The paper presents a system for transforming programs expressed as first-order recursion equations to improve their efficiency. The authors describe a set of simple rules and a strategy for applying these rules to transform programs, with the aim of making them more efficient while maintaining correctness. They provide examples to illustrate the transformation process and discuss the implementation of a semi-automatic program transformation system. The system can be used to convert recursive programs to iterative form and to handle abstract data types. The authors also introduce an additional rule for redefinition, which allows for the reversal of transformations to achieve more efficient definitions. The paper concludes with a discussion on future developments and the potential for automatic generation of definitions.The paper presents a system for transforming programs expressed as first-order recursion equations to improve their efficiency. The authors describe a set of simple rules and a strategy for applying these rules to transform programs, with the aim of making them more efficient while maintaining correctness. They provide examples to illustrate the transformation process and discuss the implementation of a semi-automatic program transformation system. The system can be used to convert recursive programs to iterative form and to handle abstract data types. The authors also introduce an additional rule for redefinition, which allows for the reversal of transformations to achieve more efficient definitions. The paper concludes with a discussion on future developments and the potential for automatic generation of definitions.