title: Can it be proved that call-by-need has the minimal asymptotic time complexity among all reduction strategies?
body: <p>When I read the Church Rosser II Theorem <a href="https://en.wikibooks.org/wiki/Haskell/Graph_reduction" rel="noreferrer">here</a></p>
  <blockquote>
  <p>Theorem (Church Rosser II)</p>
  <p>If there is one terminating reduction, then outermost reduction will terminate, too.</p>
  </blockquote>
  <p>I'm wondering: Is there some theorem which strengthens the Church Rosser II Theorem so that it tells about the asymptotic time complexity instead of termination?</p>
  <p>Or, can it be proved that the call-by-need strategy has the minimal asymptotic time complexity among all reduction strategies?</p>