YES

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

C:
a() -> c()
b() -> c()
f(a(),b()) -> d()
d() -> f(a(),c())
d() -> f(c(),b())

Label:
[f(x,c()) -> f(c(),c())] = 0
[f(c(),x) -> f(c(),c())] = 0