Catalyzes the degradation of levan mainly into levanbiose (difructose) (By similarity). Can also hydrolyze inulin. Hydrolysis of (2->6)-beta-D-fructofuranan, to remove successive disaccharide residues as levanbiose, i.e. 6-(beta-D-fructofuranosyl)-D-fructose, from the end of the chain. Optimum temperature is 55 degrees Celsius. Belongs to the glycosyl hydrolase 32 family.