WORST_CASE(?,O(n^1))
* Step 1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__natsFrom(X)) -> natsFrom(X)
            afterNth(N,XS) -> snd(splitAt(N,XS))
            fst(pair(XS,YS)) -> XS
            head(cons(N,XS)) -> N
            natsFrom(N) -> cons(N,n__natsFrom(s(N)))
            natsFrom(X) -> n__natsFrom(X)
            sel(N,XS) -> head(afterNth(N,XS))
            snd(pair(XS,YS)) -> YS
            splitAt(0(),XS) -> pair(nil(),XS)
            splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
            tail(cons(N,XS)) -> activate(XS)
            take(N,XS) -> fst(splitAt(N,XS))
            u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
        - Signature:
            {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
            ,n__natsFrom/1,nil/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail
            ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(14)
          activate :: [A(0)] -(2)-> A(0)
          afterNth :: [A(14) x A(10)] -(12)-> A(0)
          cons :: [A(0) x A(0)] -(0)-> A(0)
          cons :: [A(0) x A(11)] -(11)-> A(11)
          fst :: [A(0)] -(2)-> A(0)
          head :: [A(0)] -(2)-> A(0)
          n__natsFrom :: [A(0)] -(0)-> A(0)
          n__natsFrom :: [A(0)] -(0)-> A(1)
          n__natsFrom :: [A(0)] -(0)-> A(2)
          natsFrom :: [A(0)] -(1)-> A(0)
          nil :: [] -(0)-> A(14)
          pair :: [A(0) x A(0)] -(0)-> A(0)
          pair :: [A(0) x A(0)] -(0)-> A(1)
          pair :: [A(0) x A(0)] -(0)-> A(9)
          s :: [A(14)] -(14)-> A(14)
          s :: [A(0)] -(0)-> A(0)
          sel :: [A(14) x A(14)] -(15)-> A(0)
          snd :: [A(0)] -(2)-> A(0)
          splitAt :: [A(14) x A(0)] -(5)-> A(1)
          tail :: [A(11)] -(10)-> A(0)
          take :: [A(14) x A(2)] -(15)-> A(0)
          u :: [A(0) x A(0) x A(0) x A(0)] -(3)-> A(8)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0)
          activate :: [A_cf(0)] -(0)-> A_cf(0)
          cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          n__natsFrom :: [A_cf(0)] -(0)-> A_cf(0)
          natsFrom :: [A_cf(0)] -(0)-> A_cf(0)
          nil :: [] -(0)-> A_cf(0)
          pair :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          s :: [A_cf(0)] -(0)-> A_cf(0)
          splitAt :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          u :: [A_cf(0) x A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1)
          cons_A :: [A(0) x A(1)] -(1)-> A(1)
          n__natsFrom_A :: [A(0)] -(0)-> A(1)
          nil_A :: [] -(0)-> A(1)
          pair_A :: [A(0) x A(0)] -(0)-> A(1)
          s_A :: [A(1)] -(1)-> A(1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        activate(X) -> X
        activate(n__natsFrom(X)) -> natsFrom(X)
        afterNth(N,XS) -> snd(splitAt(N,XS))
        fst(pair(XS,YS)) -> XS
        head(cons(N,XS)) -> N
        natsFrom(N) -> cons(N,n__natsFrom(s(N)))
        natsFrom(X) -> n__natsFrom(X)
        sel(N,XS) -> head(afterNth(N,XS))
        snd(pair(XS,YS)) -> YS
        splitAt(0(),XS) -> pair(nil(),XS)
        splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
        tail(cons(N,XS)) -> activate(XS)
        take(N,XS) -> fst(splitAt(N,XS))
        u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
    - Signature:
        {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
        ,n__natsFrom/1,nil/0,pair/2,s/1}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail
        ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
Following problems could not be solved:
  - Strict TRS:
      activate(X) -> X
      activate(n__natsFrom(X)) -> natsFrom(X)
      afterNth(N,XS) -> snd(splitAt(N,XS))
      fst(pair(XS,YS)) -> XS
      head(cons(N,XS)) -> N
      natsFrom(N) -> cons(N,n__natsFrom(s(N)))
      natsFrom(X) -> n__natsFrom(X)
      sel(N,XS) -> head(afterNth(N,XS))
      snd(pair(XS,YS)) -> YS
      splitAt(0(),XS) -> pair(nil(),XS)
      splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
      tail(cons(N,XS)) -> activate(XS)
      take(N,XS) -> fst(splitAt(N,XS))
      u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
  - Signature:
      {activate/1,afterNth/2,fst/1,head/1,natsFrom/1,sel/2,snd/1,splitAt/2,tail/1,take/2,u/4} / {0/0,cons/2
      ,n__natsFrom/1,nil/0,pair/2,s/1}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {activate,afterNth,fst,head,natsFrom,sel,snd,splitAt,tail
      ,take,u} and constructors {0,cons,n__natsFrom,nil,pair,s}
WORST_CASE(?,O(n^1))