0.00/0.34	YES
0.00/0.35	
0.00/0.35	
0.00/0.35	The system was filtered by the following matrix interpretation
0.00/0.35	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.35	
0.00/0.35	a is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 2 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	b is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 3 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	c is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 8 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	d is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 4 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	
0.00/0.35	Remains to prove termination of the 3-rule system
0.00/0.35	{ a a a -> b b ,
0.00/0.35	  c -> d d ,
0.00/0.35	  d -> a a }
0.00/0.35	
0.00/0.35	
0.00/0.35	The system was filtered by the following matrix interpretation
0.00/0.35	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.35	
0.00/0.35	a is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	b is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	c is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 1 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	d is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	
0.00/0.35	Remains to prove termination of the 2-rule system
0.00/0.35	{ a a a -> b b ,
0.00/0.35	  d -> a a }
0.00/0.35	
0.00/0.35	
0.00/0.35	The system was filtered by the following matrix interpretation
0.00/0.35	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.35	
0.00/0.35	a is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	b is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	c is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	d is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 1 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	
0.00/0.35	Remains to prove termination of the 1-rule system
0.00/0.35	{ a a a -> b b }
0.00/0.35	
0.00/0.35	
0.00/0.35	The system was filtered by the following matrix interpretation
0.00/0.35	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.35	
0.00/0.35	a is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 1 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	b is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	c is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	d is interpreted by
0.00/0.35	 /   \
0.00/0.35	| 1 0 |
0.00/0.35	| 0 1 |
0.00/0.35	 \   /
0.00/0.35	
0.00/0.35	Remains to prove termination of the 0-rule system
0.00/0.35	{ }
0.00/0.35	
0.00/0.35	
0.00/0.35	The system is trivially terminating.
0.00/0.38	EOF