All breakups are tough. But the divorces we have learned to fear the most are protracted, conflict-prone and ultimately unresolved. All the signs are that China and America are in the middle of one of these messy divorces between abusive couples who hate and need one another at the same time. As Washington and Beijing prepare for new political leaderships, they cannot avoid a major renegotiation of the terms of their relationship.

Since the global financial crisis in 2008, we have been living through the slow and painful end of Chimerica — the period when the American and Chinese economies acted as one. It drove one of the longest periods of global growth and prosperity in history. This perfect symbiotic relationship — popularized by the historian Niall Ferguson — was based on China saving half of its GDP while America borrowed the money to finance a spending binge it could not afford. The romance ended in September 2008 with the collapse of Lehman Brothers. Now the terms of the separation between the two nations risk awkward discomfort for the rest of the world.

On a recent visit to Beijing, I was struck by the near-universal assumption that American demand will not return to pre-2008 levels. This has led to a lively debate about how to reorient China’s economy. On the one hand, China is hedging against the dollar by investing in companies and assets outside the U.S. On the other hand, Beijing is bracing itself for slower growth, while looking for substitutes for exports and fixed investment.

There is an ongoing discussion in China about how to encourage the growth of small and medium-sized enterprises, how to stimulate domestic consumption and how to invest in social welfare rather than infrastructure. The American economic debate is less strategic, but there is a realization that the level of debt incurred in the boom years is unsustainable and some of the stimulus measures like quantitative easing will make it increasingly unattractive for the Chinese government to stockpile Treasury Bills.

As if in anticipation of the “Great Decoupling,” the political atmosphere between Washington and Beijing has soured. A film released in the U.S. this week called “Death by China” — narrated by the nation’s favorite fictional president, Martin Sheen — says that “China is the only major power that is systematically preparing to kill Americans.” A publicity poster features a blood-soaked map of the United States stabbed by a huge knife that is engraved with the words “made in China.” But the fear-mongering in the film is moderate when compared with the daily attacks on “perfidious” American leaders on Sina Weibo (the Chinese answer to Twitter) or in best-selling books such as “China is Unhappy” (an ultranationalist tract that sold over 1 million non-pirated copies in 2009).