YES

---- CR(R)
---- Hot decreasingness.
R:
g(a()) -> f(g(a()))
g(b()) -> c()
a() -> b()
f(x) -> h(x,x)
h(x,y) -> c()

C:
g(b()) -> c()
a() -> b()
f(x) -> h(x,x)
h(x,y) -> c()

Label:
[g(a()) -> f(g(a()))] = 0