Subquadratic maximum running time conjecture for graph bootstrap percolation

For $r\geqslant 5$, let $M_r(n)$ denote the maximum number of time steps for which the $K_r$-bootstrap process on $n$ vertices can run before stabilizing. Subquadratic running-time conjecture. For all $r\geqslant 5$,

$$M_r(n)=o(n^2).$$

The exact maximum running time is unknown for $r\geqslant 5$, and even proving any non-trivial upper bound on $M_r(n)$ is open. The conjecture gives a weaker proposed bound than the heuristic estimate discussed immediately beforehand.