correct, and incorrect (bolded).
if I had my way, the term "cruel and unusual punishment" would be struck off in cases where the taking of life is involved (including abortion), and the punishment will be one which truly fits the crime, literally.
if the murder was committed slowly, then his life will be taken slowly, as in stoning.
(by a row of computerized slingshots that can throw 15-pound stones ? :laugh

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however, there is nothing in Scripture that says believers are to insist on the death penalty.
what is in scripture is to submit to authority, that is, be law-abiding, and I take that to include not agitating for the death penalty where such is not in a state, or country's, laws.
now, if an elected lawmaker should propose the institution or return whatever the case may be of such a punishment, then, by all means, throw him our support.
and I might include add a provision for a quick and thorough review of the investigative procedures and culling of evidences, and a quick process of appeals not to exceed 6 months, after which, if everything is satisfactory, then put the criminal out of his miserable existence.