 We say that a function \(f:\mathbb{N}^k \rightarrow \mathbb{N}\) is partial recursive if \(f \in \mathbf{PartREC}\). Additionally we say that \(f\) is recursive if \(f \in \mathbf{PartREC}\) and \(f\) is total. The set of recursive functions will be denoted by \(\mathbf{REC}\). 