As with Thistlethwaite's Algorithm, he would search through the right coset space formula_8 to take the cube to group formula_9. Next he searched the optimal solution for group formula_9. The searches in formula_8 and formula_9 were both done with a method equivalent to IDA*. The search in formula_8 needs at most 12 moves and the search in formula_9 at most 18 moves, as Michael Reid showed in 1995. By also generating suboptimal solutions that take the cube to group formula_9 and looking for short solutions in formula_9, much shorter overall solutions are usually obtained. Using this algorithm solutions are typically found of fewer than 21 moves, though there is no proof that it will always do so.