [b, a] [a, b] [b, a] ->= [a, a] [a, c] [c, b] [b, a] ,
33.38/8.73	  [a, c] [c, a] [a, a] [a, b] ->= [a, b] [b, a] [a, b] [b, b] }
33.38/8.73	
33.38/8.73	
33.38/8.73	The system is trivially terminating.
33.42/8.78	EOF