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The process is reparameterization, where, in the example, there is one supernumerary parameter that makes the system unnecessarily underdetermined. An alternative reparameterization is to $\frac{X_1}{X_1-\alpha X_2}$. The set $\{a,b\}$ has one more parameter than needed, but it is arbitrary to say which one, as it is the set that is overdefined, not $a$ or $b$ taken separately. Thus, $b$ by itself is only one of the two parameters that are problematic, and would likely not have a stand alone name. It is the set that is redundant, and would result in regression instability in a spuriously underdefined system such that reparameterization is not optional, it is indicated.