I found this statement in B. Cavallo, D. Kahrobaei's paper arXiv:1311.7117 Secret Sharing using Non-Commutative Groups and the Shortlex Order, page 7.

"C′(1/6) continue to be an ideal platform for this protocol because reducing words to a minimal length has polynomial time complexity using a deterministic version of Dehn’s algorithm. In fact, it is the same algorithm used to solve the word problem. "

Could someone provide a reference that Dehn algorithm reduces words to normal forms in C'(1/6) groups in polynomial time? If this is not true, then in which classes of groups except virtually free gps is this true? Thanks, Olga