Weary wombat function

The weary wombat function, denoted \(\text{WW}(n)\), is an "inverse" of the frantic frog function. \(\text{WW}(n)\) is defined as the minimum number of steps taken before halting by an \(n\)-state machine that prints \(\text{PP}(n)\) 1's given blank input. It was first investigated and named by James Harland, as part of his "Zany Zoo" Turing machine research project.