  A generalized lexicographic order on words is a lexicographic order where the
total order of the alphabet depends on the position of the comparison. A
generalized Lyndon word is a finite word which is strictly smallest among its
class of rotations with respect to a generalized lexicographic order. This
notion can be extended to infinite words: an infinite generalized Lyndon word
is an infinite word which is strictly smallest among its class of suffixes. We
prove a conjecture of Dolce, Restivo, and Reutenauer: every infinite word has a
unique nonincreasing factorization into finite and infinite generalized Lyndon
words. When this factorization has finitely many terms, we characterize the
last term of the factorization. Our methods also show that the infinite
generalized Lyndon words are precisely the words with infinitely many
generalized Lyndon prefixes.
