Strong Normalisation Proofs for Cut Elimination in Gentzen's Sequent Calculi

We deene a variant LKsp of the Gentzen sequent calculus LK. In LKsp weakenings or contractions can be done in parallel. This modiication allows us to interpret a symmetrical system of mix elimination rules ELKsp by a nite rewriting system; the termination of this rewriting system can be checked by machines. We give also a self-contained strong normalisation proof by structural induction. We give another strong normalisation proof by a strictly monotone subrecursive interpretation; this interpretation gives subrecursive bounds for the length of derivations. We give a strong normalisation proof by applying orthogonal term rewriting results for a connuent restriction of the mix elimination system ELKsp.