Torsion in the tensor product of an ideal with its inverse

Let (R, m) be a one-dimensional Noetherian local domain. Assume the integral closure (R) over bar is a discrete valuation ring with maximal ideal <(R)over bar x>. Let I be a non-principal ideal of R. A question, motivated by the work of Auslander in the early 1960's, is whether the torsion submodule of I x (R) I-1 is always non-zero. In this paper we will show that if both m and I are generated by powers of x, the residue fields of R and (R) over bar are the same and the multiplicity of is at most seven, then mu(R)(I)mu(R)(I-1) > mu(R)(II-1). It follows that I x I-R(-1) has torsion under these conditions.