Incremental termination proofs and the length of derivations

Incremental termination proofs, a concept similar to termination proofs by quasi-commuting orderings, are investigated. In particular, we show how an incremental termination proof for a term rewriting system T can be used to derive upper bounds on the length of derivations in T. A number of examples show that our results can be applied to yield (sharp) low-degree polynomial complexity bounds.