Arc-annotated sequences are useful for representing struc- tural information of RNAs and have been extensively used for compar- ing RNA structures in both terms of sequence and structural similari- ties. Among the many paradigms referring to arc-annotated sequences and RNA structures comparison (see [2] for more details), the most im- portant one is the general edit distance. The problem of computing an edit distance between two non-crossing arc-annotated sequences was in- troduced in [5]. The introduced model uses edit operations that involve either single letters or pairs of letters (never considered separately) and is solvable in polynomial-time [12]. To account for other possible RNA structural evolutionary events, new edit operations, allowing to consider either silmutaneously or separately letters of a pair were introduced in [9]; unfortunately at the cost of com- putational tractability. It has been proved that comparing two RNA sec- ondary structures using a full set of biologically relevant edit operations is NP-complete. Nevertheless, in [8], the authors have used a strong com- binatorial restriction in order to compare two RNA stem-loops with a full set of biologically relevant edit operations; which have allowed them to design a polynomial-time and space algorithm for comparing general secondary RNA structures. In this paper we will prove theoretically that comparing two RNA struc- tures using a full set of biologically relevant edit operations cannot be done without strong combinatorial restrictions.