On completeness of word reversing

AbstractWord reversing is a combinatorial operation on words that detects pairs of equivalent words in monoids that admit a presentation of a certain form. Here we give conditions for this method to be complete in the sense that every pair of equivalent words can be detected by word reversing. In addition, we obtain explicit upper bounds on the complexity of the process. As an application, we show that Artin groups of Coxeter type B embed into Artin groups of type A and are left orderable