YES

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

C:


Label:
[f(a()) -> f(g(b(),b()))] = 1
[a() -> g(c(),c())] = 0
[c() -> d()] = 1
[d() -> b()] = 0
[b() -> d()] = 0