To see what is going on, we first have to remind ourselves that we have assigned a parameter (a natural number) to every variable "x""i". Second, we do see a successor-operator at work iterating "y" (i.e. the "y' "). And third, we see that the function μ"y" "y"<"z"χ("y", x) is just producing instances of χ("y",x) i.e. χ(0,x), χ(1,x), ... until an instance yields 0. Fourth, when an instance χ("n", x) yields 0 it causes the middle term of τ, i.e. v = π(x, "y' ") to yield 0. Finally, when the middle term "v" = 0, μ"y""y"<"z"χ("y") executes line (iii) and "exits". Kleene's presentation of equations (ii) and (iii) have been exchanged to make this point that line (iii) represents an "exit"—an exit taken only when the search successfully finds a "y" to satisfy χ("y") and the middle product-term π(x, "y' ") is 0; the operator then terminates its search with τ("z' ", 0, "y") = "y".