Will a body executing pure rolling on a rough surface stop, neglecting air drag and other heat losses but not friction? If yes, due to which friction it will stop, static or kinetic and how?
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When a perfect/ideal cylinder (or a sphere, disc, ring, etc) pure rolls, the velocity of the lowermost point is zero (condition for pure rolling). As the relative velocity between the surfaces at the point of contact is zero, there is no "kinetic" friction (if there is no external force, there will be zero static friction).
Therefore, the cylinder will continue to roll forever in your case.
DarkSideofPhy
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