;; permutates the collection into all possible slices
(defn permutate [coll]
  (let [n (+ (count coll) 1)]
    (for [start (range n) stop (reverse (range n))
     :while (< (+ start 1) stop)]
      (subvec coll start stop))))

;; check if each element in the collection is larger than the previous
(defn increasing? [coll]
  (loop [acc (rest coll) last (first coll)]
    (if-not (empty? acc)
      (if (> (first acc) last)
        (recur (rest acc) (first acc))
        false)
      true)))

;; elegant solution, but breaks the requirement that you must keep the
;; first sequence of the largest length. returns nil for no candidates
(defn alternative_solution [coll]
  (let [perms (permutate coll)
        scores (for [perm perms :when (increasing? perm)] perm)]
    (last (sort scores)))) ; clojure sorts by sequence length