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Among the languages implementing the rewriting logic, we quote CafeOBJ (1b) [56| and Maude [15, 16].
Meseguer, the Maude language [15, 16] is one of the most powerful implementations of the rewriting logic.
With the exception of the rewriting logic, which is helped by an elegant, although sophisticated semantics, this indicates why one had to await completeness results of the proposed reasoning systems for so long.
The rewriting logic, having a sound and complete semantics, was introduced by Meseguer [14].