PITTSBURGH — The University of Pittsburgh Medical Center asked the Pennsylvania Supreme Court on Tuesday to vacate a lower court’s order forcing UPMC to maintain cheaper, in-network rates for Highmark Inc.’s 182,000 Medicare Advantage customers.

Commonwealth Court Judge Dan Pellegrini ordered UPMC in May to maintain the cheaper rates through 2019 for Medicare Advantage subscribers who use UPMC’s doctors and hospitals. His ruling came after UPMC tried to cancel its in-network contract with Highmark’s Medicare Advantage plan.

UPMC attorney Stephen Cozen argued Tuesday that it’s an “undisputed right of UPMC to cancel with proper notice.”

But whether the state’s highest court agrees when it rules in several months seems to depend on what legal language the justices focus on, and how they interpret a state-mediated consent decree between the feuding health care giants. The legalese is so complex that Justice Max Baer told the attorneys that he, “frankly, didn’t follow” part of it.

The state mediated the decree to protect customers after UPMC refused to extend its in-network provider agreement for all of Highmark’s insurance products, starting this year.

Highmark and UPMC have been fighting since Highmark purchased the financially ailing West Penn Allegheny Health System in 2013. That became the backbone of Highmark’s since-renamed, seven-hospital Allegheny Health Network, and made Highmark more of a rival to the much larger 20-hospital UPMC network, which has its own health insurance plan.

UPMC threatened to end all of its in-network provider agreements with Highmark, saying they gave Highmark the unfair advantage of continuing to offer UPMC doctors and hospitals at low rates while competing with UPMC’s Health Plan for subscribers.

Medicare Advantage is a Medicare Part C plan. Part C plans are private insurance approved by Medicare for people enrolled in the government-run Medicare Part A, or hospitalization, and Part B, or medical insurance, programs.

Customers pay a premium for Medicare Advantage plans and must still pay their Part B premiums. But they can sometimes still save money because the out-of-pocket deductibles and co-pays for the private insurance can be cheaper those in the government-run programs.

Attorneys for the commonwealth and Highmark argued Tuesday that the consent decree requires the Medicare Advantage deal to run through 2019, period.