Notice I said irreducible, not irreversible. Yes, you can reverse the computation; but there's no known way to "shortcut" the forward process to predict the outcome of the series I mentioned any faster than simply letting it run. Letting it run is not prediction in the sense I mean here. By "predict" I mean foretell in advance what the system will do without needing to let it run.
> Simple rules can create a very complex emergent system, but that doesn't mean it cannot still be reduced to it's component rules. That's what makes them rules and not just guidelines.
I agree, with a minor caveat about language: you can describe a system which may display complex emergent behavior in terms of its underlying rules, but doing so is not guaranteed to give you useful information about (i.e., allow you to "predict", in the sense described above) the emergent behaviors. In contexts like these, to "reduce" typically means to describe in terms of a lower-level formalism while preserving predictive ability, AFAIK. In other words, the low-level formalism provides full information about the behavior of the entire system, such that you don't need to observe the system to know what it will do. In the Life example this is not the case.
You can absolutely reversibly compute conways game of life state, and you can compute it forward as well (after all, it is a game). That's prediction.
> It's well established that simple low-level rules can generate [...] irreducible complexity.
Simple rules can create a very complex emergent system, but that doesn't mean it cannot still be reduced to it's component rules. That's what makes them rules and not just guidelines.