Add to ORKGIn the field of implicit computational complexity, we are con- sidering in this paper the fruitful branch of interpretation methods. Due to their good intensional properties, they have been widely developped. Among usual issues is the synthesis problem which has been solved by the use of Tarski's decision procedure, and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (well-) ordering of N employed to bound the complexity of programs. We show that, actually, polynomials over the reals benefit from some properties that allows their safe use for complexity. We illustrate this by two char- acterizations, one of PTIME and one of PS...