In startrek they probably have some sort of machine that splits CO2 into C and O2 - but there exist no such machine right now, does it? So I was thinking, that if you wanted a complete carbon-cycle in a minimal space, you would still need some sort of photosyntesis on board. One idea I had, is that if you have little park of fast-growing trees on the ship, then these trees can be turned into some sort of more digestable tree-pourage (it probably wont taste so good, but Im not planning for a luxury-cruise) with shorter carbon-hydrates, or whatever it is those cellulose-molecules need to be manipulated into in order to be eatable. Also, water would have to be destilled in an endless cycle, and all forms of organic waste must be turned into soil for the tree-park. If you find the right type of fast-growing tree, and have a way of turning the wood into food without spending oxygen in the process, then you can travel for a very long time without needing fresh supplies? Kind of? I imagine that the tree-pourage would need some vitamins and minerals added in order to give the body all it needs, but this will only be a drop of this and a hint of this - so it wont be so space-consuming to bring along.