Non-terminating runs of the right-reversing algorithm are necessarily cyclic, enabling computation of minimal Garside families via cycle detection.
Dehornoy, Braid groups and left distributive operations,Transactions of the Amer- ican Mathematical Society345(1994) 115–150
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Computing least common multiples in monoids with a finite Garside family
Non-terminating runs of the right-reversing algorithm are necessarily cyclic, enabling computation of minimal Garside families via cycle detection.