automatable

The story

1. Proto-Hellenic*autós
2. Proto-Indo-European*h₂ew
3. Ancient Greekαὖ (aû)
4. Ancient Greekτόν (tón)
5. Ancient Greekαὐτός (autós)
6. Ancient Greekαὐτο- (auto-)
7. Proto-Indo-European*mn̥tós
8. Proto-Hellenic*mətós
9. Ancient Greekαὐτόμᾰτος (autómătos)
10. Ancient Greekαὐτόμᾰτον (autómăton)
11. Classical Latinautomatum
12. New Latinautomaticus
13. Englishautomatic
14. Englishautomationbf.
15. Englishautomate
16. English todayautomatable

From automate + -able.