Formal reasoning about computational complexity turns out to be quite cumbersome as it often requires to manipulate explicit time bounds for a specific machine model. Implicit Computational Complexity is a research area which provides techniques and complexity classes characterisations to avoid this. We have formally verified the soundness (and part of the completeness) of such a technique − called quasi-interpretations − using the Coq proof assistant. In particular, we turned this into a tool to
help guarantee the polynomial complexity of programs (here, term rewriting systems).