“…To be formal, we should make both tasks explicit in the form of an abstract machine. The work of Accattoli and coauthors [6,9,4] has however repeatedly showed that these tasks require an overhead linear in the number of β-steps and the size of the initial term, and in some cases even logarithmic in the size of the initial term (see the companion paper [7])-in the terminology of this paper, the costs of search and α-renaming are negligible. At the technical level, for the study of cost models we mostly adopt the techniques and the terminology (linear substitution calculus, subterm invariant, harmony, etc) developed by Accattoli and his coauthors (Dal Lago, Barenbaum, Mazza, Sacerdoti Coen, Guerrieri) in [10,6,9,11,4].…”