= Free reduction
<Free reduction> removes adjacent inverse-letter pairs. A stack algorithm scans the letters, canceling the top letter when the next is its inverse. The resulting reduced word is unique: deleting an inverse pair before scanning does not change the final stack, so every cancellation sequence gives the same result. In any <group presentation> these deletions preserve the represented element, and in a <free group> the reduced word is the identity exactly when it is empty.
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