57.97/15.02	YES
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 3:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 2 1 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	 \     /
57.97/15.04	b is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 3 0 2 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 1 |
57.97/15.04	 \     /
57.97/15.04	d is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 1 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	 \     /
57.97/15.04	c is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 1 |
57.97/15.04	 \     /
57.97/15.04	f is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 1 1 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	 \     /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 5-rule system
57.97/15.04	{ a b -> b d ,
57.97/15.04	  a c -> d d d ,
57.97/15.04	  b d -> a c b ,
57.97/15.04	  c f -> d d c ,
57.97/15.04	  d d -> f }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 3:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 1 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	 \     /
57.97/15.04	b is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	 \     /
57.97/15.04	d is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 0 |
57.97/15.04	 \     /
57.97/15.04	c is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 0 |
57.97/15.04	 \     /
57.97/15.04	f is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 0 |
57.97/15.04	 \     /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 4-rule system
57.97/15.04	{ a c -> d d d ,
57.97/15.04	  b d -> a c b ,
57.97/15.04	  c f -> d d c ,
57.97/15.04	  d d -> f }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 3:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 2 1 |
57.97/15.04	 \     /
57.97/15.04	b is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 1 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 0 3 |
57.97/15.04	 \     /
57.97/15.04	d is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 1 |
57.97/15.04	 \     /
57.97/15.04	c is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 1 1 |
57.97/15.04	 \     /
57.97/15.04	f is interpreted by
57.97/15.04	 /     \
57.97/15.04	| 1 0 0 |
57.97/15.04	| 0 1 0 |
57.97/15.04	| 0 2 1 |
57.97/15.04	 \     /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 3-rule system
57.97/15.04	{ a c -> d d d ,
57.97/15.04	  c f -> d d c ,
57.97/15.04	  d d -> f }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 2:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 1 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	b is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	d is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	c is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	f is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 2-rule system
57.97/15.04	{ c f -> d d c ,
57.97/15.04	  d d -> f }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 4:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /       \
57.97/15.04	| 1 0 0 0 |
57.97/15.04	| 0 1 0 0 |
57.97/15.04	| 0 0 0 0 |
57.97/15.04	| 0 0 0 0 |
57.97/15.04	 \       /
57.97/15.04	b is interpreted by
57.97/15.04	 /       \
57.97/15.04	| 1 0 0 0 |
57.97/15.04	| 0 1 0 0 |
57.97/15.04	| 0 0 0 0 |
57.97/15.04	| 0 0 0 0 |
57.97/15.04	 \       /
57.97/15.04	d is interpreted by
57.97/15.04	 /       \
57.97/15.04	| 1 0 0 0 |
57.97/15.04	| 0 1 0 0 |
57.97/15.04	| 0 1 0 1 |
57.97/15.04	| 0 0 1 0 |
57.97/15.04	 \       /
57.97/15.04	c is interpreted by
57.97/15.04	 /       \
57.97/15.04	| 1 0 1 0 |
57.97/15.04	| 0 1 0 0 |
57.97/15.04	| 0 0 1 0 |
57.97/15.04	| 0 0 1 0 |
57.97/15.04	 \       /
57.97/15.04	f is interpreted by
57.97/15.04	 /       \
57.97/15.04	| 1 0 0 0 |
57.97/15.04	| 0 1 0 0 |
57.97/15.04	| 0 1 1 0 |
57.97/15.04	| 0 0 0 0 |
57.97/15.04	 \       /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 1-rule system
57.97/15.04	{ d d -> f }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system was filtered by the following matrix interpretation
57.97/15.04	of type E_J with J = {1,...,2} and dimension 2:
57.97/15.04	
57.97/15.04	a is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	b is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	d is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 1 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	c is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	f is interpreted by
57.97/15.04	 /   \
57.97/15.04	| 1 0 |
57.97/15.04	| 0 1 |
57.97/15.04	 \   /
57.97/15.04	
57.97/15.04	Remains to prove termination of the 0-rule system
57.97/15.04	{ }
57.97/15.04	
57.97/15.04	
57.97/15.04	The system is trivially terminating.
58.15/15.09	EOF