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On the uplink of a DS-CDMA system with the imperfect successive interference cancellation (SIC) technique, K active users correspond to K! decoding orders. Due to the constraint of the received power, not all the possible decoding orders may be feasible, rendering the failure of SIC algorithm. Meanwhile, examining the feasibility of the system among all these decoding orders directly by the exhaustive search method (ESM) is prohibitively time-consuming. In this paper, we investigate the fast method of examining the feasibility of the SIC algorithm in a DS-CDMA system. The computational complexity involved in examining the feasibility of the SIC algorithm by the proposed method is significantly less than that of ESM. Subsequently, the greatly reduced examining time will be beneficial to the quick decision of admission control or scheduling schemes. Extensive numerical results valid our analysis.