A paper that was suggested to me (not mentioned in the linked blog post) is:
"Practical Improvements to the Construction and Destruction of Static Single Assignment Form", by Preston Briggs, Keith D. Cooper, Timothy J. Harvey, I. Taylor Simpson all at Rice University SOFTWARE—PRACTICE AND EXPERIENCE, VOL. 28(8), 1–28 (July 1998)
Note also if you’re dealing with weird control flow you might get oddities in translating out of SSA form: https://www.tjhsst.edu/~rlatimer/papers/sreedharTranslatingO.... Sreedhar’s algorithm for translating out of SSA form is relatively easy to implement.
This is probably useless to you unless you know Common Lisp, but I put together a couple of toy implementations of these algorithms years ago to help myself learn them. There’s a couple of nits the papers gloss over that are noted in comments. You’ll need to compute liveness and dominance frontiers. Examples for those are in the project too. https://github.com/rayiner/portfolio/blob/master/ssa_analysi...
https://github.com/rayiner/portfolio/blob/master/ssa_analysi...