Consider a program that solves the traveling salesman problem in the following fashion. It searches for an algorithm that solves the traveling salesman problem

Consider a program that solves the traveling salesman problem in the following fashion. It searches for an algorithm that solves the traveling salesman problem and proof that such an algorithm runs in polynomial time, and then uses said algorithm to find a solution for the input, simultaneously while trying to solve the traveling salesman problem with some non-polynomial time algorithm that takes O(g(n)) time. Let f(n) be the worst case running time that program has on inputs of size n. Whether O(f(n)) = O(g(n)) is not obvious. Edit: Actually you asked for an example, and I'm not sure I gave one.