AG Mat for Pool Steps - Will a 1 inch rubber mat work?

I have 4 pool steps going into my 24' x 52" AG. I have used rugs under the steps in the past but they move. I saw a post that used a 45 ml poly as a mat which is not that thick but durable.
I was thinking about using a 3'x3' rubber mat with the holes that people put in their workshops as it helps on your feet standing on concrete. The mat is called anti-fatigue and is about 1 inch thick with the holes.
Will rubber breakdown with chlorine as most things are vinyl in pool but gaskets are made of rubber?
The mat is $20 at Lowes and looks like it will hold in place. I just do not want liitle pieces of rubber floating around or water getting black from the color. Any thoughts or experiences on it would be appreciated.