This paper is concerned with minimal length representatives of equivalence
classes of F_2 under Aut F_2. We give a simple inequality characterizing words
of minimal length in their equivalence class. We consider an operation that
"grows" words from other words, increasing the length, and we study root words
-- minimal words that cannot be grown from other words. Root words are "as
minimal as possible" in the sense that their characterization is the boundary
case of the minimality inequality.