YES

1 decompositions
 #0 -----------
   1: F(H(x),y) -> G(H(x))
   2: H(I(x)) -> I(x)
   3: F(I(x),y) -> G(I(x))

@Strongly Commuting
--- R
   1: F(H(x),y) -> G(H(x))
   2: H(I(x)) -> I(x)
   3: F(I(x),y) -> G(I(x))

--- S
   1: F(H(x),y) -> G(H(x))
   2: H(I(x)) -> I(x)
   3: F(I(x),y) -> G(I(x))