0.00/0.44	YES
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 1 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	Q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	p is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 6-rule system
0.00/0.47	{ p p -> q q ,
0.00/0.47	  p Q Q -> Q Q p ,
0.00/0.47	  Q p q -> q p Q ,
0.00/0.47	  q q p -> p q q ,
0.00/0.47	  q Q -> ,
0.00/0.47	  Q q -> }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	Q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 1 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	p is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 4-rule system
0.00/0.47	{ p p -> q q ,
0.00/0.47	  p Q Q -> Q Q p ,
0.00/0.47	  Q p q -> q p Q ,
0.00/0.47	  q q p -> p q q }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	Q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	p is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 1 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	q is interpreted by
0.00/0.47	 /   \
0.00/0.47	| 1 0 |
0.00/0.47	| 0 1 |
0.00/0.47	 \   /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 3-rule system
0.00/0.47	{ p Q Q -> Q Q p ,
0.00/0.47	  Q p q -> q p Q ,
0.00/0.47	  q q p -> p q q }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	Q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 1 1 0 |
0.00/0.47	 \       /
0.00/0.47	p is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 1 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 1 0 |
0.00/0.47	| 0 0 1 0 |
0.00/0.47	 \       /
0.00/0.47	q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 2-rule system
0.00/0.47	{ Q p q -> q p Q ,
0.00/0.47	  q q p -> p q q }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	Q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 1 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	| 0 0 1 0 |
0.00/0.47	 \       /
0.00/0.47	p is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 1 1 0 |
0.00/0.47	 \       /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 1-rule system
0.00/0.47	{ q q p -> p q q }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system was filtered by the following matrix interpretation
0.00/0.47	of type E_J with J = {1,...,2} and dimension 4:
0.00/0.47	
0.00/0.47	P is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	Q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 0 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	| 0 0 0 0 |
0.00/0.47	 \       /
0.00/0.47	p is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 1 0 1 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	 \       /
0.00/0.47	q is interpreted by
0.00/0.47	 /       \
0.00/0.47	| 2 0 1 0 |
0.00/0.47	| 0 1 0 0 |
0.00/0.47	| 0 0 0 1 |
0.00/0.47	| 0 0 1 0 |
0.00/0.47	 \       /
0.00/0.47	
0.00/0.47	Remains to prove termination of the 0-rule system
0.00/0.47	{ }
0.00/0.47	
0.00/0.47	
0.00/0.47	The system is trivially terminating.
1.12/0.87	EOF