Shokurov's boundedness of complements conjecture

Let $d,p\in\mathbb N$ be natural numbers and let $R\subset[0,1]$ be a finite set of rational numbers. Let $(X',B'+M')$ be a projective lc generalized pair of dimension $d$, let $X\to Z$ be a contraction, assume $B'\in\Phi(R)$, $pM$ is b-Cartier, $X'$ is Fano type over $Z$, and $-(K_{X'}+B'+M')$ is nef over $Z$.

Shokurov's boundedness of complements conjecture. There exists a constant $n$ depending only on $d$, $p$, and $R$ such that $K_{X'}+B'+M'$ has an $n$-complement $K_{X'}+B^{\prime+}+M'$ with $B^{\prime+}\geq B'$ over any point $z\in Z$.

This conjecture is closely related to the BAB conjecture and was proved in characteristic zero by induction on dimension, separating the exceptional and non-exceptional cases. Its positive-characteristic validity is part of the boundedness problem studied here.