We define two transformations from term rewriting systems (TRSs) to
context-sensitive TRSs in such a way that termination of the target system
implies outermost termination of the original system. In the transformation
based on 'context extension', each outermost rewrite step is modeled by exactly
one step in the transformed system. This transformation turns out to be
complete for the class of left-linear TRSs. The second transformation is called
`dynamic labeling' and results in smaller sized context-sensitive TRSs. Here
each modeled step is adjoined with a small number of auxiliary steps.

As a result state-of-the-art termination methods for context-sensitive
rewriting become available for proving termination of outermost rewriting. Both
transformations have been implemented in Jambox, making it the most successful
tool in the category of outermost rewriting of the last edition of the annual
termination competition.