In 1936 Whitehead presented an algorithm for determining whether an element (or a set of elements) in a free group F is part of a free generating set for F . We will give a more detailed discussion of Whitehead's algorithm and a new proof that the algorithm works. We will see that in fact Whitehead's algorithm actually determines whether or not an element (or a set of elements) is diskbusting. If an element is not diskbusting, then Whitehead's algorithm produces the smallest free factor of F in which lies, and in that free factor is diskbusting.
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Richard Stong (1997) studied this question.