The overall work done by a system is the integral of the force vector dot product the direction of movement. If you have a conservative force setup (no friction) then any motion that takes you back to where you started does no work. We did this in first year physics at university (we also did it in high school, but other school systems probably don't work the same way).

You're confusing work and energy. Energy is expended, but work is not. Work relates to the change in potential energy of a system -- which will not change in a conservative system (assuming you return to the original point). https://en.wikipedia.org/wiki/Work_(physics)