We show that a proof term in a string rewrite system can be mapped to its causal graph and that the latter is a unique representative of the permutation equivalence class of the former. We then map the causal graph back to a proof term of a special shape, a so-called greedy multistep reduction. Com- posing both transformations yields a simple and effective way of constructing the greedy multistep reduction of a proof term, and thereby of deciding permutation equivalence of proof terms in general, and of (multistep) reductions in particular.