0.00/0.52	YES
0.00/0.56	
0.00/0.56	
0.00/0.56	Applying context closure of depth 1 in the following form: System R over Sigma
0.00/0.56	maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
0.00/0.56	where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})
0.00/0.56	
0.00/0.56	Remains to prove termination of the 27-rule system
0.00/0.56	{ [a, a] [a, a] [a, b] [b, a] -> [a, b] [b, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, a] [a, a] [a, b] [b, b] -> [a, b] [b, a] [a, b] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, a] [a, b] [b, c] -> [a, b] [b, a] [a, c] ,
0.00/0.56	  [a, c] [c, b] [b, c] -> [a, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, a] -> [b, b] [b, a] [a, a] ,
0.00/0.56	  [b, c] [c, b] [b, a] -> [b, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [b, a] [a, a] ->= [b, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, b] -> [b, b] [b, a] [a, b] ,
0.00/0.56	  [b, c] [c, b] [b, b] -> [b, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, c] -> [b, b] [b, a] [a, c] ,
0.00/0.56	  [b, c] [c, b] [b, c] -> [b, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, c] [c, b] [b, a] -> [c, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, b] -> [c, b] [b, a] [a, b] ,
0.00/0.56	  [c, c] [c, b] [b, b] -> [c, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, c] -> [c, b] [b, a] [a, c] ,
0.00/0.56	  [c, c] [c, b] [b, c] -> [c, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 20-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, c] [c, b] [b, c] -> [a, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, a] -> [b, b] [b, a] [a, a] ,
0.00/0.56	  [b, c] [c, b] [b, a] -> [b, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [b, a] [a, a] ->= [b, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [b, c] [c, b] [b, b] -> [b, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, c] [c, b] [b, c] -> [b, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, c] [c, b] [b, a] -> [c, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, c] [c, b] [b, b] -> [c, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, c] [c, b] [b, c] -> [c, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 17-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, c] [c, b] [b, c] -> [a, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, a] -> [b, b] [b, a] [a, a] ,
0.00/0.56	  [b, a] [a, a] ->= [b, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, c] [c, b] [b, a] -> [c, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, c] [c, b] [b, b] -> [c, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, c] [c, b] [b, c] -> [c, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 14-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, c] [c, b] [b, c] -> [a, b] [b, a] [a, b] [b, c] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, a] -> [b, b] [b, a] [a, a] ,
0.00/0.56	  [b, a] [a, a] ->= [b, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 1 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 1 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 13-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, a] [a, b] [b, a] -> [b, b] [b, a] [a, a] ,
0.00/0.56	  [b, a] [a, a] ->= [b, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 3 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	 \     /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 1 1 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 1 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /     \
0.00/0.56	| 1 0 0 |
0.00/0.56	| 0 1 0 |
0.00/0.56	| 0 0 0 |
0.00/0.56	 \     /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 11-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, c] [c, b] [b, b] -> [a, b] [b, a] [a, b] [b, b] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 1 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 1 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	 \       /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /       \
0.00/0.56	| 1 0 0 0 |
0.00/0.56	| 0 1 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	| 0 0 0 0 |
0.00/0.56	 \       /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 10-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, a] ->= [a, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 6:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 1 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 1 0 0 1 0 |
0.00/0.56	| 0 0 0 0 1 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 1 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 1 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 1 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /           \
0.00/0.56	| 1 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 |
0.00/0.56	 \           /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 9-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] [a, b] [b, a] -> [c, b] [b, a] [a, a] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 7:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 1 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 1 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 1 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 1 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 1 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 1 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /             \
0.00/0.56	| 1 0 0 0 0 0 0 |
0.00/0.56	| 0 1 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	| 0 0 0 0 0 0 0 |
0.00/0.56	 \             /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 8-rule system
0.00/0.56	{ [a, c] [c, b] [b, a] -> [a, b] [b, a] [a, b] [b, a] ,
0.00/0.56	  [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system was filtered by the following matrix interpretation
0.00/0.56	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.56	
0.00/0.56	[a, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[a, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 1 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, a] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, b] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[b, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	[c, c] is interpreted by
0.00/0.56	 /   \
0.00/0.56	| 1 0 |
0.00/0.56	| 0 1 |
0.00/0.56	 \   /
0.00/0.56	
0.00/0.56	Remains to prove termination of the 7-rule system
0.00/0.56	{ [a, a] [a, b] ->= [a, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [a, a] [a, c] ->= [a, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [b, a] [a, b] ->= [b, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [b, a] [a, c] ->= [b, a] [a, c] [c, a] [a, c] ,
0.00/0.56	  [c, a] [a, a] ->= [c, a] [a, c] [c, a] [a, a] ,
0.00/0.56	  [c, a] [a, b] ->= [c, a] [a, c] [c, a] [a, b] ,
0.00/0.56	  [c, a] [a, c] ->= [c, a] [a, c] [c, a] [a, c] }
0.00/0.56	
0.00/0.56	
0.00/0.56	The system is trivially terminating.
1.56/0.60	EOF