YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
g(0,1) -> 0
g(0,1) -> 1
h(g(x:S,y:S)) -> h(x:S)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(0,1,g(x:S,y:S),z:S) -> F(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 F(0,1,g(x:S,y:S),z:S) -> H(x:S)
 H(g(x:S,y:S)) -> H(x:S)
-> Rules:
 f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 g(0,1) -> 0
 g(0,1) -> 1
 h(g(x:S,y:S)) -> h(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,1,g(x:S,y:S),z:S) -> F(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 F(0,1,g(x:S,y:S),z:S) -> H(x:S)
 H(g(x:S,y:S)) -> H(x:S)
-> Rules:
 f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 g(0,1) -> 0
 g(0,1) -> 1
 h(g(x:S,y:S)) -> h(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 H(g(x:S,y:S)) -> H(x:S)
->->-> Rules:
 f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 g(0,1) -> 0
 g(0,1) -> 1
 h(g(x:S,y:S)) -> h(x:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 H(g(x:S,y:S)) -> H(x:S)
-> Rules:
 f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 g(0,1) -> 0
 g(0,1) -> 1
 h(g(x:S,y:S)) -> h(x:S)
->Projection:
 pi(H) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0,1,g(x:S,y:S),z:S) -> f(g(x:S,y:S),g(x:S,y:S),g(x:S,y:S),h(x:S))
 g(0,1) -> 0
 g(0,1) -> 1
 h(g(x:S,y:S)) -> h(x:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.