YES

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

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

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