The verification of final termination for counter systems is undecidable. For non flattable counter systems, the verification of this type of property is generally based on the exhibition of a ranking function. Proving the existence of a ranking function for general counter systems is also undecidable. We provide a framework in which the verification whether a given function is a ranking function is decidable. This framework is applicable to convex counter systems which admit a Presburger or a LPDS ranking function. This extends the results of [A. Bradley, Z. Manna, and B. Sipma. Termination analysis of integer linear loops. In CONCUR 2005 - Concurrency Theory, 16th International Conference, CONCUR 2005, San Francisco, CA, USA, volume 3653 of Lecture Notes in Computer Science, pages 488–502. Springer, 2005]. From this framework, we derive a model-checking algorithm to verify whether a final termination property is satisfied or not. This approach has been successfully applied to the verification of a parametric version of the ZCSP protocol.