YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 G(X:S,s(Y:S)) -> G(X:S,Y:S)
-> Rules:
 f(X:S,Y:S,g(X:S,Y:S)) -> h(0,g(X:S,Y:S))
 g(0,Y:S) -> 0
 g(X:S,s(Y:S)) -> g(X:S,Y:S)
 h(X:S,Z:S) -> f(X:S,s(X:S),Z:S)
->Projection:
 pi(G) = 2

Problem 1: 

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

The problem is finite.