What shouldn't go in your compost bin?

I wonder how many of us have ground elder?

It regrows from just a tiny broken root.
I went to wisley a few years back and they had a trial bed where they were trying to eradicate by removing all lands and using weed killer. I didn't go back last year so I don't know what happened to it.

I would be too worried to put it in the compost. I have one bed I weeded today, it has a few leaves of it every time I look there. The issue is that the roots are coming through an old drystone wall. So I can never dig the roots out.