Suppose formula_86, formula_87, formula_88 and formula_89. If we take formula_90 then formula_91 is a finite ring (not a field since formula_92 is not maximal in formula_93). The Euclidean algorithm applied to the images of formula_94 in <math>(D/I)succeeds and returns 1. This implies that the GCD of formula_94 in formula_96 must be 1 as well. Note that this example could easily be handled by any method because the degrees were too small for expression swell to occur, but it illustrates that if two polynomials have GCD 1, then the modular algorithm is likely to terminate after a single ideal formula_92.