You still have conservation of 'convex curvy bits'. You can eliminate a convex curvy bit by mating it with a concave curvy bit, but cutting out a concave curvy

You still have conservation of 'convex curvy bits'. You can eliminate a convex curvy bit by mating it with a concave curvy bit, but cutting out a concave curvy bit will again produce a convex curvy bit. Can't get rid of the curvy bits!