User blog comment:Vel!/Laver.c/@comment-5150073-20140822085835/@comment-25418284-20140822161232

Oh. right. Then in that case, it could be q(n + 1) = q(n) + 1 when n is in a certain infinite set of numbers that cannot be proven to exist in PRA, and q(n + 1) = q(n) + 2 otherwise.

Both of my usages of the word "growth rate" were informal. The second sentence could be taken to mean "q might not be total."