Flip conjecture II

Let $\pi:(X,\Delta)\to S$ be a projective morphism such that $(X,\Delta)$ is a $\mathbb Q$-factorial log canonical pair. A sequence of flips

$$(X_0,\Delta_0)\dashrightarrow (X_1,\Delta_1)\dashrightarrow (X_2,\Delta_2)\dashrightarrow\cdots$$

Flip conjecture II. The sequence terminates after finitely many steps; equivalently, there is no infinite sequence of flips. The source explains that the minimal model program can be run for such pairs but that termination is not known.