0.00/0.03	YES
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	(VAR v_NonEmpty:S X:S X1:S X2:S)
0.00/0.03	(RULES
0.00/0.03	a__f(0) -> cons(0,f(s(0)))
0.00/0.03	a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.03	a__f(X:S) -> f(X:S)
0.00/0.03	a__p(s(0)) -> 0
0.00/0.03	a__p(X:S) -> p(X:S)
0.00/0.03	mark(0) -> 0
0.00/0.03	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.03	mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.03	mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.03	mark(s(X:S)) -> s(mark(X:S))
0.00/0.03	) 
0.00/0.03	(STRATEGY INNERMOST)
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Dependency Pairs Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 A__F(s(0)) -> A__F(a__p(s(0)))
0.00/0.03	 A__F(s(0)) -> A__P(s(0))
0.00/0.03	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.03	 MARK(f(X:S)) -> A__F(mark(X:S))
0.00/0.03	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.03	 MARK(p(X:S)) -> A__P(mark(X:S))
0.00/0.03	 MARK(p(X:S)) -> MARK(X:S)
0.00/0.03	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.03	-> Rules:
0.00/0.03	 a__f(0) -> cons(0,f(s(0)))
0.00/0.03	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.03	 a__f(X:S) -> f(X:S)
0.00/0.03	 a__p(s(0)) -> 0
0.00/0.03	 a__p(X:S) -> p(X:S)
0.00/0.03	 mark(0) -> 0
0.00/0.03	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.03	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.03	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.03	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 A__F(s(0)) -> A__F(a__p(s(0)))
0.00/0.03	 A__F(s(0)) -> A__P(s(0))
0.00/0.04	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.04	 MARK(f(X:S)) -> A__F(mark(X:S))
0.00/0.04	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(p(X:S)) -> A__P(mark(X:S))
0.00/0.04	 MARK(p(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.04	-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 A__F(s(0)) -> A__F(a__p(s(0)))
0.00/0.04	->->-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.04	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(p(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.04	->->-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	
0.00/0.04	
0.00/0.04	The problem is decomposed in 2 subproblems.
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	Reduction Pairs Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 A__F(s(0)) -> A__F(a__p(s(0)))
0.00/0.04	-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	-> Usable rules:
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	->Interpretation type:
0.00/0.04	 Linear
0.00/0.04	->Coefficients:
0.00/0.04	 Natural Numbers
0.00/0.04	->Dimension:
0.00/0.04	 1
0.00/0.04	->Bound:
0.00/0.04	 2
0.00/0.04	->Interpretation:
0.00/0.04	 
0.00/0.04	[a__f](X) = 0
0.00/0.04	[a__p](X) = 2
0.00/0.04	[mark](X) = 0
0.00/0.04	[0] = 2
0.00/0.04	[cons](X1,X2) = 0
0.00/0.04	[f](X) = 0
0.00/0.04	[fSNonEmpty] = 0
0.00/0.04	[p](X) = 2
0.00/0.04	[s](X) = 2.X
0.00/0.04	[A__F](X) = 2.X
0.00/0.04	[A__P](X) = 0
0.00/0.04	[MARK](X) = 0
0.00/0.04	
0.00/0.04	Problem 1.1: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 Empty
0.00/0.04	-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	 There is no strongly connected component
0.00/0.04	
0.00/0.04	The problem is finite.
0.00/0.04	
0.00/0.04	Problem 1.2: 
0.00/0.04	
0.00/0.04	Subterm Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.04	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(p(X:S)) -> MARK(X:S)
0.00/0.04	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.04	-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	->Projection:
0.00/0.04	 pi(MARK) = 1
0.00/0.04	
0.00/0.04	Problem 1.2: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 Empty
0.00/0.04	-> Rules:
0.00/0.04	 a__f(0) -> cons(0,f(s(0)))
0.00/0.04	 a__f(s(0)) -> a__f(a__p(s(0)))
0.00/0.04	 a__f(X:S) -> f(X:S)
0.00/0.04	 a__p(s(0)) -> 0
0.00/0.04	 a__p(X:S) -> p(X:S)
0.00/0.04	 mark(0) -> 0
0.00/0.04	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.04	 mark(f(X:S)) -> a__f(mark(X:S))
0.00/0.04	 mark(p(X:S)) -> a__p(mark(X:S))
0.00/0.04	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.04	->Strongly Connected Components:
0.00/0.04	 There is no strongly connected component
0.00/0.04	
0.00/0.04	The problem is finite.
0.00/0.04	EOF