With the SPD declaring itself unwilling to enter another coalition with the CDU/CSU, the only majority would seem to be a three-way alliance between the conservatives, the Greens and the Free Democrats (FDP).

Called a "Jamaica coalition" because the party colors correspond to that country's flag, such a constellation would represent something new and different in German national politics. But there's a catch. Traditionally these two parties hate each others' guts.

"The FDP and the Greens both claim the same territory," Jürgen Dittberner - a professor emeritus of political science with connections to the FDP - told DW. "And competitors often aren't very nice to one another."

Despite some recent attempts to tone down the animosity, Greens and Liberals, as the FDP are also known, have a long tradition of sniping at one another - sometimes in sandbox fashion. The Greens, for instance, have produced parodies of FDP campaign posters depicting Liberal top candidate Christian Lindner as a Porsche-driving sunny boy, while Liberals rarely resist mocking Greens as tree-hugging know-it-alls. Old habits die hard.

The history of FDP-Green hostility

The animosity has as much to do with past origins as with present policies. Founded in 1948, the FDP goes back to the beginnings of the Federal Republic of Germany. The party for a long time was the third force and kingmaker in German politics, occupying the centrist political space between the union of conservative Christian Democrats (CDU) and their Bavarian Christian Social Union (CSU) sister party, and the Social Democrats - forming coalitions with both.

When the Greens rose to prominence in the late 1970s and early 1980s, entering the Bundestag in 1983, they challenged the Free Democrats' status. Moreover, the rise of the left-wing Greens coincided with the Liberals' turn to the right, demarcated by the party's abandonment of SPD Chancellor Helmut Schmidt and its partnership with his conservative replacement Helmut Kohl. A perceived dichotomy established itself between the pro-business, laissez-faire FDP and the environmentalist, anti-big-government Greens.

"The Greens were founded at a later point and promote non-materialistic goals, while the FDP is more of a party representing older people and the first half of the Federal Republic," Dittberner explained.

The rivalry often had a personal character. The Liberals seethed when the Greens got their first crack at government in a coalition with the Social Democrats under Gerhard Schröder. The Greens burst into applause in front of TV cameras after the 2013 national election, when it was announced that the FDP had failed to clear the five-percent hurdle members needed for parliamentary representation. FDP haven't forgotten that.

The irony is that over time the parties have come to be mirror images in many ways. Prominent members of the FDP defected to the Greens and vice versa, and nowadays they both appeal primarily to affluent white-collar voters. The generational conflict has also been reversed. The Greens' lead candidates, Cem Özdemir and Katrin Göring-Eckardt are both 51 years old, while Lindner is only 38. Could that help build bridges between the rivals?

The same impulse toward reform

Both Lindner and Göring-Eckardt declared ahead of the election that they "lacked the imagination" to picture a collaboration with the Greens, but in the traditional TV roundtable after the results were announced on September 24, there were signs of rapprochement. In what might have been a harbinger moment, Lindner said that the Liberals had "no problem" with Green-style  environmentalism, a statement that drew a positive response from Göring Eckardt.

Markus Löning, a former FDP member of the Bundestag who was also previously a Green, says there is considerable common ground in policy.

"There are large overlaps, as I know very well from my work on civil liberties," Löning told DW. "There's a whole series of points where they agree, and both have the same impulse to reform and modernize the country."

Löning says that the FDP and the Greens could agree on a joint agenda. For example, he says, by marrying Liberals' demands to expand Germany's digital network with the Greens' proposals for using technology to increase sustainability, it could bring fresh air to a new government under Chancellor Angela Merkel. And there is a regional precedent for a Jamaica coalition. In the northern state of Schleswig-Holstein, the conservatives, FDP and Greens concluded a coalition agreement in June, and the initial reviews are glowing.

"Everyone likes it and wants it to succeed," the leader of that coalition, conservative state premier Daniel Günther, told Spiegel magazine before the national election.

My enemy's enemy is my friend

Needs must. In view of the outcome of the national vote, Jamaica has emerged as the most likely form for the new government. But can all the parties agree? Löning says: Why not?

"The time is ripe," he explained. "The FDP has changed in the past four years, and the Greens have changed, too, over the years and decades."

But Oskar Niedermayer, possibly Germany's leading expert on political parties, says that there are still "dramatic differences" between the Liberals and Greens on issues ranging from refugees to the combustion engine to domestic security and the EU. 

Even if the Liberals and Greens make peace, Niedermayer adds, the latter would have trouble co-existing with the more right-wing CSU. 

"The FDP are somewhat more flexible in their demands - they could make compromises," Niedermayer said. "But the CSU and the Greens have drawn lines in the sand, for example, on the combustion engine and coal-burning power plants."

"Forming a government," he said with a somewhat mischievous smile, "is going to be a lot more exciting than the election itself."