There is a strong and somewhat renewed interest in production and business rule systems. For example it is significant that in April 2004Gardner published a comparative study of the different business rule systems and vendors and estimated that the current market of 200millions of dollars was promised to a sustained increased for several years. Production systems, as we will call them from now on, are widely appreciated in industry for their agility, reactivity and flexibility. But putting them in action is also delicate since their semantics is unclear or even unknown and therefore make the development of large systems quite depend of test and experience. Term rewriting is a different kind a rule based systemthat emerged fromautomated deduction and semantics of programming languages in the early seventies. It is nowa prettywell understood concept and many implementations show their usefulness, robustness and efficiency. This report intends to bridge these a priori different views of rule based systems.