Concerning the Witch King

[Oroaranion]

I presume that he was completely defeated because *runs for copy of LotR* Glorfindel says

Far off yet is his doom, and not by the hand of man will he fall.

in Appendix A, part iv.

Doom usually implies that this is the end of somthing. I think that even if the Witch-King had survived, he would not do very well without his master, Sauron, after the fall.