YES

---- CR(R)
---- Hot decreasingness.
R:
F(H(x),y) -> F(H(x),I(I(y)))
F(x,G(y)) -> F(I(x),G(y))
I(x) -> x

C:
I(x) -> x

Label:
[F(H(x),y) -> F(H(x),I(I(y)))] = 0
[F(x,G(y)) -> F(I(x),G(y))] = 0