Weak Generalised Nonvanishing Conjecture

Let $(X,\Delta)$ be a $\mathbb{Q}$-factorial projective klt pair of dimension $n$ such that $X$ is not uniruled and $K_X+\Delta$ is nef. Let $L$ be a nef $\mathbb{Q}$-divisor on $X$ such that $n(X,K_X+\Delta+L)=n$. Then for every $t\geq0$ the numerical class of the divisor $K_X+\Delta+tL$ belongs to the effective cone.

Weak Generalised Nonvanishing Conjecture. Under these hypotheses, the numerical class of $K_X+\Delta+tL$ belongs to the effective cone for every $t\geq0$.

This is presented as a reduction of the Generalised Nonvanishing Conjecture and is intended to weaken its assumptions considerably. The supplied context does not report a resolution of this statement.