0.00/0.09	YES
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	(VAR v_NonEmpty:S x1:S)
0.00/0.09	(RULES
0.00/0.09	f(0(x1:S)) -> 0(x1:S)
0.00/0.09	f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	p(s(x1:S)) -> x1:S
0.00/0.09	)
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	Innermost Equivalent Processor:
0.00/0.09	-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
0.00/0.09	 
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	Dependency Pairs Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 F(s(x1:S)) -> F(p(s(x1:S)))
0.00/0.09	 F(s(x1:S)) -> P(s(x1:S))
0.00/0.09	-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 F(s(x1:S)) -> F(p(s(x1:S)))
0.00/0.09	 F(s(x1:S)) -> P(s(x1:S))
0.00/0.09	-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	->Strongly Connected Components:
0.00/0.09	->->Cycle:
0.00/0.09	->->-> Pairs:
0.00/0.09	 F(s(x1:S)) -> F(p(s(x1:S)))
0.00/0.09	->->-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	Reduction Pairs Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 F(s(x1:S)) -> F(p(s(x1:S)))
0.00/0.09	-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	-> Usable rules:
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	->Interpretation type:
0.00/0.09	 Linear
0.00/0.09	->Coefficients:
0.00/0.09	 All rationals
0.00/0.09	->Dimension:
0.00/0.09	 1
0.00/0.09	->Bound:
0.00/0.09	 2
0.00/0.09	->Interpretation:
0.00/0.09	 
0.00/0.09	[f](X) = 0
0.00/0.09	[p](X) = 1/2.X
0.00/0.09	[0](X) = 0
0.00/0.09	[fSNonEmpty] = 0
0.00/0.09	[s](X) = 2.X + 1/2
0.00/0.09	[F](X) = 2.X
0.00/0.09	[P](X) = 0
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 Empty
0.00/0.09	-> Rules:
0.00/0.09	 f(0(x1:S)) -> 0(x1:S)
0.00/0.09	 f(s(x1:S)) -> s(s(f(p(s(x1:S)))))
0.00/0.09	 p(s(x1:S)) -> x1:S
0.00/0.09	->Strongly Connected Components:
0.00/0.09	 There is no strongly connected component
0.00/0.09	
0.00/0.09	The problem is finite.
0.00/0.09	EOF