We present a survey on a method to analyse the program time and space complexity, based on termination orderings and quasi-interpretation. This method can be implemented to certify the runtime (or space) of programs. We demonstrate that the class of functions computed by first order functional programs over free algebras which terminate by permutation Path Ordering (resp. Lexicographic Path Ordering) and admit a quasi-interpretation bounded by a polynomial, is exactly the class of functions computable in polynomial time (resp. space).