WORST_CASE(?,O(n^1))
* Step 1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
            g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
            goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
            lt0(x,Nil()) -> False()
            lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
            lt0(Nil(),Cons(x',xs)) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        - Weak TRS:
            f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
            f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
            g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
            g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
        - Signature:
            {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
            ,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
            ,notEmpty,number4} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3}
    + Details:
        Signatures used:
        ----------------
          Cons :: [A(0) x A(4)] -(4)-> A(4)
          Cons :: [A(0) x A(0)] -(0)-> A(0)
          Cons :: [A(0) x A(1)] -(1)-> A(1)
          Cons :: [A(0) x A(3)] -(3)-> A(3)
          Cons :: [A(0) x A(7)] -(7)-> A(7)
          Cons :: [A(0) x A(8)] -(8)-> A(8)
          False :: [] -(0)-> A(10)
          False :: [] -(0)-> A(14)
          Nil :: [] -(0)-> A(4)
          Nil :: [] -(0)-> A(1)
          Nil :: [] -(0)-> A(0)
          Nil :: [] -(0)-> A(3)
          Nil :: [] -(0)-> A(15)
          Nil :: [] -(0)-> A(13)
          Nil :: [] -(0)-> A(12)
          True :: [] -(0)-> A(10)
          True :: [] -(0)-> A(14)
          f :: [A(7) x A(4)] -(3)-> A(0)
          f[Ite][False][Ite] :: [A(10) x A(7) x A(4)] -(0)-> A(0)
          g :: [A(8) x A(4)] -(4)-> A(0)
          g[Ite][False][Ite] :: [A(10) x A(8) x A(4)] -(0)-> A(0)
          goal :: [A(15) x A(15)] -(15)-> A(0)
          lt0 :: [A(0) x A(1)] -(1)-> A(12)
          notEmpty :: [A(3)] -(9)-> A(0)
          number4 :: [A(0)] -(15)-> A(0)
        
        
        Cost-free Signatures used:
        --------------------------
          Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          False :: [] -(0)-> A_cf(0)
          Nil :: [] -(0)-> A_cf(0)
          True :: [] -(0)-> A_cf(0)
          f :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          f[Ite][False][Ite] :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          g :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          g[Ite][False][Ite] :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          lt0 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          Cons_A :: [A(0) x A(1)] -(1)-> A(1)
          False_A :: [] -(0)-> A(1)
          Nil_A :: [] -(0)-> A(1)
          True_A :: [] -(0)-> A(1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
        f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
        g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
        goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
        lt0(x,Nil()) -> False()
        lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
        lt0(Nil(),Cons(x',xs)) -> True()
        notEmpty(Cons(x,xs)) -> True()
        notEmpty(Nil()) -> False()
        number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
    - Weak TRS:
        f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
        f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
        g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
        g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
    - Signature:
        {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
        ,Nil/0,True/0}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
        ,notEmpty,number4} and constructors {Cons,False,Nil,True}
Following problems could not be solved:
  - Strict TRS:
      f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
      f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
      g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs))
      g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
      goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil()))
      lt0(x,Nil()) -> False()
      lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs)
      lt0(Nil(),Cons(x',xs)) -> True()
      notEmpty(Cons(x,xs)) -> True()
      notEmpty(Nil()) -> False()
      number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil()))))
  - Weak TRS:
      f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y))
      f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs)
      g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y))
      g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs)
  - Signature:
      {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0
      ,Nil/0,True/0}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0
      ,notEmpty,number4} and constructors {Cons,False,Nil,True}
WORST_CASE(?,O(n^1))