Proving yourself is crucial. Initially, the Green won't care about what you think. Thus, a compliment from you would be meaningless, because she initially considers you an insignificant source. Only after you have established yourself as an expert in the Green's eyes will she accept a compliment from you. At that time, you can refer to her mental process, vast knowledge or ingenuity.
Greens appear slow and methodical.
That's because they need time to process the information you give to them. They represent a sales rep's worst nightmare. Here's how it works. You present your product and ask for a check. Ms. Green says she can't make a decision, that she needs to process the information.