Yeah, I agree with all of the above. In addition, I'd check the belt for any glazing or cracking. If noted, replace. I'd also check for correct fit. I was told years ago by a Gates rep., IIRC, that a 'v' belt should fit into the pulleys no more than 1/16th of an inch above the groove and no more than
1/8th of an inch below to insure a proper fit.
Another source of slippage is misalignment from pulley to pulley. You can check this with a straigt edge or by eyball if you have access to align the pulleys up by
line of sight.
The 1/2 inch deflection of the belt is a good test, but another way of checking if you have enough tension on the belt is to get a rag and with a good grip on the cooling fins of the alternator pulley, try to make the pulley slip in either direction. If it does, adjustment is in order. Good luck.
Bob