MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          app(Cons(x,xs),ys) -> Cons(x,app(xs,ys))
          app(Nil(),ys) -> ys
          goal(xs) -> quicksort(xs)
          notEmpty(Cons(x,xs)) -> True()
          notEmpty(Nil()) -> False()
          part(x,xs) -> app(quicksort(partLt(x,xs)),Cons(x,quicksort(partGt(x,xs))))
          partGt(x,Nil()) -> Nil()
          partGt(x',Cons(x,xs)) -> partGt[Ite][True][Ite](>(x,x'),x',Cons(x,xs))
          partLt(x,Nil()) -> Nil()
          partLt(x',Cons(x,xs)) -> partLt[Ite][True][Ite](<(x,x'),x',Cons(x,xs))
          quicksort(Cons(x,Cons(x',xs))) -> part(x,Cons(x',xs))
          quicksort(Cons(x,Nil())) -> Cons(x,Nil())
          quicksort(Nil()) -> Nil()
      - Weak TRS:
          <(x,0()) -> False()
          <(0(),S(y)) -> True()
          <(S(x),S(y)) -> <(x,y)
          >(0(),y) -> False()
          >(S(x),0()) -> True()
          >(S(x),S(y)) -> >(x,y)
          partGt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partGt(x',xs)
          partGt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partGt(x',xs))
          partLt[Ite][True][Ite](False(),x',Cons(x,xs)) -> partLt(x',xs)
          partLt[Ite][True][Ite](True(),x',Cons(x,xs)) -> Cons(x,partLt(x',xs))
      - Signature:
          {</2,>/2,app/2,goal/1,notEmpty/1,part/2,partGt/2,partGt[Ite][True][Ite]/3,partLt/2,partLt[Ite][True][Ite]/3
          ,quicksort/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {<,>,app,goal,notEmpty,part,partGt,partGt[Ite][True][Ite]
          ,partLt,partLt[Ite][True][Ite],quicksort} and constructors {0,Cons,False,Nil,S,True}
  + Applied Processor:
      Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT}
  + Details:
      The input can not be schown compatible.
MAYBE