The problem occurs when the power paths are reunited before going into a differential and out to the wheel. At this point, the torques are being added together (or subtracted etc.). So for one path, the efficiency may be n1*n2*n3 and the other path may be n4*n5*n6 such that, from the diagram...
I'm trying to figure out an expression for the total power efficiency from engine to wheel of a parallel transmission in terms of the efficiency of all the components in between (i.e. spur gears, motors, pumps, etc.) such that
P_{engine} = \eta(\eta_{i})*2P_{wheel}
See attached image.