how much can you do with a system where for all functions f f(f(x)) = f(x)?
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doesn't seem like a strict enough limitation to prevent much, especially if there are infinitely many functions and ...
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e.g. say x is a compound of 2 numbers, and f_1 is a function. f_1({n, i}) = if i != 1 then {2 * n, 1} else {n, i}.
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create near-identical functions f_2, f_3, ... and you can repeat this operation indefinitely, all while following your rule
End of conversation
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