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I'm not an expert but yes, I'm pretty sure it all works out perfectly. For example, let's say a spaceship is moving "near" the speed of light. Then you could measure its kinetic energy, using its apparant mass (or inertia) instead of its rest mass. This will tell you exactly how much work/energy has been put into moving the spaceship. If it weren't for relativity, the spaceship would be moving faster instead of "weighing" extra, but either way, the energy's the same. That's also exactly how much work/energy it would take to slow it down. So basically, none of the work is wasted. Please correct me if I'm wrong about this!