Slowest growing upper bound for the minimum length of a complementary prefix regular expression
Wikipedia says that taking the complement "can cause a double exponentially blow-up of its length" and cites the following paper:

Succinctness of the Complement and Intersection of Regular Expressions.  Wouter Gelade and Frank Neven.  STAC 2008.

In particular, they give a concrete language that triggers the doubly exponential blowup.  See Theorem 4.1 in the paper.

That paper considers the normal representation for regexps rather than postfix, but I don't see any reason to expect that to change the bottom line.  You could work through their example and their proof if you want to be sure.