We define a tier based type system to capture the class of Basic Feasible Functionals on an imperative programming language with oracles. Following the seminal work by Kapron and Steinberg on Oracle Turing Machine, we try to ensure a polynomial step count and a bounded lookahead revision on typable and terminating programs. We obtain a soundness result. An open issue is to know whether the polynomial step count can be computed by typable and terminating programs. Consequently, we have only a weak form of completeness.