The construction of the residual transducer for non-commutative N-polyregular functions has significant implications. In the non-commutative case, the residual transducer provides a canonical model of computation for N-polyregular functions by generalizing the notion of residual transducers previously introduced in Z-polyregular functions. This allows for the effective computation of functions that are not necessarily commutative, extending the applicability of the concept beyond commutative functions. By leveraging the residual transducer construction, decision problems related to non-commutative N-polyregular functions can be addressed in a systematic and structured manner, providing a clear framework for analyzing and understanding the behavior of these functions.