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Comment by adrianN | Hacker News Reader

There is no general solution to deciding whether a program is O(n^k).[1] So either your static analysis won't know the answer for some programs or report a wrong bound, or report a ridiculous overestimate.

[1] https://cstheory.stackexchange.com/questions/5004/are-runtim...

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So? Static analysis doesn't need to always produce an answer, only produce an answer most of the time. The question isn't whether you can do it in general for all inputs (this is not possible for basically anything you would want to know), it's whether you can do it enough of the time on the kind of code which people actually write.

Can you point me towards some source code where a human can't find the algorithmic complexity?

It's not hard to implement the construction in the proof. Generally you'll encounter problems in the wild in any interpreter. Similarly you can encode many open mathematical problems into simple programs where finding runtime bounds is equal to solving the problem. The Collatz Conjecture for example.

Once you leave primitive recursive functions[0], reasoning quickly becomes very non-trivial.

[0]: https://en.wikipedia.org/wiki/Primitive_recursive_function

Humans can't tell you whether this program will run forever on any particular (positive integer) input, or whether all inputs terminate.

  def collatz(n):
      while n != 1:
          print(n)
      if n % 2 == 0:
          n = n // 2 
      else:
          n = n * 3 + 1

      print(1)

I think your indentation needs to be adjusted? Like so:

  def collatz(n):
      while n != 1:
          print(n)
          if n % 2 == 0:
              n = n // 2 
          else:
              n = n * 3 + 1

      print(1)

Otherwise, n = 1 terminates, and n != 1 gets stuck looping at lines 2-3.

Thank you!

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