The paper entield "Weighted Rewriting: Semiring Semantics for Abstract Reduction Systems" by Emma Ahrens, Jan-Christoph Kassing, Jürgen Giesl and Joost-Pieter Katoen has been accepted for the 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025) in Birmingham (UK). This paper introduces a general semantics of the (possibly infinite) reduction sequences of an abstract reduction system in a semi-ring that is a complete lattice (for its natural ordering defined by addition). Various examples show that this framework can be used to solve disyinct problems (termination, complexity, safety, etc.) using different semi-rings.