The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the introduction of redundant arguments in the functions defined in the program. Redundancy of a parameter means that replacing it by any expression does not change the result. In this work, we provide a method for the analysis and elimination of redundant arguments in term rewriting systems as a model for the programs that can be written in more sophisticated languages. On the basis of the uselessness of redundant arguments, we also propose an erasure procedure which may avoid wasteful computations while still preserving the semantics (under ascertained conditions). A prototype implementation of these methods has been undertaken, which demonstrates the practicality of our approach.