The insights from this work on commutative N-polyregular functions provide valuable contributions to the broader landscape of function classes and their decision problems, as depicted in Figure 1. By addressing key questions and providing decidable characterizations for commutative N-polyregular functions, this research enhances our understanding of the relationships between different classes of functions and their computational properties. The results obtained in this study contribute to the ongoing efforts to classify and analyze function classes based on their computational power and expressiveness. The systematic approach taken in this work sheds light on the decidability of membership problems and provides effective conversion algorithms, which can have implications for decision problems in related function classes. Overall, the insights from this work contribute to the advancement of theory in computational models and automata extensions.