Normal form of derivations in the nonassociative and commutative lambek calculus with product

We show that derivations in the nonassociative and commutative Lambek calculus with product can be transformed to a normal form as it is the case with derivations in noncommutative calculi. As an application we obtain that the class of languages generated by categorial grammars based on the nonassociative and commutative Lambek calculus with product is included in the class of CF-languages. MSC: 68Q50, 03D15, 03B65.