By an additional interpretation of the templates of these yield functions in the algebra of dependency trees (with the overt lexical items as roots), the LCFRS generates both strings and (possibly non-projective) dependency structures.
the running time of LCFRS parsers is generally very high, still polynomial in the sentence length, but with a degree determined by properties of the grammar; difficulties involved in running LCFRS parsers for natural languages are described by (Kallmeyer and Maier, 2013).