Is there a normalizing (or perpetual) reduction strategy for untyped combinators?

Inspired by this question, I was curious whether there was a reduction strategy for untyped SKI combinators that was known to be either normalizing or perpetual.

As described here (Twelfed here), the nondeterminstic rules of the combinator calculus are these:

$Ix \rightarrow x$

$Kxy \rightarrow x$

$Sxyz \rightarrow xz(yz)$

$xy \rightarrow x'y$ if $x \rightarrow x'$

$xy \rightarrow xy'$ if $y \rightarrow y'$