I need some help with indoor flooring please

So Bear has started to chew the rug yaaaay!
At 1st I thought I'd just leave it done till it was bald, but the amount of fluff that's coming our of it I'm worried about him ingesting it.
There on a wood floor and I have no idea what to put down instead, it needs to cover quite a big surface area and be non slip. Also we still use there room as a bedroom so it need to not look to offensive!

This is what I'm working with, eventually the crate will go altogether but we have no where to up it at the moment!

Personally I think I'd get some black lino and put that down. You can easily fold it away when guests come over, but because it matches the cage of the crate it won't look too bad sitting there all the time. Possibly

http://www.onlinecarpets.co.uk/vinyl-flooring/colour/black-vinyl-flooring-1.html?dir=asc&order=price

I have parquet floor and a rug but I'm luck as Doughnut isn't really a chewer or a digger, well she only has an interest in my lining paper not rugs!

I've gone lino in her playpen and that's easy to clean. I haven't stuck them to the floor just to each other so can it's one big piece if that makes sense but hasn't ruined the floor.

I have to say though I can't believe the gorgeous Bear would do such a thing, look at that innocent face!!

Is lino slippery for them?
They run around and binky a lot on the rug and really struggle on the wood.

I just get cheap ones from Wilkinsons which are a bit rough so she has some traction. If you don't get the really smooth ones they should be fine. I think a pack of about 5 is only a few pounds so maybe see how they get on with them in a small area. Unless you get something like a ratten mat which won't harm them but not sure it will last a long time with Bear!