Multifraction reduction IV: Padding and Artin-Tits monoids of sufficiently large type

We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property H. As an application, we show that all Artin-Tits groups of sufficiently large type satisfy some weakened version Conjecture Apadded of Conjecture A, thus showing that the reduction approach is relevant for these groups.