I guess it all depends on what you want.
Do you want a lot of compost when you are done or do you just want to process a lot?
They reduce waste down to 5 or 10%, so not much left over.
They might process it but paper, cardboard and
yard waste is really a hindrance to their endeavors.
On the other hand, you didn't invite them to your party so they will have to play by your rules.