YES

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

C:
F(H(x),y) -> G(H(x))
H(I(x)) -> I(x)
F(I(x),y) -> G(I(x))

Label: