Analytic termination conjecture for the minimal model program for log canonical pairs

Let $\pi\colon X\to Y$ be a projective morphism from a normal analytic variety $X$ to a Stein space $Y$, and let $W\subset Y$ be a compact subset such that $\pi$ and $W$ satisfy (P). Let $(X,\Delta)$ be a log canonical (lc) pair.

Analytic MMP termination conjecture. After shrinking $Y$ around $W$, there exists a finite sequence of steps of a $(K_X+\Delta)$-minimal model program over $Y$ around $W, represented by bimeromorphic contractions over$Y$, that terminates with a good minimal model or a Mori fiber space over$Y$around$W.

This is the complex-analytic analogue of the algebraic termination conjecture for lc pairs and is intended to relate analytic minimal model theory to the projective case. Its resolution is not supplied in the source.