0.80/0.89	YES
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	(VAR v_NonEmpty:S x1:S)
0.80/0.89	(RULES
0.80/0.89	P(p(x1:S)) -> x1:S
0.80/0.89	P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	Q(q(x1:S)) -> x1:S
0.80/0.89	p(P(x1:S)) -> x1:S
0.80/0.89	p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	q(Q(x1:S)) -> x1:S
0.80/0.89	q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	)
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Dependency Pairs Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 P#(x1:S) -> Q#(Q(p(x1:S)))
0.80/0.89	 P#(x1:S) -> Q#(p(x1:S))
0.80/0.89	 P#(x1:S) -> p#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> Q#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 P#(x1:S) -> Q#(Q(p(x1:S)))
0.80/0.89	 P#(x1:S) -> Q#(p(x1:S))
0.80/0.89	 P#(x1:S) -> p#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> Q#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> Q#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> Q#(x1:S)
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = 2.X + 1
0.80/0.89	[p#](X) = 2.X + 1
0.80/0.89	[q#](X) = 2.X + 1
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> p#(Q(x1:S))
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = 2.X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(p(x1:S))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = X + 2
0.80/0.89	[p#](X) = X + 2
0.80/0.89	[q#](X) = X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> p#(x1:S)
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = 2.X
0.80/0.89	[Q](X) = 2.X + 1
0.80/0.89	[p](X) = 2.X + 1
0.80/0.89	[q](X) = 2.X + 1
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = 2.X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(q(x1:S))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = 2.X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = X
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = X
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 p#(p(x1:S)) -> q#(x1:S)
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = 2.X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = 2.X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(q(x1:S))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = 2.X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = 2.X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> q#(x1:S)
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 Natural Numbers
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = X
0.80/0.89	[Q](X) = 2.X + 2
0.80/0.89	[p](X) = 2.X + 2
0.80/0.89	[q](X) = 2.X + 2
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 2
0.80/0.89	[q#](X) = 2.X + 2
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	->->Cycle:
0.80/0.89	->->-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	->->-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	Reduction Pair Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 Q#(p(q(x1:S))) -> q#(p(Q(x1:S)))
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	-> Usable rules:
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Interpretation type:
0.80/0.89	 Linear
0.80/0.89	->Coefficients:
0.80/0.89	 All rationals
0.80/0.89	->Dimension:
0.80/0.89	 1
0.80/0.89	->Bound:
0.80/0.89	 2
0.80/0.89	->Interpretation:
0.80/0.89	 
0.80/0.89	[P](X) = 1/2.X
0.80/0.89	[Q](X) = 2.X + 1/2
0.80/0.89	[p](X) = 2.X
0.80/0.89	[q](X) = 1/2.X
0.80/0.89	[Q#](X) = 2.X + 2
0.80/0.89	[p#](X) = 2.X + 1
0.80/0.89	[q#](X) = 1/2.X + 1
0.80/0.89	
0.80/0.89	Problem 1: 
0.80/0.89	
0.80/0.89	SCC Processor:
0.80/0.89	-> Pairs:
0.80/0.89	 p#(Q(Q(x1:S))) -> Q#(Q(p(x1:S)))
0.80/0.89	 q#(q(p(x1:S))) -> p#(q(q(x1:S)))
0.80/0.89	-> Rules:
0.80/0.89	 P(p(x1:S)) -> x1:S
0.80/0.89	 P(x1:S) -> Q(Q(p(x1:S)))
0.80/0.89	 Q(p(q(x1:S))) -> q(p(Q(x1:S)))
0.80/0.89	 Q(q(x1:S)) -> x1:S
0.80/0.89	 p(P(x1:S)) -> x1:S
0.80/0.89	 p(Q(Q(x1:S))) -> Q(Q(p(x1:S)))
0.80/0.89	 p(p(x1:S)) -> q(q(x1:S))
0.80/0.89	 q(Q(x1:S)) -> x1:S
0.80/0.89	 q(q(p(x1:S))) -> p(q(q(x1:S)))
0.80/0.89	->Strongly Connected Components:
0.80/0.89	 There is no strongly connected component
0.80/0.89	
0.80/0.89	The problem is finite.
0.80/0.89	EOF