# The Generalized Multiset Ordering is NP-Complete

 Title: The Generalized Multiset Ordering is NP-Complete Authors: René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) and Lukas Schmidinger Submission date: 2022-04-20 Abstract: We consider the problem of comparing two multisets via the generalized multiset ordering. We show that the corresponding decision problem is NP-complete. To be more precise, we encode multiset-comparisons into propositional formulas or into conjunctive normal forms of quadratic size; we further prove that satisfiability of conjunctive normal forms can be encoded as multiset-comparison problems of linear size. As a corollary, we also show that the problem of deciding whether two terms are related by a recursive path order is NP-hard, provided the recursive path order is based on the generalized multiset ordering. BibTeX: @article{Multiset_Ordering_NPC-AFP, author = {René Thiemann and Lukas Schmidinger}, title = {The Generalized Multiset Ordering is NP-Complete}, journal = {Archive of Formal Proofs}, month = apr, year = 2022, note = {\url{https://isa-afp.org/entries/Multiset_Ordering_NPC.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Weighted_Path_Order Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.