Recent actions by South Korea President Moon Jae-in and China's President Xi Jinping have raised questions about the sincerity of both countries in helping the U.S. reign in North Korea's nuclear program.

President Trump invited President Xi to visit Mar-a-Lago last winter, and expressed optimism about the good intentions of President Xi in this Monday tweet: "North Korea has shown great disrespect for their neighbor, China, by shooting off yet another ballistic missile...but China is trying hard!"

But some analysts believe President Xi and South Korean President Moon are playing a duplicitous game – with China hoping to pull South Korea, as well as North Korea, closer into its orbit and away from the U.S. sphere of influence.

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South Korea's President Moon lashed out at the U.S. on Tuesday after his own defense ministry failed to notify him that the Pentagon sent four more batteries of THAAD (Theatre High Altitude Area Defense missiles) to South Korea.

China is also wary of those missiles, fearing the U.S. may place them in Japan, too, as a part of a NATO-like alliance of Japan, South Korea and the U.S. to block Chinese ambitions.

"It's another symptom of the fact that relations between the U.S. and South Korea today and will become ever more troubled as we see the events on the Korean peninsula unfold," said Graham Allison, professor of government at Harvard's Kennedy School of Government and author of the new book, "Destined for War: Can America and China Escape Thucydides's Trap?"

South Korea's Jeju Air said on Tuesday that China had approved a plan to double its flights to China starting Friday. Cultural exchanges between the two countries are also being increased.

That, as it becomes clear China's moratorium on the purchase of North Korean coal exports have largely been a ruse.

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"We know that the Chinse bought North Korean coal in February after the announcement [of the moratorium] in March, in April, and in May," said Gordon Chang, author of "The Coming Collapse of China." "The Chinese have been buying minerals that the UN Security Council resolution prohibits North Korea from selling.”

Indeed, in the first quarter of 2017, China-North Korea trade was up 37.4 percent from the same period in 2016.

Yet, the U.S. remains hopeful that it will be Chinese influence that ultimately gets North Korea to halt its nuclear program.

"At this point, I do believe – and I think the administration believes – that China is doing back-channel networking with North Korea in a way that's getting them to try and stop the nuclear testing," UN Ambassador Nikki Haley told reporters on Tuesday.

But many experts agree that only U.S. action will force North Korea's hand – either a concession like pulling out U.S. THAAD missiles out of South Korea, or a tougher stance – perhaps sanctioning Chinese banks that are helping to fund North Korea's nuclear program.

Either way, the growing consensus is time is running short.