The U.S. Supreme Court will hear arguments Tuesday in the case of an inmate sentenced to death for killing an Alabama police officer in 1985 but who lawyers say can no longer remember the murder because of stroke-induced dementia.

Justices will decide if it would violate the constitutional ban on cruel and unusual punishment to execute Vernon Madison, 68, because of the mental declines he has experienced resulting from strokes. Madison was convicted of killing Mobile police officer Julius Schulte in 1985.

The U.S. Supreme Court has said death row prisoners must have "rational understanding" that they are about to be executed and why.

Atorneys for Madison say he has an IQ score of 72, suffers from vascular dementia and memory loss as a result of brain damage from several strokes and "does not remember the crime for which he has been convicted and does not have a rational understanding of why the state of Alabama seeks to execute him."

"The execution of Vernon Madison consequently is prohibited by the Eighth Amendment's essential commitment to human dignity," attorney Bryan Stevenson of the Equal Justice Initiative wrote.

Madison's lawyers in court filings described him as a physically and mentally frail man who attended a competency hearing in a wheelchair. They say he is incontinent, legally blind, frequently confused, can no longer recite the alphabet and repeatedly asks for his deceased mother to visit him.

A state court in 2016 ruled that Madison was competent. A neuropsychologist hired by the defense team said that Madison has no independent recollection of the murder. A court-appointed psychologist found that while Madison had suffered a mental and physical decline, he was able to recall details of his case and appeals.

The Alabama attorney general's office cast doubt on the defense description of Madison's mental state in court filings. They argued he claimed as far back as 1990 to have amnesia about the murder and that the court-appointed expert concluded he could recall and understood many details about his life, trial and looming death sentence.

But ultimately, the state argued the Eighth Amendment doesn't prohibit executing someone who lost can't remember their crime.