The emergence of Application-specific Instruction-set Processor (ASIP) has encouraged the proliferation of tool-chains used to streamline its design flow. One of the features much sought-after in these tool-chains is notably the automatic generation of Application-specific Functional Units (AFUs) which, in turn, involves the custom instruction generation as a crucial step. Whereupon an additional step is assumed to pipeline the patterns identified for fulfilling the I/O constraint, custom instructions that correspond to maximal valid subgraphs are mostly beneficial to the speedup gain. Therefore, we present in this paper a propositional satisfiability approach to efficiently identify the custom instructions which contain a large number of valid nodes. Our approach is different substantially from the previous works where it uses an edge classification method to reduce the search space for convexity checking. The experiment results show that our method can, in a matter of few seconds, identify a set of custom instructions that speed up the application to a few times faster.