The Supreme Court is kicking off its new term with arguments in two grisly murder cases that will test constitutional provisions concerning the rights of those accused of criminal offenses.

The cases, which the justices will hear over the course of two hours on Monday, concern whether the state can abolish the so-called "insanity defense" and the right of defendants to a unanimous jury in state trials.

They were brought by two men convicted of murder in Kansas and Louisiana.

The justices will hear first from attorneys for James Kraig Kahler, who was convicted of murdering his wife, two children, and his wife's grandmother in a fit of rage over Thanksgiving weekend in 2009. After his wife left him and pursued a relationship with a female co-worker, Kahler grew obsessed, turned to stalking, and was fired from his job.

While in a state that one doctor described as "stress induced short-term dissociation," he shot and killed his family members while chasing them room to room through their home in a spree that was partially recorded on the grandmother's Life Alert system.

Kahler's attorneys have argued that an idiosyncrasy of Kansas law prevented their client from receiving fair trial before he was convicted in 2011 and sentenced to death. In Kansas and four other states, defendants are barred from invoking the so-called "insanity defense," or claiming that a mental illness prevented them from understanding that their actions were wrong.

"Although he knew that he was shooting human beings, his mental state was so disturbed at the time that he was unable to control his actions," attorney Jeffrey Green wrote in a brief with the court.

Green wrote that Kansas's abolition of the insanity defense violates the Eighth and Fourteenth Amendments, which bar cruel and unusual punishment and guarantee due process. It "defies a fundamental, centuries-old precept of our legal system: People cannot be punished for crimes for which they are not morally culpable," he wrote.

The case has spawned an unusual flurry of philosophical and medical debate, prompting briefs from professors of philosophy and the American Psychiatric Association, both in Kahler's favor. The American Civil Liberties Union also submitted a brief arguing that the abolition of the insanity defense is unconstitutional. On the other side, the Trump administration has weighed in in favor of Kansas.

"This Court has long recognized that States have broad discretion to make the moral, legal, and medical judgments necessary to determine when mental illness should excuse criminal conduct," Solicitor General Noel Francisco wrote in a brief with the top court.

The Kansas Supreme Court ruled against Kahler in May of 2018, finding that eliminating the insanity defense does not violate either the state or federal constitution.