On list primitive recursion and the complexity of computinginf

We present a primitive recursive programinf_with_lists computing the minimum of two natural numbersn andp (written in unary notation) and using primitive recursion on lists. This program has at first sight the required property of visiting simultaneously its inputs, so it is a counterexample to a theorem showing that such a program cannot be written in the language of primitive recursion on natural numbers, in the more general framework of primitive recursion on term algebras. However, its complexity is at leastinf(n,p)² so it does not implement the algorithm we have in mind to computeinf(n,p).