The S-adic conjecture on sub-linear complexity

Let $f53f$ be a sequence over a finite alphabet. An $S$-adic sequence is one admitting an $S$-adic representation for some set $S$ of morphisms; in particular, the representation is given by morphisms $f70f_n:A_{n+1}^*\to A_n^*$ and letters $a_n\in A_n$, with $f53f=\lim_{n\to+\infty}f70f_0f70f_1\cdotsf70f_n(a_{n+1}^{\omega})$ and lengths tending to infinity. The factor complexity of a sequence is the function counting its distinct factors of each length. $S$-adic conjecture. There exists a condition $C$ such that a sequence has sub-linear complexity if and only if it is an $S$-adic sequence satisfying condition $C$ for some finite set $S$ of morphisms. This is posed as an open problem concerning the relationship between low factor complexity and finite-set $S$-adic representations; the source gives no resolution.