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This paper presents a novel approach for identifying non-robustly unsensitizable paths using the bounded delay model for gate delays. A unique feature is that the unsensitizable paths are identified by working on a data structure that stores selected circuit paths instead of the netlist. It is shown that unless the delay of untestable paths are ignored, many non-robust paths will remain undetected. Experimental results show the approach implicitly identifies a large number of non-robustly unsensitizable paths, which were not identified with other existing techniques.