An SOS Message: Conservative Extension in Higher-Order Positive/Negative Conditional Term Rewriting Wan Fokkink Chris Verhoef General theorems in structured operational semantics can be transformed into related results in conditional term rewriting. We apply this approach to obtain a conservative extension theorem for higher-order conditional term rewriting systems with negative conditions. This result is useful, for instance, in modular specification of abstract data types, and in software renovation factories.