YES

   1: F(H(x1),x2) -> G(H(x1))
   2: H(I(x1)) -> I(x1)
   3: F(I(x1),x2) -> G(I(x1))

@Jouannaud and Kirchner's criterion
--- R
   1: F(H(x1),x2) -> G(H(x1))
   2: H(I(x1)) -> I(x1)
   3: F(I(x1),x2) -> G(I(x1))

--- S
   1: F(H(x1),x2) -> G(H(x1))
   2: H(I(x1)) -> I(x1)
   3: F(I(x1),x2) -> G(I(x1))