Combing braids

Hello

When considering the subgroup of pure braids, it is possible to write
each pure braid as a unique product of so called "combed braids" i.e
pure braids such that all but one string are trivial. This process
leads to a normal form and it was described by Artin. Does anyone know
what is the complexity of this algorithm? Could someone point me to a
paper having this explained?

Many thanks

Tri7

.

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