A Connection Between Strangeness-Free Delay Differential-Algebraic and Neutral Type Systems * *This work was supported by the Programme of Interuniversity Attraction Poles of the Belgian Federal Science Policy Office, by the Optimization in Engineering Center OPTEC of the KU Leuven, the Research Foundation-Flanders, and by the project UCoCoS, funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 675080. Alexey Egorov acknowledge Saint-Petersburg State University for a research grant 9.42.1396.2015.