The commutativity problem is decidable for shuffle-finite series over a finite alphabet (paper §6). This is the meta-theorem ($EffectivePrevarietyCommutativityDecidable$) applied to $shuffleEffectivePrevariety$, the effective prevariety of shuffle-finite series: its boolean decider on a presentation $A$ decides $IsCommutative (shuffleEffectivePrevariety.sem A)$, and since $shuffleEffectivePrevariety.sem A = A.recognised$, it decides $IsCommutative (A.recognised)$.