Can I restream RTMP stream to FMS?

See if you have those 4 or as many URL's - that does not matter. In your case when you say you have 4 URL as stated : that means "livestream1" is getting published to "serverip1" and so on and so forth. So you can do multi-point publish like how i said in other post for that many streams.

Now if your question is other way round i.e. all first servers (serverip1,serverip2 ...) are not under your control but you have right to access them then you can do pull the streams in two ways (provided you know exactly where streams are getting published) , one using Stream.play method passing remote connections or use ProxyStream API.

Stream.play - http://help.adobe.com/en_US/flashmediaserver/ssaslr/WS5b3ccc516d4fbf351e63e3d11a11afc95e-7e42.html#WS5b3ccc516d4fbf351e63e3d11a11afc95e-7f36

in this case your code would somewhat look like below (i have put bare minimum code): - 

streamObj = Stream.get("livestream1")

nc = new NetConnection();

nc.connect("rtmp://serverip/appName");

streamObj.play("livestream1",-1,-1,true,nc);  //where appName is application where livetsream1 is getting published

ProxyStream API :http://help.adobe.com/en_US/flashmediaserver/ssaslr/WSA9A478FD-0254-4161-867B-47B64CD15907.html