Bounding the degrees of generators of a homogeneous dimension 2 toric ideal

Let I be the toric ideal defined by a 2 x n matrix of integers, A = ((1 1 … 1)(a_1 a_2 … a_n)) with a_1<a_2<…<a_n. We give a combinatorial proof that I is generated by elements of degree at most the sum of the two largest differences a_i - a_(i-1). The novelty is in the method of proof: the result has already been shown by L’vovsky using cohomological arguments.