I have a matter duplicator. May I kill you?

I have invented a device which can make perfect duplicates of any object, including living things like people. All I need to do is put a big pile of raw materials into the hopper (pizza crusts, apple cores, and potato peelings are all I need for humans), and out pops whatever object I need duplicated.

As an experiment, I would like to make a perfect duplicate of you, perfect in every way. It will have all of your memories, think just like you, and go about your life. Then I will shoot the original you, since we can’t have two of you running about.

My question is, have I committed murder? After all, I haven’t killed anyone, you’re still out there paying taxes and making babies and looking at shitty porn. No court in the land could convict me; all I’d have to do is point to you: Look! Still there!