The Supreme Court appeared willing Tuesday to extend protection from capital punishment to people with dementia who can't recall their crime or understand the circumstances of their execution.

The eight justices heard arguments in the case of Alabama death row inmate Vernon Madison, who killed a police officer in 1985 but has suffered strokes that his lawyers say have left him with severe dementia.

The high court has previously said the constitutional ban on cruel and unusual punishment means that people who are insane, delusional or psychotic cannot be executed.

A ruling for Madison probably would mean a new hearing in state court over whether his condition renders him ineligible for execution.

Chief Justice John Roberts and the court's four liberal justices seemed most willing to rule for Madison. The other three justices, Samuel Alito, Neil Gorsuch and Clarence Thomas, are unlikely to side with Madison because they voted to allow his execution to proceed when their colleagues blocked it in January, setting up the current case.

In a reflection of the changed dynamics on the court, Roberts' vote would appear to be decisive since a 4-4 split would leave in place a state court ruling against Madison and allow Alabama to try again to execute him. The high court is down one justice, following Anthony Kennedy's retirement in July and a delay in a vote to confirm Brett Kavanaugh so that the FBI can investigate allegations against him of sexual misconduct.

Kennedy had been the conservative justice most likely to vote with the liberals on death penalty cases. The court agreed to hear the appeal while Kennedy was on the bench. He had been a key voice in limiting capital punishment, having voted to bar the execution of people under 18, the intellectually disabled and those who lack a rational understanding of why they are to be put to death.