ᴺS. [N.] ^rein n. “slot, spoor, track, footprint” (Category: Foot)
A noun appearing as N. rhein “slot, spoor, track, footprint” in The Etymologies of the 1930s under the root ᴹ√RUN “flat of hand or sole of foot” (Ety/RUN). It seems to be derived from ᴹ✶runya, with an intermediate form rhoein, where the ancient u became o via a-affection, then this o became œ via i-affection and then later e, while the y [ı̯] intruded into the preceding syllable after the loss of -a made it final.
Neo-Sindarin: This word was adapted as ᴺS. rein in Hiswelókë’s Sindarin Dictionary (HSD), with the usual removal of Noldorin-style voiceless rh. However, the actual phonological results in Sindarin would probably be ᴺS. ruin; compare S. ruin “fiery red” with Quenya cognate runya (PM/366). Since ruin already has several meanings in Sindarin, I would retain ᴺS. rein as an obscure dialectical variant.
Reference ✧ Ety/RUN ✧ “slot, spoor, track, footprint”
|#ᴹ✶runya > rhoein > rhein||[runja] > [ronja] > [ronia] > [rœnia] > [rœni] > [rœin] > [r̥œin] > [r̥ein]||✧ Ety/RUN|