MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          a__U11(X1,X2,X3) -> U11(X1,X2,X3)
          a__U11(tt(),N,XS) -> a__U12(tt(),N,XS)
          a__U12(X1,X2,X3) -> U12(X1,X2,X3)
          a__U12(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
          a__U21(X1,X2) -> U21(X1,X2)
          a__U21(tt(),X) -> a__U22(tt(),X)
          a__U22(X1,X2) -> U22(X1,X2)
          a__U22(tt(),X) -> mark(X)
          a__U31(X1,X2) -> U31(X1,X2)
          a__U31(tt(),N) -> a__U32(tt(),N)
          a__U32(X1,X2) -> U32(X1,X2)
          a__U32(tt(),N) -> mark(N)
          a__U41(X1,X2,X3) -> U41(X1,X2,X3)
          a__U41(tt(),N,XS) -> a__U42(tt(),N,XS)
          a__U42(X1,X2,X3) -> U42(X1,X2,X3)
          a__U42(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
          a__U51(X1,X2) -> U51(X1,X2)
          a__U51(tt(),Y) -> a__U52(tt(),Y)
          a__U52(X1,X2) -> U52(X1,X2)
          a__U52(tt(),Y) -> mark(Y)
          a__U61(X1,X2,X3,X4) -> U61(X1,X2,X3,X4)
          a__U61(tt(),N,X,XS) -> a__U62(tt(),N,X,XS)
          a__U62(X1,X2,X3,X4) -> U62(X1,X2,X3,X4)
          a__U62(tt(),N,X,XS) -> a__U63(tt(),N,X,XS)
          a__U63(X1,X2,X3,X4) -> U63(X1,X2,X3,X4)
          a__U63(tt(),N,X,XS) -> a__U64(a__splitAt(mark(N),mark(XS)),X)
          a__U64(X1,X2) -> U64(X1,X2)
          a__U64(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
          a__U71(X1,X2) -> U71(X1,X2)
          a__U71(tt(),XS) -> a__U72(tt(),XS)
          a__U72(X1,X2) -> U72(X1,X2)
          a__U72(tt(),XS) -> mark(XS)
          a__U81(X1,X2,X3) -> U81(X1,X2,X3)
          a__U81(tt(),N,XS) -> a__U82(tt(),N,XS)
          a__U82(X1,X2,X3) -> U82(X1,X2,X3)
          a__U82(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
          a__afterNth(N,XS) -> a__U11(tt(),N,XS)
          a__afterNth(X1,X2) -> afterNth(X1,X2)
          a__fst(X) -> fst(X)
          a__fst(pair(X,Y)) -> a__U21(tt(),X)
          a__head(X) -> head(X)
          a__head(cons(N,XS)) -> a__U31(tt(),N)
          a__natsFrom(N) -> cons(mark(N),natsFrom(s(N)))
          a__natsFrom(X) -> natsFrom(X)
          a__sel(N,XS) -> a__U41(tt(),N,XS)
          a__sel(X1,X2) -> sel(X1,X2)
          a__snd(X) -> snd(X)
          a__snd(pair(X,Y)) -> a__U51(tt(),Y)
          a__splitAt(X1,X2) -> splitAt(X1,X2)
          a__splitAt(0(),XS) -> pair(nil(),mark(XS))
          a__splitAt(s(N),cons(X,XS)) -> a__U61(tt(),N,X,XS)
          a__tail(X) -> tail(X)
          a__tail(cons(N,XS)) -> a__U71(tt(),XS)
          a__take(N,XS) -> a__U81(tt(),N,XS)
          a__take(X1,X2) -> take(X1,X2)
          mark(0()) -> 0()
          mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
          mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
          mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
          mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
          mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
          mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
          mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
          mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
          mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
          mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
          mark(U61(X1,X2,X3,X4)) -> a__U61(mark(X1),X2,X3,X4)
          mark(U62(X1,X2,X3,X4)) -> a__U62(mark(X1),X2,X3,X4)
          mark(U63(X1,X2,X3,X4)) -> a__U63(mark(X1),X2,X3,X4)
          mark(U64(X1,X2)) -> a__U64(mark(X1),X2)
          mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
          mark(U72(X1,X2)) -> a__U72(mark(X1),X2)
          mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
          mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
          mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
          mark(cons(X1,X2)) -> cons(mark(X1),X2)
          mark(fst(X)) -> a__fst(mark(X))
          mark(head(X)) -> a__head(mark(X))
          mark(natsFrom(X)) -> a__natsFrom(mark(X))
          mark(nil()) -> nil()
          mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
          mark(s(X)) -> s(mark(X))
          mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
          mark(snd(X)) -> a__snd(mark(X))
          mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
          mark(tail(X)) -> a__tail(mark(X))
          mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
          mark(tt()) -> tt()
      - Signature:
          {a__U11/3,a__U12/3,a__U21/2,a__U22/2,a__U31/2,a__U32/2,a__U41/3,a__U42/3,a__U51/2,a__U52/2,a__U61/4,a__U62/4
          ,a__U63/4,a__U64/2,a__U71/2,a__U72/2,a__U81/3,a__U82/3,a__afterNth/2,a__fst/1,a__head/1,a__natsFrom/1
          ,a__sel/2,a__snd/1,a__splitAt/2,a__tail/1,a__take/2,mark/1} / {0/0,U11/3,U12/3,U21/2,U22/2,U31/2,U32/2,U41/3
          ,U42/3,U51/2,U52/2,U61/4,U62/4,U63/4,U64/2,U71/2,U72/2,U81/3,U82/3,afterNth/2,cons/2,fst/1,head/1,natsFrom/1
          ,nil/0,pair/2,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,tt/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U22,a__U31,a__U32,a__U41,a__U42
          ,a__U51,a__U52,a__U61,a__U62,a__U63,a__U64,a__U71,a__U72,a__U81,a__U82,a__afterNth,a__fst,a__head
          ,a__natsFrom,a__sel,a__snd,a__splitAt,a__tail,a__take,mark} and constructors {0,U11,U12,U21,U22,U31,U32,U41
          ,U42,U51,U52,U61,U62,U63,U64,U71,U72,U81,U82,afterNth,cons,fst,head,natsFrom,nil,pair,s,sel,snd,splitAt,tail
          ,take,tt}
  + Applied Processor:
      MI {miKind = Automaton Nothing, miDimension = 3, miUArgs = NoUArgs, miURules = NoURules, miSelector = Nothing}
  + Details:
      Incompatible
MAYBE