0.00/0.38	YES
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.39	
0.00/0.39	a is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	b is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	 \     /
0.00/0.39	d is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 1 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 1 |
0.00/0.39	 \     /
0.00/0.39	c is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 4-rule system
0.00/0.39	{ a b -> a ,
0.00/0.39	  d c -> c ,
0.00/0.39	  a ->= d a ,
0.00/0.39	  c ->= c b }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.39	
0.00/0.39	a is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 1 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	b is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 1 1 |
0.00/0.39	 \     /
0.00/0.39	d is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	c is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 3-rule system
0.00/0.39	{ d c -> c ,
0.00/0.39	  a ->= d a ,
0.00/0.39	  c ->= c b }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system was filtered by the following matrix interpretation
0.00/0.39	of type E_J with J = {1,...,2} and dimension 3:
0.00/0.39	
0.00/0.39	a is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	b is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 0 |
0.00/0.39	 \     /
0.00/0.39	d is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 1 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 0 1 |
0.00/0.39	 \     /
0.00/0.39	c is interpreted by
0.00/0.39	 /     \
0.00/0.39	| 1 0 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	| 0 1 0 |
0.00/0.39	 \     /
0.00/0.39	
0.00/0.39	Remains to prove termination of the 2-rule system
0.00/0.39	{ a ->= d a ,
0.00/0.39	  c ->= c b }
0.00/0.39	
0.00/0.39	
0.00/0.39	The system is trivially terminating.
0.00/0.42	EOF