MAYBE

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
-----------------------------------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a__U11(tt(), N, XS) -> a__U12(tt(), N, XS)
     , a__U12(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , a__U21(tt(), X) -> a__U22(tt(), X)
     , a__U22(tt(), X) -> mark(X)
     , a__U31(tt(), N) -> a__U32(tt(), N)
     , a__U32(tt(), N) -> mark(N)
     , a__U41(tt(), N, XS) -> a__U42(tt(), N, XS)
     , a__U42(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__U51(tt(), Y) -> a__U52(tt(), Y)
     , a__U52(tt(), Y) -> mark(Y)
     , a__U61(tt(), N, X, XS) -> a__U62(tt(), N, X, XS)
     , a__U62(tt(), N, X, XS) -> a__U63(tt(), N, X, XS)
     , a__U63(tt(), N, X, XS) ->
       a__U64(a__splitAt(mark(N), mark(XS)), X)
     , a__U64(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
     , a__U71(tt(), XS) -> a__U72(tt(), XS)
     , a__U72(tt(), XS) -> mark(XS)
     , a__U81(tt(), N, XS) -> a__U82(tt(), N, XS)
     , a__U82(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__U11(tt(), N, XS)
     , a__fst(pair(X, Y)) -> a__U21(tt(), X)
     , a__head(cons(N, XS)) -> a__U31(tt(), N)
     , a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__sel(N, XS) -> a__U41(tt(), N, XS)
     , a__snd(pair(X, Y)) -> a__U51(tt(), Y)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) -> a__U61(tt(), N, X, XS)
     , a__tail(cons(N, XS)) -> a__U71(tt(), XS)
     , a__take(N, XS) -> a__U81(tt(), N, XS)
     , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
     , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , 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(head(X)) -> a__head(mark(X))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , 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(fst(X)) -> a__fst(mark(X))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(tt()) -> tt()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__U11(X1, X2, X3) -> U11(X1, X2, X3)
     , a__U12(X1, X2, X3) -> U12(X1, X2, X3)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__U21(X1, X2) -> U21(X1, X2)
     , a__U22(X1, X2) -> U22(X1, X2)
     , a__U31(X1, X2) -> U31(X1, X2)
     , a__U32(X1, X2) -> U32(X1, X2)
     , a__U41(X1, X2, X3) -> U41(X1, X2, X3)
     , a__U42(X1, X2, X3) -> U42(X1, X2, X3)
     , a__head(X) -> head(X)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__U51(X1, X2) -> U51(X1, X2)
     , a__U52(X1, X2) -> U52(X1, X2)
     , a__U61(X1, X2, X3, X4) -> U61(X1, X2, X3, X4)
     , a__U62(X1, X2, X3, X4) -> U62(X1, X2, X3, X4)
     , a__U63(X1, X2, X3, X4) -> U63(X1, X2, X3, X4)
     , a__U64(X1, X2) -> U64(X1, X2)
     , a__U71(X1, X2) -> U71(X1, X2)
     , a__U72(X1, X2) -> U72(X1, X2)
     , a__U81(X1, X2, X3) -> U81(X1, X2, X3)
     , a__U82(X1, X2, X3) -> U82(X1, X2, X3)
     , a__fst(X) -> fst(X)
     , a__natsFrom(X) -> natsFrom(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__tail(X) -> tail(X)
     , a__take(X1, X2) -> take(X1, X2)}

Proof Output:    
  The input cannot be shown compatible