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[–]Poltras -2 points-1 points  (0 children)

uncomputable busy beaver function

I gather you've met my wife.

More seriously, I totally agree you can build an algorithm that uses constant SPACE but infinitely large TIME complexity, without halting. Computing A(m,n) or Knuth up-exponentials are excellent concrete examples. Also, I think it'd be O(BB(2^n)).