YES

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

C:
a() -> b()

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