Even commercial composting operations such as zoodoo separate the feces of herbivores from carnivores, and only process the former for sale as compost.
The problem is that no home composting system can guarantee that the correct temperatures will always be reached each time they're used.
If you're going to process the feces of a carnivore, they normally ask you to let it stand for a year, and not to use it for growing leaf and root vegetables.
http://www.the-compost-gardener.com/composting-pet-waste.html
Edit: Mother Earth tested in 2003 a number of tumbling compost makers and found that they didn't make compost any faster, finishing the compost in 10 weeks.