Extendability conjecture for finite generalized Lyndon words

Let $A$ be a finite alphabet, and let $w$ be a finite generalized Lyndon word over $A$. The length of $w$ is denoted by $|w|$. Extendability conjecture. Every finite generalized Lyndon word $w$ with $|w|\geq 2$ is a prefix of an infinite generalized Lyndon word. The conjecture identifies all finite generalized Lyndon words except the maximum one-letter word as potential prefixes of infinite generalized Lyndon words.