We give an example of a Cayley graph Γ for the group F 2 × F 2 which is not minimally almost convex (MAC). On the other hand, the standard Cayley graph for F 2 × F 2 does satisfy the falsification by fellow traveler property (FFTP), which is strictly stronger. As a result, any Cayley graph property K lying between FFTP and MAC (i.e., FFTP ⇒ K ⇒ MAC) is dependent on the generating set. This includes the well known properties FFTP and almost convexity, which were already known to depend on the generating set as well as Poénaru's condition P (2) and the basepoint loop shortening property for which dependence on the generating set was previously unknown. We also show that the Cayley graph Γ does not have the loop shortening property, so this property also depends on the generating set.