Termination proofs by multiset path orderings imply primitive recursive derivation lengths
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
Term rewriting and all that
Analysing the implicit complexity of programs
Information and Computation - Special issue: ICC '99
Quasi-interpretations and small space bounds
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Dependency Pairs and Polynomial Path Orders
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Complexity analysis by rewriting
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
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We define a new path order ${\prec_{\textsc{pop}}}$ so that for a finite rewrite system R compatible with ${\prec_{\textsc{pop}}}$, the complexity or derivation length function Dl$_{R}^{f}$ for each function symbol f is guaranteed to be bounded by a polynomial in the length of the inputs. Our results yield a simplification and clarification of the results obtained by Beckmann and Weiermann (Archive for Mathematical Logic, 36:11–30, 1996).