/home/nowonder/forschung/aprove/TPDB05/TRS/higher-order/AProVE_HO/TakeDropWhile.trs

The program

(VAR x y p xs)
(RULES
  app(app(app(if, true), x), y) -> x
  app(app(app(if, true), x), y) -> y
  app(app(takeWhile, p), nil) -> nil
  app(app(takeWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil)
  app(app(dropWhile, p), nil) -> nil
  app(app(dropWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs))
)

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