First - SoaK up as much pee as possible with paper towels.
Second - Dilute Listerine Green.
      3 parts water to one part Listerine.
Third - Test the solution on a hidden area of the rug first.
Next - Use the solution to clean pee spot soaking up with cloth or paper towels.

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For dried pee.
Spray hydrogen peroxide on the area to wet it well, then sprinkle a generous amount of baking soda over the area and let dry before vacuuming.

For heavily soiled areas you may need to scrub the treatment into the carpet, then let dry and vacuum.

Repeat as needed until stains and smells are gone.