Johannes Waldmann

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We present a new method for automatically proving termination of term rewriting. It is based on the well-known idea of interpretation of terms where every rewrite step causes a decrease, but instead of the usual natural numbers we use vectors of natural numbers, ordered by a particular nontotal well-founded ordering. Function symbols are interpreted by(More)
We present a new method for proving termination of term rewriting systems automatically. It is a generalization of the match bound method for string rewriting. To prove that a term rewriting system terminates on a given regular language of terms, we first construct an enriched system over a new signature that simulates the original derivations. The enriched(More)
We introduce the arctic matrix method for automatically proving termination of term rewriting. We use vectors and matrices over the arctic semi-ring: natural numbers extended with −∞, with the operations “max” and “plus”. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the Dependency(More)
For a given (terminating) term rewriting system one can often estimate its derivational complexity indirectly by looking at the proof method that established termination. In this spirit we investigate two instances of the interpretation method: matrix interpretations and context dependent interpretations. We introduce a subclass of matrix interpretations,(More)
We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages. To this end, letters are annotated with natural numbers, called match heights. If the minimal height of all positions in a redex is h then every position in the reduct(More)