Just to be annoying, the "City of Neualtenburg" is not just the bit inside the walls... that is the "inner city" only but the valley is naturally part of the city as well!
Around here, cities have "urban" and "rural" areas (for administrative purposes, and also some legislative ones); they're not defined by their "walls" only.
Federations (and confederations) can be republics, too, and use that in their names. Examples are the [url=http://en.wikipedia.org/wiki/Germany:hobavh2y]Federal Republic of Germany[/url:hobavh2y] and the [url=http://en.wikipedia.org/wiki/Brazil:hobavh2y]Federative Republic of Brazil[/url:hobavh2y], just to name a few of the most obvious ones (Nigeria and Ethiopia are federal republics as well). See http://en.wikipedia.org/wiki/Federal_republic for the usage of this weird combination. The Wikipedia's author of that text seems to distinguish "federal republics" from federations that are actually monarchies, like Canada, Australia, or Malaysia.
Switzerland is a [i:hobavh2y]very[/i:hobavh2y] special case It's traditionally "Confederatio Helvetica", although technically, a federal republic. Traditionally, it has no "head of state", but a "Federal Council" of seven members, although also traditionally, one of them is elected president for a year. This is at the same time a legislative body (also traditionally!), although, unlike most modern governments with a cabinet (or similar council), formed of members nominated by a single faction/party elected by the citizens, in Switzerland this strange executive body has members from all parties. Also, almost everything in Swiss law is based upon direct democracy, and has been so for uncountable years. Any citizen can contest a law, any citizen can propose amendments to the constitution... yes, it's that weird (My apologies to any Swiss members of N'burg; to redeem myself, I'll just say that part of my family lives in Switzerland  my cousins are the only persons I know that enjoy [i:hobavh2y]triple[/i:hobavh2y] nationality  as well as several of my very close friends) One would expect that such a system wouldn't work for 7 million people  but it has worked rather well for over 700 years.
Of course, to fully understand how it works, you have to be born a Swiss We foreigners will only frown upon their alien ways; Switzerland has really a totally unique government system which [i:hobavh2y]works[/i:hobavh2y]  for [i:hobavh2y]them[/i:hobavh2y], not for us common human beings