<p>In Partially Observable Petri Nets, a necessary parameter is the guaranteed horizon, which allows the modelling of the estimation problem with the counter form and can be exploited in estimation for any linear criterion: a problem is the on-line estimation of the guaranteed horizon, which is a maximum sequence length relevant to a sliding horizon or a receding horizon starting from the initial marking. Considering large scale Petri nets, the objective of this paper is to facilitate the resolution by the construction of a triangular form guiding a sequential resolution of the problem based on substructures. This study shows that the classical Dulmage-Mendelsohn decomposition can be applied to a class of Petri nets where the unobservable induced Petri Net is mainly Forward Conflict Free. An extension of this result to any Petri net based on the building of an associated Petri net is made.</p>