(VAR N X X1 X2 X3 X4 XS Y YS ZS )
(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)
        
)