For finite even lists, these definitions take at most linear time:
halve :: [a] -> ([a],[a])
halve xs = splitAt (length xs `div` 2) xs

pairs :: [a] -> [(a,a)]
pairs [] = []
pairs (x:y:xs) = (x,y) : pairs xs
pairs [_] = error "pairs: odd length"
The length calculation and the prefix split each take time. The second operation consumes two constructors per step and emits one pair. Under the stated even-length precondition, neither definition encounters an unmatched final element.

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