Wanting to animate a belt around spinning pulley


I am unsure of how to tackle the belt in my blend file
I am using keyshapes in NLR to allow the belt having flex and wobble.

I was thinking of mapping a texture to the belt and then using node setup to change location and keyframe it to look like the belt is moving.
I am unsure if the texture location can be reset to 0 to mimic a cyclic movement.

I would be interested in seeing if anyone have a method for a good look.Belt and Pulley.blend (755.8 KB)