This follows from the facts that the functions of this form are the most quickly growing primitive recursive functions, and that a function is primitive recursive if and only if its time complexity is bounded by a primitive recursive function. For the former, see Linz, Peter (2011), An Introduction to Formal Languages and Automata, Jones & Bartlett Publishers, p.332, ISBN9781449615529. For the latter, see Moore, Cristopher; Mertens, Stephan (2011), The Nature of Computation, Oxford University Press, p.287, ISBN9780191620805
