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.
$Ix \rightarrow x$
$Kxy \rightarrow x$
$Sxyz \rightarrow xz(yz)$
$xy \rightarrow x'y$ if $x \rightarrow x'$
$xy \rightarrow xy'$ if $y \rightarrow y'$