Madrid(CNN) President Joe Biden departed the first of his two summits in Europe this week committing with other top world leaders to back Ukraine in its war against Russia "for as long as it takes."
But exactly how long that might be remains an open question -- and a source of anxiety -- for leaders now departing the Bavarian Alps after a two-day summit of the G7.
Ukrainian President Volodymyr Zelensky told the group he wanted the conflict to be over by year's end. But Russian strikes on civilian targets in Ukraine -- including residential buildings and a shopping mall -- sent a clear message to the summit: Russian President Vladimir Putin is not backing down.
Here are four takeaways from Biden's first major summit of his latest international trip:
The war in Ukraine has brought Western leaders together in condemning Russia and applying punishing sanctions. But as the war enters its fifth month, the economic consequences of isolating Russia are being felt in high gas prices, a major political liability. Meanwhile, momentum in the war appears to be favoring Russia.
Reversing those parallel trends was the principal objective of this year's G7 summit. Leaders committed to new security assistance for Ukraine, including a new missile defense system from the United States, the same model used to defend the airspace in Washington, DC. Ammunition and radar systems are also expected in the latest shipment.
But another shipment of arms isn't likely to bring an end to the war. Without a clear path to a battlefield victory, leaders have been left wondering how much longer the fighting will last -- and, by extension, how much longer the economic consequences of the war will drag down the global economy.
Zelensky's remarks to the group on Monday provided at least his view of the matter: He wants the war ended by the time winter rolls around. He pressed the group to support a major military offensive to take back the initiative against Russia.
"Zelensky was very much focused on trying to ensure that Ukraine is in as advantageous a position on the battlefield as possible in the next months as opposed to the next years, because he believes that a grinding conflict is not in the interest of the Ukrainian people," US national security adviser Jake Sullivan said after the meeting.
The West's withering set of sanctions on Russia has taken a dramatic toll. On Monday, the country defaulted on its foreign debt for the first time since the Bolshevik revolution more than a century ago.
The White House said the default showed the power of Western sanctions imposed on Russia since it invaded Ukraine. At the G7 this week, leaders slapped on new measures, including a ban on importing new Russian gold.
At the same time, the sanctions have inflicted pain on Americans through higher gas prices, an effect of global bans on importing Russian energy.
Targeting Russian energy has been a point of contention since the start of the war. And the complexities of going after one of the world's largest producers have been borne out in the following months. As Americans and Europeans are suffering high gas prices, Moscow is still reaping massive revenues from its oil exports -- due in part to the skyrocketing prices.
A plan from US Treasury Secretary Janet Yellen seeks to reverse that. Over the past several months, she has pressed G7 nations to apply a price cap on Russian oil, limiting the amount of money Russia makes from the places it is still exporting.
Leaders agreed to the idea at the summit this week. But the precise mechanism for doing so remains undecided. Officials said they were confident Western nations wield enough leverage through their transportation and distribution networks to enforce the caps.
How and when to engage Putin had divided some of the G7 leaders, who have sometimes aired differences of opinion on whether the time is right to pursue a negotiated settlement or to push ahead for a decisive victory on the battlefield.
British Prime Minister Boris Johnson entered the talks this week vowing to rally the leaders behind a plan to help Zelensky sustain the fight. And while French President Emmanuel Macron had previously warned against "humiliating" Putin, he appeared to come into agreement with Johnson on support for Ukraine after meeting at the G7.
Biden, meanwhile, has pledged billions of dollars in security assistance to Ukraine. His main goal appears to be keeping Western leaders aligned in their objectives at moments when fractures begin emerging.
"We have to stay together, because Putin has been counting on since the beginning that somehow the G7 or NATO would somehow splinter but we haven't and we are not going to," he said when meeting German Chancellor Olaf Scholz. "We can't let this aggression take the form it has and get away with it."
As the G7 concluded, it did not appear the leaders had come to any consensus on when to renew their attempts at negotiating with Putin. But the Russian leader was still very much on leaders' minds as they sat down to a working lunch Sunday.
"We have to show that we're tougher than Putin," Johnson told the group as he sat down.
Canadian Prime Minister Justin Trudeau made a suggestion: "Barechested horseback ride," he said, as the leaders chuckled.
On his first day at the summit, Biden told reporters the Supreme Court decision from two days earlier overturning Roe v. Wade hadn't come up at the G7 summit.
But for his fellow leaders, it was a troubling signal from the United States. European Union Commission chief Ursula von der Leyen said that "many voices" at the G7 summit were left "very sad and very worried" by the decision.
"We have discussed gender equality and indeed, there were many voices, very sad and very worried," von der Leyen said when asked by CNN's Christiane Amanpour about the Supreme Court decision.
Johnson, in an interview with CNN's Jake Tapper, called the ruling a "backward step."
Biden has decried the decision and vowed to explore ways to protect access to abortion. He and his aides have framed the ruling as a major step back for women's rights, and gender equality was one of the themes of this year's G7, where leaders dedicated an entire working session to the subject.
Yet during the customary family photos and working meals, the lack of gender equality among the group -- eight men and one woman -- was striking. It was the first time in 16 years without a nationally elected woman in the group.