Determine area in Closed Cycle

I'm doing an assignment in which I need to calculate the work done on a piston inside a deisel engine cylinder. We've been given the data in order to graph a Pressure-Volume Diagram, the area encased in the closed cycle that is made by the motion of the cylinder is the total work done. I can calculate this work using the trapz function but it's more complicated than that.

When the data is plotted it looks somthing similar to this, at some point through the exhaust stroke the data intersects and the piston is instead doing work on the gas instead of the other way around so this data and this area needs to be subtracted from the total area inside the closed cycle. Does anyone know how I might go about calculating the area in each respective enclosed loop and subtracting one from the other?

Any help is appriciated thankyou.