MathDB

Ababa plays with a word made up of the letters of his name and has set certain rules: If you find an

A

followed immediately by a

B

, you can substitute

BAA

for them. If you find two consecutive

B

's, you can delete them. If you find three consecutive

A

's, you can delete them. Ababa begins with the word

ABABABAABAAB

. With the above rules, how many letters do you have the shortest word you can come up with? Why can't you come up with one more word shorter?

Problem Statement