1.40/0.57	YES
1.40/0.58	
1.40/0.58	
1.40/0.58	The system was filtered by the following matrix interpretation
1.40/0.58	of type E_J with J = {1,...,2} and dimension 6:
1.40/0.58	
1.40/0.58	b is interpreted by
1.40/0.58	 /           \
1.40/0.58	| 1 0 1 0 0 0 |
1.40/0.58	| 0 1 0 0 0 0 |
1.40/0.58	| 0 0 0 0 0 0 |
1.40/0.58	| 0 0 1 0 0 0 |
1.40/0.58	| 0 0 0 0 0 0 |
1.40/0.58	| 0 0 1 0 0 0 |
1.40/0.58	 \           /
1.40/0.58	a is interpreted by
1.40/0.58	 /           \
1.40/0.58	| 1 0 0 0 0 0 |
1.40/0.58	| 0 1 0 0 0 0 |
1.40/0.58	| 0 0 0 1 0 0 |
1.40/0.58	| 0 1 0 0 1 0 |
1.40/0.58	| 0 0 0 0 0 0 |
1.40/0.58	| 0 0 0 0 0 0 |
1.40/0.58	 \           /
1.40/0.58	c is interpreted by
1.40/0.58	 /           \
1.40/0.58	| 1 0 0 0 1 0 |
1.40/0.58	| 0 1 0 0 0 0 |
1.40/0.58	| 0 0 0 0 0 0 |
1.40/0.58	| 0 0 0 0 1 0 |
1.40/0.58	| 0 0 0 0 0 1 |
1.40/0.58	| 0 0 0 0 1 0 |
1.40/0.58	 \           /
1.40/0.58	
1.40/0.58	Remains to prove termination of the 4-rule system
1.40/0.58	{ a c a -> b c a ,
1.40/0.58	  b b c ->= c c a ,
1.40/0.58	  a b b ->= b c b ,
1.40/0.58	  c c b ->= b a b }
1.40/0.58	
1.40/0.58	
1.40/0.58	The system was filtered by the following matrix interpretation
1.40/0.58	of type E_J with J = {1,...,2} and dimension 4:
1.40/0.58	
1.40/0.58	b is interpreted by
1.40/0.58	 /       \
1.40/0.58	| 1 0 0 2 |
1.40/0.58	| 0 1 0 0 |
1.40/0.58	| 0 0 0 0 |
1.40/0.58	| 0 1 0 0 |
1.40/0.58	 \       /
1.40/0.58	a is interpreted by
1.40/0.58	 /       \
1.40/0.58	| 1 0 0 0 |
1.40/0.58	| 0 1 0 0 |
1.40/0.58	| 0 0 0 0 |
1.40/0.58	| 0 1 0 0 |
1.40/0.58	 \       /
1.40/0.58	c is interpreted by
1.40/0.58	 /       \
1.40/0.58	| 1 1 1 0 |
1.40/0.58	| 0 1 0 0 |
1.40/0.58	| 0 0 0 1 |
1.40/0.58	| 0 0 1 0 |
1.40/0.58	 \       /
1.40/0.58	
1.40/0.58	Remains to prove termination of the 2-rule system
1.40/0.58	{ a c a -> b c a ,
1.40/0.58	  b b c ->= c c a }
1.40/0.58	
1.40/0.58	
1.40/0.58	The system was filtered by the following matrix interpretation
1.40/0.58	of type E_J with J = {1,...,2} and dimension 2:
1.40/0.58	
1.40/0.58	b is interpreted by
1.40/0.58	 /   \
1.40/0.58	| 1 1 |
1.40/0.58	| 0 1 |
1.40/0.58	 \   /
1.40/0.58	a is interpreted by
1.40/0.58	 /   \
1.40/0.58	| 1 2 |
1.40/0.58	| 0 1 |
1.40/0.58	 \   /
1.40/0.58	c is interpreted by
1.40/0.58	 /   \
1.40/0.58	| 1 0 |
1.40/0.58	| 0 1 |
1.40/0.58	 \   /
1.40/0.58	
1.40/0.58	Remains to prove termination of the 1-rule system
1.40/0.58	{ b b c ->= c c a }
1.40/0.58	
1.40/0.58	
1.40/0.58	The system is trivially terminating.
1.40/0.60	EOF