YES

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

C:
W(W(x)) -> W(x)
B(I(x)) -> W(x)
W(B(x)) -> B(x)
G(x) -> x

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