Seeking compositionality in holistic proto-language without substructure – do counterexamples overwhelm the fractionation process?

In holistic theories of protolanguage, a vital step is the fractionation process where holistic utterances are broken down into segments, and segments associated with semantic components. One problem for this process may be the occurrence of counterexamples to any segment-meaning connection. The actual abundance of such counterexamples is a contentious issue \cite{smith06,taller07}. Here I present calculations of the prevalence of counterexamples in model languages.  It is found that counterexamples are indeed abundant, much more numerous than positive examples for any plausible holistic language.