This paper aims to handle scenario durations of t-timed Petri nets without constructing the class graph. We use a linear logic characterization of scenarios based on the equivalence between reachability in Petri nets and provability of a class of linear logic sequents. It has been shown that it was possible to characterize a scenario with concurrency induced both by the Petri net structure and by the marking. This approach, based on the rewriting of the linear logic sequent proof, is limited because some structural concurrency cannot be expressed. In this paper we develop a new approach based on a canonical proof of the sequent. It does not explicitly characterize the scenario but it delimits its duration through an algebraic symbolic expression. It allows handling non safe or cyclic Petri nets and structures which cannot be uniquely characterized by "sequence" and "parallel" operations.