Conjecture on padded semi-convergence for Artin–Tits monoids

Let $M$ be an Artin–Tits monoid. A padding of a multifraction is obtained by inserting an even number of trivial components at its beginning; semi-convergence up to $f$-padding means that a multifraction representing the identity reduces to the trivial multifraction after padding by a Turing-computable map $f$. Padded semi-convergence conjecture. For every Artin–Tits monoid, $\mathcal{R}$-reduction is semi-convergent up to $f$-padding for some Turing-computable map $f$. This weakening of semi-convergence is proposed because it still suffices for decidability of the word problem; the source does not state that it is known or resolved.