  We introduce proof terms for string rewrite systems and, using these, show
that various notions of equivalence on reductions known from the literature can
be viewed as different perspectives on the notion of causal equivalence. In
particular, we show that permutation equivalence classes (as known from the
lambda-calculus and term rewriting) are uniquely represented both by trace
graphs (known from physics as causal graphs) and by so-called greedy multistep
reductions (as known from algebra). We present effective maps from the former
to the latter, topological multi-sorting TM, and vice versa, the proof term
algebra [[ ]].
