The NOT gate might be difficult to build ;)
Note: this is not level based logic, but billiard ball logic. If I understood that better I'd write a concise, illuminating explanation of why ¬a∧¬b is missing in the AND gate's outputs.
With regards to crab supply, I think the sufficient study of reversible computing, and in particular their charge conservation properties, would address that.
You'll still have to have a mechanism to spray bits of dead fish around to feed the thing.
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