This paper investigates the semantics of conditional term rewriting systems with negation which do not satisfy useful properties like termination. It is shown that the approach used by Fitting  for Prolog-style logic programs is applicable in this context. A monotone operator is developed, whose fixpoints describe the semantics of conditional rewriting. Several examples illustrate this semantics for non-terminating rewrite systems which could not be easily handled by previous approaches.
Mohan, Chilukuri K., "Fitting Semantics for Conditional Term Rewriting" (1990). Electrical Engineering and Computer Science Technical Reports. Paper 79.