0.00/0.29	YES
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	b is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 3 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	c is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 3 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	d is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 2 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	a is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 3 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 4-rule system
0.00/0.30	{ c c -> d d d ,
0.00/0.30	  d d d -> a c ,
0.00/0.30	  a a ->= b c ,
0.00/0.30	  b c ->= a a }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	b is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	c is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 2 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	d is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	a is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 3-rule system
0.00/0.30	{ d d d -> a c ,
0.00/0.30	  a a ->= b c ,
0.00/0.30	  b c ->= a a }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system was filtered by the following matrix interpretation
0.00/0.30	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.30	
0.00/0.30	b is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	c is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	d is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 1 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	a is interpreted by
0.00/0.30	 /   \
0.00/0.30	| 1 0 |
0.00/0.30	| 0 1 |
0.00/0.30	 \   /
0.00/0.30	
0.00/0.30	Remains to prove termination of the 2-rule system
0.00/0.30	{ a a ->= b c ,
0.00/0.30	  b c ->= a a }
0.00/0.30	
0.00/0.30	
0.00/0.30	The system is trivially terminating.
0.00/0.33	EOF