How can killing four people, among them an innocent eight-year-old child, or maiming hundreds of fellow Americans be considered "the pursuit of justice"? It cannot; not by any stretch of the imagination.
If indeed Tamerlan's increased religious devotion led him to become a terrorist, then it could not be a truly sincere religiosity. It cannot be true piety. The Quran itself says so:
True piety does not consist in turning your faces towards the east or the west—but truly pious is he who believes in God, and the Last Day; and the angels, and revelation, and the prophets; and spends his substance—however much he himself may cherish it—upon his near of kin, and the orphans, and the needy, and the wayfarer, and the beggars, and for the freeing of human beings from bondage; and is constant in prayer, and renders the purifying dues; and [truly pious are] they who keep their promises whenever they promise, and are patient in misfortune and hardship and in time of peril: it is they that have proved themselves true, and it is they, they who are conscious of God." (2:177)
Nowhere in this formula can the murder of innocent human beings be inserted. It simply cannot be the case.
This type of phenomenon—one being both a "devoted Muslim" and a terrorist barbarian—is not new. It is a very similar type of religiosity of the Kharijites, who were religious rebels that emerged during the civil war between Ali and Mu'awiyah. The Kharijites had a very devoted religious practice, but they were barbaric murderers. In fact, they assassinated the Caliph Ali himself.
In fact, I have called these modern-day terrorists committing murder in Islam's name "neo-Kharijites." It is a much better term than "Islamic terrorists," "jihadists," or even "Islamo-fascists." No matter what you call them, the point remains: No sincere religiosity, no true piety, can include the murder of innocent people. A Godly human being, if he or she is truly sincere, does not kill an innocent fellow human being. Anything to the contrary is satanic trickery.