Every function computed by a streaming string transducer is regular (Theorem C.3.2 of Transducers, the implication from sst to regular). The sst is first normalised — the register update depends only on the letter read, and no register occurs twice in a final output string — by annotating the input with the states through a rational function; a two-way transducer then expands the final output string depth-first, moving left to expand a register and right when an expansion is finished, the copyless restriction making the place to resume an expansion a function of the register and the letter returned to. Two-way transducers compute regular functions (Theorem C.2.9).