The most ferocious slugging match at this week’s GOP debate didn’t feature The bombastic Donald vs. the newly energized Jeb Bush. That, by now, is old stuff.

Instead, it pitted Texas Sen. Ted Cruz vs. his fellow Cuban-American, Florida Sen. Marco Rubio, as they sparred over opposing foreign policy visions — and in the process revealed the growing rift within the GOP over the role America should play in the Middle East.

This is big stuff, even though the candidates’ errors of fact and Mideast misconceptions were distracting (when in doubt, “bomb, bomb, bomb” seemed to be the common theme.) But Cruz and Rubio, both battling to overtake Trump, tussled over something much deeper: whether or not America should be trying to remove foreign dictators in the Mideast or elsewhere, including Syria’s Bashar Assad.

Coherent alternative?

Until this dispute is resolved it will be difficult for the GOP to present a coherent or plausible alternative to President Barack Obama’s Mideast policy — beyond calling for more air strikes. (No such alternative emerged from this foreign policy debate.)

Cruz is trying to position himself as a foreign policy realist in the tradition of Ronald Reagan, whom he refers to incessantly whenever he talks. He damns Obama for having pressed for the ouster of Arab dictators, including Assad, Libya’s Moammar Gadhafi, and Egypt’s Hosni Mubarak. (In reality, Obama was reluctantly persuaded by European and Arab allies to enter an alliance against Gadhafi, and reluctantly endorsed the popular uprising that doomed Mubarak.)

Cruz argues that America has more to gain from reverting to Reagan’s policy of allying with “friendly dictators.” That includes Assad, who Obama has insisted must leave power before the Syrian conflict can be ended. “If we topple Assad, the result will be ISIS will take over Syria, and it will worsen U.S. national security interests,” Cruz said, using an acronym for the Islamic State group. He has a point.

The Texan attacked Rubio for arguing that Assad must go. He claimed that the Floridian had “too often supported Hillary Clinton and Barack Obama” in undermining Mideast governments that fought radical Islamists. With wildly varying degrees of coherence, Trump, Rand Paul, and Ben Carson all seemed to agree that Assad should stay.

Two things make this GOP dispute over “regime change” particularly fascinating. First, Cruz is essentially repudiating the Bush Doctrine. George W. Bush said “the calling of our time” was to support democratic movements abroad “with the ultimate goal of ending tyranny in our world.”

Not surprisingly, Cruz never mentioned Bush’s ouster of Saddam Hussein, although that “regime change” opened the door to the Islamic State. Yet it is Bush’s neoconservative doctrine of democracy promotion that he is eager to bury. Rubio endorses the Bush Doctrine and has worked with some of Bush’s team.

Dealing with Bush legacy

So we are witnessing an internal GOP battle over whether and how to exorcise the Bush legacy, without ever mentioning its author or admitting that the Iraq War triggered the Mideast breakdown.

Which brings us to point two: Cruz never laid out a clear strategy of how to combat ISIS if Assad retains power. And what he did lay out revealed a very confused picture of the Syrian war.

The senator never addressed the fact that, by endorsing Assad’s retention of power, he was implicitly aligning himself with Russia and Iran, which are propping the dictator up. Nor did he mention that Assad’s Russian ally has less interest in fighting the Islamic State than in giving America a black eye. (Instead, there was plenty of rhetoric on stage, led by Gov. Christie, about bombing Russian planes.)

As for fighting the Islamic State, the Texas senator called for “carpet bombing” the group as the United States supposedly did to Saddam’s army in the first Gulf War (never mind that U.S. forces used targeted strikes in that war). When asked if he would “carpet bomb” cities held by the Islamic State, he said “the object is not to bomb the city. You would bomb where ISIS is.” Unfortunately, the Islamic State is mainly located in cities such as Raqqa and Mosul, where it uses civilians as shields, so Cruz’s carpet bombing would take thousands of innocent lives.

More homework needed

In fact, watching the debate, one got the sense that the GOP candidates had yet to master their briefing books. Rubio, who seems to have done the most homework, recognized the limits of the air campaign and called for a ground force primarily made up of Sunnis. When reminded by a questioner that the neighboring Arab states weren’t eager to provide ground troops, he blamed this on mistrust of Obama. The reality is far more complex.

Yet the debate begun by Cruz and Rubio is an important one. The Bush Doctrine of regime change (pursued by Obama reluctantly and often in the breach) has failed repeatedly. At this point, it may be impossible to remove Assad for the foreseeable future, something the Obama team is beginning to recognize. Negotiations now ongoing with Russia, Iran, and Arab allies about how to end the Syrian civil war are grappling with this dilemma.

That reality, however, doesn’t provide a clear formula for combating the Islamic State. Neither Obama nor the GOP candidates have yet figured that one out.

— Trudy Rubin is a columnist and editorial-board member for the Philadelphia Inquirer.