Consider the same two planes but flying head on, the looper will meet the leveler with more "energy" despite the fact that the leveler has traveled farther in the same time span.
But they won't, unless one of the planes lead-turns a decent distance before the merge. If the looper ONLY loops at/after the merge, he won't catch the straight and level aircraft.
What you're confusing is if the chasing plane (the looper) manages to get within guns range before losing his small boost in airspeed - that's not an "E" advantage. Unless the other plane can catch up to the same point as the plane that went straight (0 horizontal distance between them), the looping plane has lost energy. The looping plane has traded energy for a positional advantage. Sure, he did it in a very conservational manner, but he still lost some energy. In air combat, we don't care about perfect energy conservation, because we want to shoot the other guy down, so loosing some energy in trade for advantage is acceptable. That being said, the looper will never catch back up to the plane that went straight. He might get within 200, 400, 800yds, X-distance and stay there, but he'll never completely close the distance.
This concept, again, is fundamental to the energy fighting aspect of ACM. Without this, you could continue looping infinitely to catch someone in front of you.
What I would like to understand better is how to decide whether tis better to climb or accelerate upon spotting a con.
PM'd you.