Let $k$ be an algebraically closed field of characteristic $p>0$.

I have been trying to find out unsuccessfully if there is a mmp for algebraic surfaces over $k$. I know minimal surfaces are classified thanks to Zariski, Mumford, others in this setting and that is not my question. I want to 'run' LMMP of pairs not to find minimal model but as a tool to prove several stuff.

In particular I would like to know if there is a Cone Theorem (i.e. giving me that extremal rays have non-positive self-intersection, I suspect the answer is yes) and if there is a contraction theorem (I suspect not yet).

By contraction theorem I mean that if given $(X,D)$ where $X$ is a surface $D$ is an effective divisor and the pair is klt, if $K_X+D$ is not nef I can find a curve $E$ with negative self-intersection such that $E$ can be contracted.

I am aware I am being vague with the formulation but I do not want to constrain your imagination.

Now, if someone also knows if flips and termination of flips are possible, please share :)