  We establish decidability for the infinitely many axiomatic extensions of the
commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a
cut-free hypersequent proof calculus (specifically: every analytic structural
rule extension). Decidability for the corresponding extensions of its
contraction counterpart FLec was established recently but their computational
complexity was left unanswered. In the second part of this paper, we introduce
just enough on length functions for well-quasi-orderings and the fast-growing
complexity classes to obtain complexity upper bounds for both the weakening and
contraction extensions. A specific instance of this result yields the first
complexity bound for the prominent fuzzy logic MTL (monoidal t-norm based
logic) providing an answer to a long-standing open problem.
