 It is still uncertain what the best treatment is for patients who have both atrial fibrillation AF and heart failure. The aim of the study is to help identify the optimal treatment for patients with these two significant medical conditions. This will be performed by comparing two alternative strategies for AF management: catheter ablation to restore normal rhythm and medical therapy to control heart rate, but not aiming ro restore normal rhythm. After random assignment, the effect of each strategy will be assessed by looking for changes in exercise capacity, symptoms, heart pump function, and quality of life during 12 months of follow-up. 