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We define an equivalent variant LKsp of the Gentzen sequent calculus LK. In LKsp weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules ELKsp by a finite rewriting system; the termination of this rewriting system can be machine checked. We give also a self-contained strong normalization proof by structural induction. We give another strong normalization proof by a strictly monotone subrecursive interpretation; this interpretation gives subrecursive bounds for the length of derivations. We give a strong normalization proof by applying orthogonal term rewriting results for a confluent restriction of the mix elimination system ELKsp .

Strong normalization proofs for cut elimination in Gentzen's sequent calculi