YES

---- CR(R)
---- Rule Labeling [van Oostrom, RTA 2008].
R:
H(I(x)) -> K(J(x))
J(x) -> K(J(x))
I(x) -> I(J(x))
J(x) -> J(K(J(x)))

Label:
[H(I(x)) -> K(J(x))] = 0
[J(x) -> K(J(x))] = 0
[I(x) -> I(J(x))] = 1
[J(x) -> J(K(J(x)))] = 1