In this paper we investigated two different methods to parse relative and noun complement clauses in English and resorted to distinct tags for their corresponding that as a relative pronoun and as a complementizer. We used an algorithm to relabel a corpus parsed with the GUM Treebank using Universal Dependency. Our second experiment consisted in using TreeTagger, a Probabilistic Decision Tree, to learn the distinction between the two complement and relative uses of postnominal "that". We investigated the effect of the training set size on TreeTagger accuracy and how representative the GUM Treebank files are for the two structures under scrutiny. We discussed some of the linguistic and structural tenets of the learnability of this distinction.