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 Y:S)
0.00/0.03	(RULES
0.00/0.03	f(s(X:S)) -> f(X:S)
0.00/0.03	g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y: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	 F(s(X:S)) -> F(X:S)
0.00/0.03	 G(cons(0,Y:S)) -> G(Y:S)
0.00/0.03	 H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S))
0.00/0.03	 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y: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	 F(s(X:S)) -> F(X:S)
0.00/0.03	 G(cons(0,Y:S)) -> G(Y:S)
0.00/0.03	 H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S))
0.00/0.03	 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Strongly Connected Components:
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 G(cons(0,Y:S)) -> G(Y:S)
0.00/0.03	->->-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
0.00/0.03	->->-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 F(s(X:S)) -> F(X:S)
0.00/0.03	->->-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	
0.00/0.03	
0.00/0.03	The problem is decomposed in 3 subproblems.
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	Subterm Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 G(cons(0,Y:S)) -> G(Y:S)
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Projection:
0.00/0.03	 pi(G) = 1
0.00/0.03	
0.00/0.03	Problem 1.1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	
0.00/0.03	Problem 1.2: 
0.00/0.03	
0.00/0.03	Reduction Pairs Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	-> Usable rules:
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	->Interpretation type:
0.00/0.03	 Linear
0.00/0.03	->Coefficients:
0.00/0.03	 Natural Numbers
0.00/0.03	->Dimension:
0.00/0.03	 1
0.00/0.03	->Bound:
0.00/0.03	 2
0.00/0.03	->Interpretation:
0.00/0.03	 
0.00/0.03	[f](X) = 0
0.00/0.03	[g](X) = 0
0.00/0.03	[h](X) = 0
0.00/0.03	[0] = 0
0.00/0.03	[cons](X1,X2) = 2.X1 + 2
0.00/0.03	[fSNonEmpty] = 0
0.00/0.03	[s](X) = 0
0.00/0.03	[F](X) = 0
0.00/0.03	[G](X) = 0
0.00/0.03	[H](X) = 2.X
0.00/0.03	
0.00/0.03	Problem 1.2: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	
0.00/0.03	Problem 1.3: 
0.00/0.03	
0.00/0.03	Subterm Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 F(s(X:S)) -> F(X:S)
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Projection:
0.00/0.03	 pi(F) = 1
0.00/0.03	
0.00/0.03	Problem 1.3: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 Empty
0.00/0.03	-> Rules:
0.00/0.03	 f(s(X:S)) -> f(X:S)
0.00/0.03	 g(cons(0,Y:S)) -> g(Y:S)
0.00/0.03	 g(cons(s(X:S),Y:S)) -> s(X:S)
0.00/0.03	 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.04	EOF