MAYBE
MAYBE
TRS:
 {
                  app(app(app(if(), true()), x), y) -> x,
                  app(app(app(if(), true()), x), y) -> y,
  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(takeWhile(), 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)
  ),
                    app(app(dropWhile(), p), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                    app(app(app(if(), true()), x), y) -> x,
                    app(app(app(if(), true()), x), y) -> y,
    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(takeWhile(), 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)
    ),
                      app(app(dropWhile(), p), nil()) -> nil()
   }
  Fail