observe at least as strong $Q\rightarrow C{=}c$, if $Q$ and $C$ were conditionally independent given dependency $X\rightarrow
C{=}c_x$? If it is more probable than the opposite, observing as strong $X\rightarrow C{=}c_x$, given $Q\rightarrow C{=}c$, then at most $r_1$ can be specious. In the opposite case, at most $r_2$ can be specious. In both cases, it is also required that the probability is sufficiently high. There is also a special case, where the probabilities are equal. Then one cannot say that either rule is specious, because we cannot have a circular argument, where $r_1$ is made specious by $r_2$ and $r_2$ by $r_1$. (Still, it suffices to report only one of the rules, if they are equivalent and the equivalence information is also reported.) Therefore, we can from now on assume that there are only three alternatives: either one of the rules is specious by the other or none of them is.

A brute-force approach for detecting specious rules would evaluate all possible rule pairs $r_1$ and $r_2$. However, this is quite an intractable solution because the universe of all possible rules defined by $k$ attributes is $\mathcal{O}(2^k)$. As a solution, we will show that when the rules are searched with 