Extensions of Girard’s linear logic by least and greatest fixed point operators (μMALL) have been an active field of research for almost two decades. Various proof systems are known viz. finitary and non-wellfounded, based on explicit and implicit (co)induction respectively. In this paper, we compare the relative expressivity, at the level of provability, of two complementary infinitary proof systems: finitely branching non-wellfounded proofs (μMALL^∞) vs. infinitely branching well-founded proofs (μMALL_{ω,∞}). Our main result is that μMALL^∞ is strictly contained in μMALL_{ω,∞}. For inclusion, we devise a novel technique involving infinitary rewriting of non-wellfounded proofs that yields a wellfounded proof in the limit. For strictness of the inclusion, we improve previously known lower bounds on μMALL^∞ provability from Π⁰₁-hard to Σ¹₁-hard, by encoding a sort of Büchi condition for Minsky machines.