YES

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
f(s(X:S)) -> f(X:S)
g(cons(0,Y:S)) -> g(Y:S)
g(cons(s(X:S),Y:S)) -> s(X:S)
h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(X:S)) -> F(X:S)
 G(cons(0,Y:S)) -> G(Y:S)
 H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S))
 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(X:S)) -> F(X:S)
 G(cons(0,Y:S)) -> G(Y:S)
 H(cons(X:S,Y:S)) -> G(cons(X:S,Y:S))
 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(cons(0,Y:S)) -> G(Y:S)
->->-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->->Cycle:
->->-> Pairs:
 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
->->-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->->Cycle:
->->-> Pairs:
 F(s(X:S)) -> F(X:S)
->->-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 G(cons(0,Y:S)) -> G(Y:S)
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Projection:
 pi(G) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 H(cons(X:S,Y:S)) -> H(g(cons(X:S,Y:S)))
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
-> Usable rules:
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 0
[g](X) = 0
[h](X) = 0
[0] = 0
[cons](X1,X2) = 2.X1 + 2
[fSNonEmpty] = 0
[s](X) = 0
[F](X) = 0
[G](X) = 0
[H](X) = 2.X

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 F(s(X:S)) -> F(X:S)
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Projection:
 pi(F) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(s(X:S)) -> f(X:S)
 g(cons(0,Y:S)) -> g(Y:S)
 g(cons(s(X:S),Y:S)) -> s(X:S)
 h(cons(X:S,Y:S)) -> h(g(cons(X:S,Y:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.