YES

   1: H(I(x1)) -> K(J(x1))
   2: J(x1) -> K(J(x1))
   3: I(x1) -> I(J(x1))
   4: J(x1) -> J(K(J(x1)))

@Rule Labeling
--- R
   1: H(I(x1)) -> K(J(x1))
   2: J(x1) -> K(J(x1))
   3: I(x1) -> I(J(x1))
   4: J(x1) -> J(K(J(x1)))

--- S
   1: H(I(x1)) -> K(J(x1))
   2: J(x1) -> K(J(x1))
   3: I(x1) -> I(J(x1))
   4: J(x1) -> J(K(J(x1)))