It´s not really a problem. Legally, Germany isn´t a form of state, but a company - a "GmbH", "Gesellschaft mit beschränkter Haftung" - the german equivalent to a "Ltd." - a "Limited". In case of bankruptcy, Germany would pay the amount of money stored for the Ltd. and not one penny more. This country learned from the reparation-payments of Worldwar One and Two ^^ - it´s Germany´s economical way to say "Fuck You!" to the world
This makes Angela Merkel the CEO of the company "Germany Ltd". So Germany has no government at the moment, but it still has the executive board. All political titles within Germany are merely words - in moments like theses it becomes pretty obvious, that politics in this country are only a false front - a facade. The strings are pulled by the industry. They could call Merkel "supreme empress of the german part of the universe". It wouldn´t make a difference. It´s all an intern solution for identification within the company Germany and representation, of course - so that other states see: "Ah, the chancellor; ah, the president!". It does behold a little danger though - the population might realise, that the government is totally superfluous... there´s villages and small towns with a dog or a cat as mayor. It would work just as well with this whole country.