Yard Machine Belts/pulleys?

I noticed my 15.5 hp yard machine taking some time to speed up from stopped position. I'm thinking a loose belt. I removed the plate the shifter extend through and I could watch what was happing as I took off. The belt from the motor comes to a pulley below. When I take off, it spins and begins to move slowly. The belt then settles down further inside the pulley and the machine picks up speed.
Is this noprmal, or is the pulley or belt worn out..or both?
I have the deck off now and would like to fix it only once.
Nothing done to it since new..about 6-7 years.