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I have completed a five-stage analysis of the 4x4x4 cube showing that it can always be solved using at most 68 turns. The analysis used the same five stages that were used in my prior posts where I claimed the 4x4x4 cube can be solved in 79 single-slice turns, or alternatively in 85 twists. The difference in this analysis is that it allows any single layer turn or double layer turn (where the two layers are any two adjacent layers and moved together) to be counted as a "turn." In some prior posts, I referred to these turns as "block turns." So the set of turns about the U-D axis that count as one turn are the following:
  U,U',U²,u,u',u²,(Uu),(Uu)',(Uu)²,
  D,D',D²,d,d',d²,(Dd),(Dd)',(Dd)²,
  (ud'),(u'd),(ud')²