which takes in nutrients, processes them to support itself, and expells waste products.
Is fire alive? it takes in nutrients (Hydro carbons+oxygens), reacts them to support itself, and expells waste products (CO2+water), in fact, that's the same input and output as many organisms. Is fire a living organisms?
you missed growth (also fire)
and reproduction (also fire, but also problematic as it means a single rabbit isn't alive but a couple are)
BTW, not an appeal to authority, just a notice that I might know what I'm talking about. I have a PhD in biology.
there are more interesting candidates for life definition, Dawkins considered that maybe the question is a waste of time and what matters is the genetic unit, "living things" are just things that spread genetic material.
Others theories are based on chaos theory, thermodynamic cascades,matter/energy waves...