Fauxgo is a language that I have just made up. (“faux” is French for false, and “go” is Japanese for language.) Fauxgo has three letters: A, B, and C. Words must be formed using certain rules:
An A can not immediately follow a pair of the same letter (eliminating “CCA”).
An A can not be immediately followed by a B (eliminating “CAB”).
A B must be doubled (eliminating “CBA”).
A C can not immediately follow a pair of the same letter (eliminating “BBC”) or follow two A’s that are at any point previous in the word (eliminating “ACAC”).
Three of the same letter in a row is not permitted (eliminating “AAA”).
Given these rules, what is the longest possible word in Fauxgo?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, September 20, 2017 at noon Pacific Time. I will post the answer shortly after.