If neither of the two purposes this Court has deemed to be a legitimate purpose for the death penalty —i.e. , retribution and deterrence— would be served by carrying out the execution of a man who has spent thirty years under a sen tence of death , would carrying out that execution viol ate the Eighth Amendment's prohibition again st cruel and unusual punishments or amount to an unnecessary infliction of excessive punishment ?

Is the death penalty as applied in Texas inherently arbitrary and therefore a violat ion of the Eighth Amendment's prohibition against the inflic tion of cruel an d unusual punishment?

Whether carrying out the execution of a man who has spent thirty years under a sentence of death would violate the Eighth Amendment's prohibition against cruel and unusual punishments or amount to an unnecessary infliction of excessive punishment if neither retribution nor deterrence would be served