YES

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

C:
f(x) -> g(k(x))
f(x) -> a()
g(x) -> a()

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