Asymptotic success probability conjecture for the edge-addition process

For fixed $x,y\geq 1$, let $a_{x,y,n}$ denote the probability that the $(x,y)$ edge-addition process on $n$ vertices generates an $(x,y)$ task-dependency graph.

Edge-addition success-probability conjecture.

$$\lim_{n\rightarrow\infty}a_{x,y,n}=1.$$

This conjecture is based on experimental results indicating that the probability approaches $1$ as the number of vertices grows. No proof or resolution is provided in the source.