Paths in a circuit share many lines and gates and hence, under specific assumptions, path delays are linearly related to each other. The delays of all the paths in a circuit can be expressed as a linear combination of the delays of a small subset of paths called the basis path set.In this paper we present a testing methodology and efficient algorithms to establish an upper bound (in most cases greater than the circuit clock period) on the circuit delay by testing only the paths in the basis path set. Since the size of the basis path set has been shown to be at most linear in the size of the circuit, this technique has the potential of drastically reducing the number of paths that have to be tested. Experimental results for benchmark circuits are given.