The factor conjecture for constant-length substitution speedups

Let $\theta$ be a constant-length left proper substitution and let $c>1$ satisfy $\gcd(c,|\theta|)=1$. If $l$ is a factor of $c$ with $1\leq l<c$, then $(X_\theta,T^l)$ and $(X_\theta,T^c)$ are the associated substitution Toeplitz flows. Factor conjecture for constant-length substitution speedups. The Toeplitz flow $(X_\theta,T^l)$ is a factor of $(X_\theta,T^c)$. The conjecture generalizes factor relationships observed in examples; no resolution is supplied in the paper.