When does a crime become a crime?

In going environmentally green, people talk about being carbon neutral.

It made me question: "When does a crime become a crime?"

I was watching this show: My name is Earl.
"You know the kind of guy who does nothing but bad things and then wonders why his life sucks? Well, that was me. Every time something good happened to me, something bad was always waiting round the corner: karma. That's when I realized that I had to change, so I made a list of everything bad I've ever done and one by one I'm gonna make up for all my mistakes. I'm just trying to be a better person. My name is Earl."
 I got that quote from the above wikipedia site.

Earl did a bunch of "bad acts" hurting people. But before he finishes his life is trying to do an 'equal and opposite reaction to his actions.' By that equal and opposite reaction to his actions that he is trying to do, he is trying to cancel out his previous actions that he considered to be bad.

Now quite personally, I don't think that is possible to do. I don't think anyone is perfect enough to be able to reverse every impact of their actions from birth so that they end up 'karmicly neutral' so to say. I think that would be impossible.
Software has a system of "garbage collection." But the Butterfly effect is just way too sensitive for a human being to be a "garbage collector" of their own karma in such a perfect way that they come out of the other end karmicly neutral. 
The air we breathe in and the gases we let out are killing living entities as you read these words. One living entities food is another living entities poison. One living entities excrement is another living entities food. Such is the universe.

But the question still remains: If you performed the perfect crime, but then you realized your mistake and there was a theoretical possibility that you could go back and leave everything intact the way you found it before you did the crime, would you be karmicly neutral?
Could you go as far as to say that you didn't act at all since there is no trace of your actions in the universe? It hasn't been recorded anywhere. No DNA evidence. Not an electron on an atom out of place. That would be a perfect "noise cancellation" device.

So if such a device existed for perfect "noise cancellation" of our impact in reality, have you still performed a crime? In whose book would you have performed the crime? Who is going to judge you?

Now let's make this question more interesting. I was listening to this song that a friend sent me:

Let us pretend that you are super-man. That you are aware of every twitch and impact that you made while acting. And let's say that I challenged you. I tell you that you have 24 hours. And in 24 hours you have the power to help the world. Naturally, the side effect of you helping some will be that you will hurt others. This is the equal and opposite effect of the Butterfly Effect. And let's say that because you had these awesome powers, you could be aware of every impact you made in the universe and could reverse it. Let us say that you spent 18 hours of your day (you're Super-man so I'll pretend you don't even sleep and don't have to consider any body maintenance) acting. And then you spent 6 hours doing "garbage collection" work cleaning up your action.

If super-man was that perfect, could anyone ever justifiably suggest that he did a crime? Forget crime. Could anyone justifiably make the argument that he acted at all? I don't feel like they could.

That would be like blowing the bubble or cloud of a dream in your mind while you sleep to only suck it back in you when you wake up. If you don't remember your dream, what records your dream? So have you dreamt at all? Where would you go to even find a trace of this dream?

How would you prove that "You had a dream?"