I'll pass on the aspect of a floor covering for this type environment! I find it hard to believe your considering a covering for a floor that takes this kind of abuse and would be prone to absorption of animal waste.
Jelly's comment about using the concrete comes close to a better way to go, providing you have concrete to work with!
A concrete that is exposed to animal waste, particurlaly urine is a breeding ground for several viruses. Parvo is common in most kennel operations if the concrete has not been protected. Waste that penetrates into the Gel-Pore, Capillary system of a concrete has an ideal bacteria growth environment. This is why so many Kennels stink to high heaven and can not be adequately cleaned to remove the smell. If you've got the smell, you have bacterial growth in the concrete.
Since you have budgetary constraints, you can waterproof and give chemical resistance to a concrete for less than $0.50 a sq. ft. I use a "Green Product " that has extremely low VOC content, which is very important if your dealing with an interior application. It is also FDA/EPA approved, if a food product is to come in contact with the treated concrete.
Good luck with your "potty training issues" ?
Glenn