  Multifraction reduction is a new approach to the word problem for Artin-Tits
groups and, more generally, for the enveloping group of a monoid in which any
two elements admit a greatest common divisor. This approach is based on a
rewrite system ("reduction") that extends free group reduction. In this paper,
we show that assuming that reduction satisfies a weak form of convergence
called semi-convergence is sufficient for solving the word problem for the
enveloping group, and we connect semi-convergence with other conditions
involving reduction. We conjecture that these properties are valid for all
Artin-Tits monoids, and provide partial results and numerical evidence
supporting such conjectures.
