YES

---- CR(R)
---- Hot decreasingness.
R:
f(0(),0()) -> f(0(),1())
f(1(),0()) -> f(0(),0())
f(x,y) -> f(y,x)

C:
f(0(),0()) -> f(0(),1())
f(1(),0()) -> f(0(),0())

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