YES

   1: W(W(x1)) -> W(x1)
   2: B(I(x1)) -> W(x1)
   3: W(B(x1)) -> B(x1)
   4: F(H(x1),x2) -> F(H(x1),G(x2))
   5: F(x1,I(x2)) -> F(G(x1),I(x2))
   6: G(x1) -> x1

@Rule Labeling
--- R
   1: W(W(x1)) -> W(x1)
   2: B(I(x1)) -> W(x1)
   3: W(B(x1)) -> B(x1)
   4: F(H(x1),x2) -> F(H(x1),G(x2))
   5: F(x1,I(x2)) -> F(G(x1),I(x2))
   6: G(x1) -> x1

--- S
   1: W(W(x1)) -> W(x1)
   2: B(I(x1)) -> W(x1)
   3: W(B(x1)) -> B(x1)
   4: F(H(x1),x2) -> F(H(x1),G(x2))
   5: F(x1,I(x2)) -> F(G(x1),I(x2))
   6: G(x1) -> x1