MAYBE

Problem:
 active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
 active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
 active(U103(tt())) -> mark(tt())
 active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
 active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
 active(U112(tt())) -> mark(tt())
 active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
 active(U122(tt())) -> mark(tt())
 active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
 active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
 active(U133(tt())) -> mark(tt())
 active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
 active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
 active(U143(tt())) -> mark(tt())
 active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
 active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
 active(U153(tt())) -> mark(tt())
 active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
 active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
 active(U181(tt(),Y)) -> mark(Y)
 active(U191(tt(),XS)) -> mark(pair(nil(),XS))
 active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
 active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
 active(U21(tt(),X)) -> mark(X)
 active(U211(tt(),XS)) -> mark(XS)
 active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
 active(U31(tt(),N)) -> mark(N)
 active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
 active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
 active(U43(tt())) -> mark(tt())
 active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
 active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
 active(U53(tt())) -> mark(tt())
 active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
 active(U62(tt())) -> mark(tt())
 active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
 active(U72(tt())) -> mark(tt())
 active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
 active(U82(tt())) -> mark(tt())
 active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
 active(U92(tt())) -> mark(tt())
 active(afterNth(N,XS)) ->
 mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
 active(and(tt(),X)) -> mark(X)
 active(fst(pair(X,Y))) ->
 mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
 active(head(cons(N,XS))) ->
 mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
 active(isLNat(nil())) -> mark(tt())
 active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
 active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
 active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
 active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
 active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
 active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
 active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
 active(isLNatKind(nil())) -> mark(tt())
 active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
 active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
 active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
 active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
 active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
 active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
 active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
 active(isNatural(0())) -> mark(tt())
 active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
 active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
 active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
 active(isNaturalKind(0())) -> mark(tt())
 active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
 active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
 active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
 active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
 active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
 active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
 active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
 active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
 active(sel(N,XS)) ->
 mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
 active(snd(pair(X,Y))) ->
 mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
 active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
 active(splitAt(s(N),cons(X,XS))) ->
 mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                      and(isLNat(XS),isLNatKind(XS)))),
           N,X,XS))
 active(tail(cons(N,XS))) ->
 mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
 active(take(N,XS)) ->
 mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
 mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
 mark(tt()) -> active(tt())
 mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
 mark(isNatural(X)) -> active(isNatural(X))
 mark(U103(X)) -> active(U103(mark(X)))
 mark(isLNat(X)) -> active(isLNat(X))
 mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
 mark(snd(X)) -> active(snd(mark(X)))
 mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
 mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
 mark(U112(X)) -> active(U112(mark(X)))
 mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
 mark(U122(X)) -> active(U122(mark(X)))
 mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
 mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
 mark(U133(X)) -> active(U133(mark(X)))
 mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
 mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
 mark(U143(X)) -> active(U143(mark(X)))
 mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
 mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
 mark(U153(X)) -> active(U153(mark(X)))
 mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(natsFrom(X)) -> active(natsFrom(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
 mark(head(X)) -> active(head(mark(X)))
 mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
 mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
 mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
 mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
 mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
 mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
 mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
 mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
 mark(fst(X)) -> active(fst(mark(X)))
 mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
 mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
 mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
 mark(U43(X)) -> active(U43(mark(X)))
 mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
 mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
 mark(U53(X)) -> active(U53(mark(X)))
 mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
 mark(U62(X)) -> active(U62(mark(X)))
 mark(isPLNat(X)) -> active(isPLNat(X))
 mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
 mark(U72(X)) -> active(U72(mark(X)))
 mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
 mark(U82(X)) -> active(U82(mark(X)))
 mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
 mark(U92(X)) -> active(U92(mark(X)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNaturalKind(X)) -> active(isNaturalKind(X))
 mark(isLNatKind(X)) -> active(isLNatKind(X))
 mark(isPLNatKind(X)) -> active(isPLNatKind(X))
 mark(tail(X)) -> active(tail(mark(X)))
 mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
 mark(0()) -> active(0())
 mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
 U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
 U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
 U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
 U101(active(X1),X2,X3) -> U101(X1,X2,X3)
 U101(X1,active(X2),X3) -> U101(X1,X2,X3)
 U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
 U102(mark(X1),X2) -> U102(X1,X2)
 U102(X1,mark(X2)) -> U102(X1,X2)
 U102(active(X1),X2) -> U102(X1,X2)
 U102(X1,active(X2)) -> U102(X1,X2)
 isNatural(mark(X)) -> isNatural(X)
 isNatural(active(X)) -> isNatural(X)
 U103(mark(X)) -> U103(X)
 U103(active(X)) -> U103(X)
 isLNat(mark(X)) -> isLNat(X)
 isLNat(active(X)) -> isLNat(X)
 U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
 U11(active(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,active(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
 snd(mark(X)) -> snd(X)
 snd(active(X)) -> snd(X)
 splitAt(mark(X1),X2) -> splitAt(X1,X2)
 splitAt(X1,mark(X2)) -> splitAt(X1,X2)
 splitAt(active(X1),X2) -> splitAt(X1,X2)
 splitAt(X1,active(X2)) -> splitAt(X1,X2)
 U111(mark(X1),X2) -> U111(X1,X2)
 U111(X1,mark(X2)) -> U111(X1,X2)
 U111(active(X1),X2) -> U111(X1,X2)
 U111(X1,active(X2)) -> U111(X1,X2)
 U112(mark(X)) -> U112(X)
 U112(active(X)) -> U112(X)
 U121(mark(X1),X2) -> U121(X1,X2)
 U121(X1,mark(X2)) -> U121(X1,X2)
 U121(active(X1),X2) -> U121(X1,X2)
 U121(X1,active(X2)) -> U121(X1,X2)
 U122(mark(X)) -> U122(X)
 U122(active(X)) -> U122(X)
 U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
 U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
 U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
 U131(active(X1),X2,X3) -> U131(X1,X2,X3)
 U131(X1,active(X2),X3) -> U131(X1,X2,X3)
 U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
 U132(mark(X1),X2) -> U132(X1,X2)
 U132(X1,mark(X2)) -> U132(X1,X2)
 U132(active(X1),X2) -> U132(X1,X2)
 U132(X1,active(X2)) -> U132(X1,X2)
 U133(mark(X)) -> U133(X)
 U133(active(X)) -> U133(X)
 U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
 U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
 U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
 U141(active(X1),X2,X3) -> U141(X1,X2,X3)
 U141(X1,active(X2),X3) -> U141(X1,X2,X3)
 U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
 U142(mark(X1),X2) -> U142(X1,X2)
 U142(X1,mark(X2)) -> U142(X1,X2)
 U142(active(X1),X2) -> U142(X1,X2)
 U142(X1,active(X2)) -> U142(X1,X2)
 U143(mark(X)) -> U143(X)
 U143(active(X)) -> U143(X)
 U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
 U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
 U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
 U151(active(X1),X2,X3) -> U151(X1,X2,X3)
 U151(X1,active(X2),X3) -> U151(X1,X2,X3)
 U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
 U152(mark(X1),X2) -> U152(X1,X2)
 U152(X1,mark(X2)) -> U152(X1,X2)
 U152(active(X1),X2) -> U152(X1,X2)
 U152(X1,active(X2)) -> U152(X1,X2)
 U153(mark(X)) -> U153(X)
 U153(active(X)) -> U153(X)
 U161(mark(X1),X2) -> U161(X1,X2)
 U161(X1,mark(X2)) -> U161(X1,X2)
 U161(active(X1),X2) -> U161(X1,X2)
 U161(X1,active(X2)) -> U161(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 natsFrom(mark(X)) -> natsFrom(X)
 natsFrom(active(X)) -> natsFrom(X)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
 U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
 U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
 U171(active(X1),X2,X3) -> U171(X1,X2,X3)
 U171(X1,active(X2),X3) -> U171(X1,X2,X3)
 U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
 head(mark(X)) -> head(X)
 head(active(X)) -> head(X)
 afterNth(mark(X1),X2) -> afterNth(X1,X2)
 afterNth(X1,mark(X2)) -> afterNth(X1,X2)
 afterNth(active(X1),X2) -> afterNth(X1,X2)
 afterNth(X1,active(X2)) -> afterNth(X1,X2)
 U181(mark(X1),X2) -> U181(X1,X2)
 U181(X1,mark(X2)) -> U181(X1,X2)
 U181(active(X1),X2) -> U181(X1,X2)
 U181(X1,active(X2)) -> U181(X1,X2)
 U191(mark(X1),X2) -> U191(X1,X2)
 U191(X1,mark(X2)) -> U191(X1,X2)
 U191(active(X1),X2) -> U191(X1,X2)
 U191(X1,active(X2)) -> U191(X1,X2)
 pair(mark(X1),X2) -> pair(X1,X2)
 pair(X1,mark(X2)) -> pair(X1,X2)
 pair(active(X1),X2) -> pair(X1,X2)
 pair(X1,active(X2)) -> pair(X1,X2)
 U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
 U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
 U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
 U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
 U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
 U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
 U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
 U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
 U202(mark(X1),X2) -> U202(X1,X2)
 U202(X1,mark(X2)) -> U202(X1,X2)
 U202(active(X1),X2) -> U202(X1,X2)
 U202(X1,active(X2)) -> U202(X1,X2)
 U21(mark(X1),X2) -> U21(X1,X2)
 U21(X1,mark(X2)) -> U21(X1,X2)
 U21(active(X1),X2) -> U21(X1,X2)
 U21(X1,active(X2)) -> U21(X1,X2)
 U211(mark(X1),X2) -> U211(X1,X2)
 U211(X1,mark(X2)) -> U211(X1,X2)
 U211(active(X1),X2) -> U211(X1,X2)
 U211(X1,active(X2)) -> U211(X1,X2)
 U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
 U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
 U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
 U221(active(X1),X2,X3) -> U221(X1,X2,X3)
 U221(X1,active(X2),X3) -> U221(X1,X2,X3)
 U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
 fst(mark(X)) -> fst(X)
 fst(active(X)) -> fst(X)
 U31(mark(X1),X2) -> U31(X1,X2)
 U31(X1,mark(X2)) -> U31(X1,X2)
 U31(active(X1),X2) -> U31(X1,X2)
 U31(X1,active(X2)) -> U31(X1,X2)
 U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
 U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
 U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
 U41(active(X1),X2,X3) -> U41(X1,X2,X3)
 U41(X1,active(X2),X3) -> U41(X1,X2,X3)
 U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
 U42(mark(X1),X2) -> U42(X1,X2)
 U42(X1,mark(X2)) -> U42(X1,X2)
 U42(active(X1),X2) -> U42(X1,X2)
 U42(X1,active(X2)) -> U42(X1,X2)
 U43(mark(X)) -> U43(X)
 U43(active(X)) -> U43(X)
 U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
 U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
 U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
 U51(active(X1),X2,X3) -> U51(X1,X2,X3)
 U51(X1,active(X2),X3) -> U51(X1,X2,X3)
 U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
 U52(mark(X1),X2) -> U52(X1,X2)
 U52(X1,mark(X2)) -> U52(X1,X2)
 U52(active(X1),X2) -> U52(X1,X2)
 U52(X1,active(X2)) -> U52(X1,X2)
 U53(mark(X)) -> U53(X)
 U53(active(X)) -> U53(X)
 U61(mark(X1),X2) -> U61(X1,X2)
 U61(X1,mark(X2)) -> U61(X1,X2)
 U61(active(X1),X2) -> U61(X1,X2)
 U61(X1,active(X2)) -> U61(X1,X2)
 U62(mark(X)) -> U62(X)
 U62(active(X)) -> U62(X)
 isPLNat(mark(X)) -> isPLNat(X)
 isPLNat(active(X)) -> isPLNat(X)
 U71(mark(X1),X2) -> U71(X1,X2)
 U71(X1,mark(X2)) -> U71(X1,X2)
 U71(active(X1),X2) -> U71(X1,X2)
 U71(X1,active(X2)) -> U71(X1,X2)
 U72(mark(X)) -> U72(X)
 U72(active(X)) -> U72(X)
 U81(mark(X1),X2) -> U81(X1,X2)
 U81(X1,mark(X2)) -> U81(X1,X2)
 U81(active(X1),X2) -> U81(X1,X2)
 U81(X1,active(X2)) -> U81(X1,X2)
 U82(mark(X)) -> U82(X)
 U82(active(X)) -> U82(X)
 U91(mark(X1),X2) -> U91(X1,X2)
 U91(X1,mark(X2)) -> U91(X1,X2)
 U91(active(X1),X2) -> U91(X1,X2)
 U91(X1,active(X2)) -> U91(X1,X2)
 U92(mark(X)) -> U92(X)
 U92(active(X)) -> U92(X)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isNaturalKind(mark(X)) -> isNaturalKind(X)
 isNaturalKind(active(X)) -> isNaturalKind(X)
 isLNatKind(mark(X)) -> isLNatKind(X)
 isLNatKind(active(X)) -> isLNatKind(X)
 isPLNatKind(mark(X)) -> isPLNatKind(X)
 isPLNatKind(active(X)) -> isPLNatKind(X)
 tail(mark(X)) -> tail(X)
 tail(active(X)) -> tail(X)
 take(mark(X1),X2) -> take(X1,X2)
 take(X1,mark(X2)) -> take(X1,X2)
 take(active(X1),X2) -> take(X1,X2)
 take(X1,active(X2)) -> take(X1,X2)
 sel(mark(X1),X2) -> sel(X1,X2)
 sel(X1,mark(X2)) -> sel(X1,X2)
 sel(active(X1),X2) -> sel(X1,X2)
 sel(X1,active(X2)) -> sel(X1,X2)

Proof:
 DP Processor:
  DPs:
   active#(U101(tt(),V1,V2)) -> isNatural#(V1)
   active#(U101(tt(),V1,V2)) -> U102#(isNatural(V1),V2)
   active#(U101(tt(),V1,V2)) -> mark#(U102(isNatural(V1),V2))
   active#(U102(tt(),V2)) -> isLNat#(V2)
   active#(U102(tt(),V2)) -> U103#(isLNat(V2))
   active#(U102(tt(),V2)) -> mark#(U103(isLNat(V2)))
   active#(U103(tt())) -> mark#(tt())
   active#(U11(tt(),N,XS)) -> splitAt#(N,XS)
   active#(U11(tt(),N,XS)) -> snd#(splitAt(N,XS))
   active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
   active#(U111(tt(),V1)) -> isLNat#(V1)
   active#(U111(tt(),V1)) -> U112#(isLNat(V1))
   active#(U111(tt(),V1)) -> mark#(U112(isLNat(V1)))
   active#(U112(tt())) -> mark#(tt())
   active#(U121(tt(),V1)) -> isNatural#(V1)
   active#(U121(tt(),V1)) -> U122#(isNatural(V1))
   active#(U121(tt(),V1)) -> mark#(U122(isNatural(V1)))
   active#(U122(tt())) -> mark#(tt())
   active#(U131(tt(),V1,V2)) -> isNatural#(V1)
   active#(U131(tt(),V1,V2)) -> U132#(isNatural(V1),V2)
   active#(U131(tt(),V1,V2)) -> mark#(U132(isNatural(V1),V2))
   active#(U132(tt(),V2)) -> isLNat#(V2)
   active#(U132(tt(),V2)) -> U133#(isLNat(V2))
   active#(U132(tt(),V2)) -> mark#(U133(isLNat(V2)))
   active#(U133(tt())) -> mark#(tt())
   active#(U141(tt(),V1,V2)) -> isLNat#(V1)
   active#(U141(tt(),V1,V2)) -> U142#(isLNat(V1),V2)
   active#(U141(tt(),V1,V2)) -> mark#(U142(isLNat(V1),V2))
   active#(U142(tt(),V2)) -> isLNat#(V2)
   active#(U142(tt(),V2)) -> U143#(isLNat(V2))
   active#(U142(tt(),V2)) -> mark#(U143(isLNat(V2)))
   active#(U143(tt())) -> mark#(tt())
   active#(U151(tt(),V1,V2)) -> isNatural#(V1)
   active#(U151(tt(),V1,V2)) -> U152#(isNatural(V1),V2)
   active#(U151(tt(),V1,V2)) -> mark#(U152(isNatural(V1),V2))
   active#(U152(tt(),V2)) -> isLNat#(V2)
   active#(U152(tt(),V2)) -> U153#(isLNat(V2))
   active#(U152(tt(),V2)) -> mark#(U153(isLNat(V2)))
   active#(U153(tt())) -> mark#(tt())
   active#(U161(tt(),N)) -> s#(N)
   active#(U161(tt(),N)) -> natsFrom#(s(N))
   active#(U161(tt(),N)) -> cons#(N,natsFrom(s(N)))
   active#(U161(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
   active#(U171(tt(),N,XS)) -> afterNth#(N,XS)
   active#(U171(tt(),N,XS)) -> head#(afterNth(N,XS))
   active#(U171(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
   active#(U181(tt(),Y)) -> mark#(Y)
   active#(U191(tt(),XS)) -> pair#(nil(),XS)
   active#(U191(tt(),XS)) -> mark#(pair(nil(),XS))
   active#(U201(tt(),N,X,XS)) -> splitAt#(N,XS)
   active#(U201(tt(),N,X,XS)) -> U202#(splitAt(N,XS),X)
   active#(U201(tt(),N,X,XS)) -> mark#(U202(splitAt(N,XS),X))
   active#(U202(pair(YS,ZS),X)) -> cons#(X,YS)
   active#(U202(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
   active#(U202(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
   active#(U21(tt(),X)) -> mark#(X)
   active#(U211(tt(),XS)) -> mark#(XS)
   active#(U221(tt(),N,XS)) -> splitAt#(N,XS)
   active#(U221(tt(),N,XS)) -> fst#(splitAt(N,XS))
   active#(U221(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
   active#(U31(tt(),N)) -> mark#(N)
   active#(U41(tt(),V1,V2)) -> isNatural#(V1)
   active#(U41(tt(),V1,V2)) -> U42#(isNatural(V1),V2)
   active#(U41(tt(),V1,V2)) -> mark#(U42(isNatural(V1),V2))
   active#(U42(tt(),V2)) -> isLNat#(V2)
   active#(U42(tt(),V2)) -> U43#(isLNat(V2))
   active#(U42(tt(),V2)) -> mark#(U43(isLNat(V2)))
   active#(U43(tt())) -> mark#(tt())
   active#(U51(tt(),V1,V2)) -> isNatural#(V1)
   active#(U51(tt(),V1,V2)) -> U52#(isNatural(V1),V2)
   active#(U51(tt(),V1,V2)) -> mark#(U52(isNatural(V1),V2))
   active#(U52(tt(),V2)) -> isLNat#(V2)
   active#(U52(tt(),V2)) -> U53#(isLNat(V2))
   active#(U52(tt(),V2)) -> mark#(U53(isLNat(V2)))
   active#(U53(tt())) -> mark#(tt())
   active#(U61(tt(),V1)) -> isPLNat#(V1)
   active#(U61(tt(),V1)) -> U62#(isPLNat(V1))
   active#(U61(tt(),V1)) -> mark#(U62(isPLNat(V1)))
   active#(U62(tt())) -> mark#(tt())
   active#(U71(tt(),V1)) -> isNatural#(V1)
   active#(U71(tt(),V1)) -> U72#(isNatural(V1))
   active#(U71(tt(),V1)) -> mark#(U72(isNatural(V1)))
   active#(U72(tt())) -> mark#(tt())
   active#(U81(tt(),V1)) -> isPLNat#(V1)
   active#(U81(tt(),V1)) -> U82#(isPLNat(V1))
   active#(U81(tt(),V1)) -> mark#(U82(isPLNat(V1)))
   active#(U82(tt())) -> mark#(tt())
   active#(U91(tt(),V1)) -> isLNat#(V1)
   active#(U91(tt(),V1)) -> U92#(isLNat(V1))
   active#(U91(tt(),V1)) -> mark#(U92(isLNat(V1)))
   active#(U92(tt())) -> mark#(tt())
   active#(afterNth(N,XS)) -> isLNatKind#(XS)
   active#(afterNth(N,XS)) -> isLNat#(XS)
   active#(afterNth(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
   active#(afterNth(N,XS)) -> isNaturalKind#(N)
   active#(afterNth(N,XS)) -> isNatural#(N)
   active#(afterNth(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
   active#(afterNth(N,XS)) ->
   and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   active#(afterNth(N,XS)) ->
   U11#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   active#(afterNth(N,XS)) ->
   mark#(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   active#(and(tt(),X)) -> mark#(X)
   active#(fst(pair(X,Y))) -> isLNatKind#(Y)
   active#(fst(pair(X,Y))) -> isLNat#(Y)
   active#(fst(pair(X,Y))) -> and#(isLNat(Y),isLNatKind(Y))
   active#(fst(pair(X,Y))) -> isLNatKind#(X)
   active#(fst(pair(X,Y))) -> isLNat#(X)
   active#(fst(pair(X,Y))) -> and#(isLNat(X),isLNatKind(X))
   active#(fst(pair(X,Y))) -> and#(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
   active#(fst(pair(X,Y))) ->
   U21#(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
   active#(fst(pair(X,Y))) ->
   mark#(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
   active#(head(cons(N,XS))) -> isLNatKind#(XS)
   active#(head(cons(N,XS))) -> isLNat#(XS)
   active#(head(cons(N,XS))) -> and#(isLNat(XS),isLNatKind(XS))
   active#(head(cons(N,XS))) -> isNaturalKind#(N)
   active#(head(cons(N,XS))) -> isNatural#(N)
   active#(head(cons(N,XS))) -> and#(isNatural(N),isNaturalKind(N))
   active#(head(cons(N,XS))) ->
   and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   active#(head(cons(N,XS))) ->
   U31#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
   active#(head(cons(N,XS))) ->
   mark#(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
   active#(isLNat(nil())) -> mark#(tt())
   active#(isLNat(afterNth(V1,V2))) -> isLNatKind#(V2)
   active#(isLNat(afterNth(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNat(afterNth(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNat(afterNth(V1,V2))) -> U41#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   active#(isLNat(afterNth(V1,V2))) -> mark#(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active#(isLNat(cons(V1,V2))) -> isLNatKind#(V2)
   active#(isLNat(cons(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNat(cons(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNat(cons(V1,V2))) -> U51#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   active#(isLNat(cons(V1,V2))) -> mark#(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active#(isLNat(fst(V1))) -> isPLNatKind#(V1)
   active#(isLNat(fst(V1))) -> U61#(isPLNatKind(V1),V1)
   active#(isLNat(fst(V1))) -> mark#(U61(isPLNatKind(V1),V1))
   active#(isLNat(natsFrom(V1))) -> isNaturalKind#(V1)
   active#(isLNat(natsFrom(V1))) -> U71#(isNaturalKind(V1),V1)
   active#(isLNat(natsFrom(V1))) -> mark#(U71(isNaturalKind(V1),V1))
   active#(isLNat(snd(V1))) -> isPLNatKind#(V1)
   active#(isLNat(snd(V1))) -> U81#(isPLNatKind(V1),V1)
   active#(isLNat(snd(V1))) -> mark#(U81(isPLNatKind(V1),V1))
   active#(isLNat(tail(V1))) -> isLNatKind#(V1)
   active#(isLNat(tail(V1))) -> U91#(isLNatKind(V1),V1)
   active#(isLNat(tail(V1))) -> mark#(U91(isLNatKind(V1),V1))
   active#(isLNat(take(V1,V2))) -> isLNatKind#(V2)
   active#(isLNat(take(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNat(take(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNat(take(V1,V2))) -> U101#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   active#(isLNat(take(V1,V2))) -> mark#(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active#(isLNatKind(nil())) -> mark#(tt())
   active#(isLNatKind(afterNth(V1,V2))) -> isLNatKind#(V2)
   active#(isLNatKind(afterNth(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNatKind(afterNth(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNatKind(afterNth(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
   active#(isLNatKind(cons(V1,V2))) -> isLNatKind#(V2)
   active#(isLNatKind(cons(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNatKind(cons(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNatKind(cons(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
   active#(isLNatKind(fst(V1))) -> isPLNatKind#(V1)
   active#(isLNatKind(fst(V1))) -> mark#(isPLNatKind(V1))
   active#(isLNatKind(natsFrom(V1))) -> isNaturalKind#(V1)
   active#(isLNatKind(natsFrom(V1))) -> mark#(isNaturalKind(V1))
   active#(isLNatKind(snd(V1))) -> isPLNatKind#(V1)
   active#(isLNatKind(snd(V1))) -> mark#(isPLNatKind(V1))
   active#(isLNatKind(tail(V1))) -> isLNatKind#(V1)
   active#(isLNatKind(tail(V1))) -> mark#(isLNatKind(V1))
   active#(isLNatKind(take(V1,V2))) -> isLNatKind#(V2)
   active#(isLNatKind(take(V1,V2))) -> isNaturalKind#(V1)
   active#(isLNatKind(take(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isLNatKind(take(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
   active#(isNatural(0())) -> mark#(tt())
   active#(isNatural(head(V1))) -> isLNatKind#(V1)
   active#(isNatural(head(V1))) -> U111#(isLNatKind(V1),V1)
   active#(isNatural(head(V1))) -> mark#(U111(isLNatKind(V1),V1))
   active#(isNatural(s(V1))) -> isNaturalKind#(V1)
   active#(isNatural(s(V1))) -> U121#(isNaturalKind(V1),V1)
   active#(isNatural(s(V1))) -> mark#(U121(isNaturalKind(V1),V1))
   active#(isNatural(sel(V1,V2))) -> isLNatKind#(V2)
   active#(isNatural(sel(V1,V2))) -> isNaturalKind#(V1)
   active#(isNatural(sel(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isNatural(sel(V1,V2))) -> U131#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   active#(isNatural(sel(V1,V2))) -> mark#(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active#(isNaturalKind(0())) -> mark#(tt())
   active#(isNaturalKind(head(V1))) -> isLNatKind#(V1)
   active#(isNaturalKind(head(V1))) -> mark#(isLNatKind(V1))
   active#(isNaturalKind(s(V1))) -> isNaturalKind#(V1)
   active#(isNaturalKind(s(V1))) -> mark#(isNaturalKind(V1))
   active#(isNaturalKind(sel(V1,V2))) -> isLNatKind#(V2)
   active#(isNaturalKind(sel(V1,V2))) -> isNaturalKind#(V1)
   active#(isNaturalKind(sel(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isNaturalKind(sel(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
   active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V2)
   active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V1)
   active#(isPLNat(pair(V1,V2))) -> and#(isLNatKind(V1),isLNatKind(V2))
   active#(isPLNat(pair(V1,V2))) -> U141#(and(isLNatKind(V1),isLNatKind(V2)),V1,V2)
   active#(isPLNat(pair(V1,V2))) -> mark#(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
   active#(isPLNat(splitAt(V1,V2))) -> isLNatKind#(V2)
   active#(isPLNat(splitAt(V1,V2))) -> isNaturalKind#(V1)
   active#(isPLNat(splitAt(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isPLNat(splitAt(V1,V2))) -> U151#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V2)
   active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V1)
   active#(isPLNatKind(pair(V1,V2))) -> and#(isLNatKind(V1),isLNatKind(V2))
   active#(isPLNatKind(pair(V1,V2))) -> mark#(and(isLNatKind(V1),isLNatKind(V2)))
   active#(isPLNatKind(splitAt(V1,V2))) -> isLNatKind#(V2)
   active#(isPLNatKind(splitAt(V1,V2))) -> isNaturalKind#(V1)
   active#(isPLNatKind(splitAt(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
   active#(isPLNatKind(splitAt(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
   active#(natsFrom(N)) -> isNaturalKind#(N)
   active#(natsFrom(N)) -> isNatural#(N)
   active#(natsFrom(N)) -> and#(isNatural(N),isNaturalKind(N))
   active#(natsFrom(N)) -> U161#(and(isNatural(N),isNaturalKind(N)),N)
   active#(natsFrom(N)) -> mark#(U161(and(isNatural(N),isNaturalKind(N)),N))
   active#(sel(N,XS)) -> isLNatKind#(XS)
   active#(sel(N,XS)) -> isLNat#(XS)
   active#(sel(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
   active#(sel(N,XS)) -> isNaturalKind#(N)
   active#(sel(N,XS)) -> isNatural#(N)
   active#(sel(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
   active#(sel(N,XS)) -> and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   active#(sel(N,XS)) ->
   U171#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   active#(sel(N,XS)) ->
   mark#(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   active#(snd(pair(X,Y))) -> isLNatKind#(Y)
   active#(snd(pair(X,Y))) -> isLNat#(Y)
   active#(snd(pair(X,Y))) -> and#(isLNat(Y),isLNatKind(Y))
   active#(snd(pair(X,Y))) -> isLNatKind#(X)
   active#(snd(pair(X,Y))) -> isLNat#(X)
   active#(snd(pair(X,Y))) -> and#(isLNat(X),isLNatKind(X))
   active#(snd(pair(X,Y))) -> and#(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
   active#(snd(pair(X,Y))) ->
   U181#(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
   active#(snd(pair(X,Y))) ->
   mark#(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
   active#(splitAt(0(),XS)) -> isLNatKind#(XS)
   active#(splitAt(0(),XS)) -> isLNat#(XS)
   active#(splitAt(0(),XS)) -> and#(isLNat(XS),isLNatKind(XS))
   active#(splitAt(0(),XS)) -> U191#(and(isLNat(XS),isLNatKind(XS)),XS)
   active#(splitAt(0(),XS)) -> mark#(U191(and(isLNat(XS),isLNatKind(XS)),XS))
   active#(splitAt(s(N),cons(X,XS))) -> isLNatKind#(XS)
   active#(splitAt(s(N),cons(X,XS))) -> isLNat#(XS)
   active#(splitAt(s(N),cons(X,XS))) -> and#(isLNat(XS),isLNatKind(XS))
   active#(splitAt(s(N),cons(X,XS))) -> isNaturalKind#(X)
   active#(splitAt(s(N),cons(X,XS))) -> isNatural#(X)
   active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(X),isNaturalKind(X))
   active#(splitAt(s(N),cons(X,XS))) ->
   and#(and(isNatural(X),isNaturalKind(X)),and(isLNat(XS),isLNatKind(XS)))
   active#(splitAt(s(N),cons(X,XS))) -> isNaturalKind#(N)
   active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
   active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(N),isNaturalKind(N))
   active#(splitAt(s(N),cons(X,XS))) ->
   and#(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                               and(isLNat(XS),isLNatKind(XS))))
   active#(splitAt(s(N),cons(X,XS))) ->
   U201#(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                    and(isLNat(XS),isLNatKind(XS)))),
         N,X,XS)
   active#(splitAt(s(N),cons(X,XS))) ->
   mark#(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                         and(isLNat(XS),isLNatKind(XS)))),
              N,X,XS))
   active#(tail(cons(N,XS))) -> isLNatKind#(XS)
   active#(tail(cons(N,XS))) -> isLNat#(XS)
   active#(tail(cons(N,XS))) -> and#(isLNat(XS),isLNatKind(XS))
   active#(tail(cons(N,XS))) -> isNaturalKind#(N)
   active#(tail(cons(N,XS))) -> isNatural#(N)
   active#(tail(cons(N,XS))) -> and#(isNatural(N),isNaturalKind(N))
   active#(tail(cons(N,XS))) ->
   and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   active#(tail(cons(N,XS))) ->
   U211#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
   active#(tail(cons(N,XS))) ->
   mark#(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
   active#(take(N,XS)) -> isLNatKind#(XS)
   active#(take(N,XS)) -> isLNat#(XS)
   active#(take(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
   active#(take(N,XS)) -> isNaturalKind#(N)
   active#(take(N,XS)) -> isNatural#(N)
   active#(take(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
   active#(take(N,XS)) -> and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   active#(take(N,XS)) ->
   U221#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   active#(take(N,XS)) ->
   mark#(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   mark#(U101(X1,X2,X3)) -> mark#(X1)
   mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3)
   mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
   mark#(tt()) -> active#(tt())
   mark#(U102(X1,X2)) -> mark#(X1)
   mark#(U102(X1,X2)) -> U102#(mark(X1),X2)
   mark#(U102(X1,X2)) -> active#(U102(mark(X1),X2))
   mark#(isNatural(X)) -> active#(isNatural(X))
   mark#(U103(X)) -> mark#(X)
   mark#(U103(X)) -> U103#(mark(X))
   mark#(U103(X)) -> active#(U103(mark(X)))
   mark#(isLNat(X)) -> active#(isLNat(X))
   mark#(U11(X1,X2,X3)) -> mark#(X1)
   mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3)
   mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
   mark#(snd(X)) -> mark#(X)
   mark#(snd(X)) -> snd#(mark(X))
   mark#(snd(X)) -> active#(snd(mark(X)))
   mark#(splitAt(X1,X2)) -> mark#(X2)
   mark#(splitAt(X1,X2)) -> mark#(X1)
   mark#(splitAt(X1,X2)) -> splitAt#(mark(X1),mark(X2))
   mark#(splitAt(X1,X2)) -> active#(splitAt(mark(X1),mark(X2)))
   mark#(U111(X1,X2)) -> mark#(X1)
   mark#(U111(X1,X2)) -> U111#(mark(X1),X2)
   mark#(U111(X1,X2)) -> active#(U111(mark(X1),X2))
   mark#(U112(X)) -> mark#(X)
   mark#(U112(X)) -> U112#(mark(X))
   mark#(U112(X)) -> active#(U112(mark(X)))
   mark#(U121(X1,X2)) -> mark#(X1)
   mark#(U121(X1,X2)) -> U121#(mark(X1),X2)
   mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2))
   mark#(U122(X)) -> mark#(X)
   mark#(U122(X)) -> U122#(mark(X))
   mark#(U122(X)) -> active#(U122(mark(X)))
   mark#(U131(X1,X2,X3)) -> mark#(X1)
   mark#(U131(X1,X2,X3)) -> U131#(mark(X1),X2,X3)
   mark#(U131(X1,X2,X3)) -> active#(U131(mark(X1),X2,X3))
   mark#(U132(X1,X2)) -> mark#(X1)
   mark#(U132(X1,X2)) -> U132#(mark(X1),X2)
   mark#(U132(X1,X2)) -> active#(U132(mark(X1),X2))
   mark#(U133(X)) -> mark#(X)
   mark#(U133(X)) -> U133#(mark(X))
   mark#(U133(X)) -> active#(U133(mark(X)))
   mark#(U141(X1,X2,X3)) -> mark#(X1)
   mark#(U141(X1,X2,X3)) -> U141#(mark(X1),X2,X3)
   mark#(U141(X1,X2,X3)) -> active#(U141(mark(X1),X2,X3))
   mark#(U142(X1,X2)) -> mark#(X1)
   mark#(U142(X1,X2)) -> U142#(mark(X1),X2)
   mark#(U142(X1,X2)) -> active#(U142(mark(X1),X2))
   mark#(U143(X)) -> mark#(X)
   mark#(U143(X)) -> U143#(mark(X))
   mark#(U143(X)) -> active#(U143(mark(X)))
   mark#(U151(X1,X2,X3)) -> mark#(X1)
   mark#(U151(X1,X2,X3)) -> U151#(mark(X1),X2,X3)
   mark#(U151(X1,X2,X3)) -> active#(U151(mark(X1),X2,X3))
   mark#(U152(X1,X2)) -> mark#(X1)
   mark#(U152(X1,X2)) -> U152#(mark(X1),X2)
   mark#(U152(X1,X2)) -> active#(U152(mark(X1),X2))
   mark#(U153(X)) -> mark#(X)
   mark#(U153(X)) -> U153#(mark(X))
   mark#(U153(X)) -> active#(U153(mark(X)))
   mark#(U161(X1,X2)) -> mark#(X1)
   mark#(U161(X1,X2)) -> U161#(mark(X1),X2)
   mark#(U161(X1,X2)) -> active#(U161(mark(X1),X2))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
   mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
   mark#(natsFrom(X)) -> mark#(X)
   mark#(natsFrom(X)) -> natsFrom#(mark(X))
   mark#(natsFrom(X)) -> active#(natsFrom(mark(X)))
   mark#(s(X)) -> mark#(X)
   mark#(s(X)) -> s#(mark(X))
   mark#(s(X)) -> active#(s(mark(X)))
   mark#(U171(X1,X2,X3)) -> mark#(X1)
   mark#(U171(X1,X2,X3)) -> U171#(mark(X1),X2,X3)
   mark#(U171(X1,X2,X3)) -> active#(U171(mark(X1),X2,X3))
   mark#(head(X)) -> mark#(X)
   mark#(head(X)) -> head#(mark(X))
   mark#(head(X)) -> active#(head(mark(X)))
   mark#(afterNth(X1,X2)) -> mark#(X2)
   mark#(afterNth(X1,X2)) -> mark#(X1)
   mark#(afterNth(X1,X2)) -> afterNth#(mark(X1),mark(X2))
   mark#(afterNth(X1,X2)) -> active#(afterNth(mark(X1),mark(X2)))
   mark#(U181(X1,X2)) -> mark#(X1)
   mark#(U181(X1,X2)) -> U181#(mark(X1),X2)
   mark#(U181(X1,X2)) -> active#(U181(mark(X1),X2))
   mark#(U191(X1,X2)) -> mark#(X1)
   mark#(U191(X1,X2)) -> U191#(mark(X1),X2)
   mark#(U191(X1,X2)) -> active#(U191(mark(X1),X2))
   mark#(pair(X1,X2)) -> mark#(X2)
   mark#(pair(X1,X2)) -> mark#(X1)
   mark#(pair(X1,X2)) -> pair#(mark(X1),mark(X2))
   mark#(pair(X1,X2)) -> active#(pair(mark(X1),mark(X2)))
   mark#(nil()) -> active#(nil())
   mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U201(X1,X2,X3,X4)) -> U201#(mark(X1),X2,X3,X4)
   mark#(U201(X1,X2,X3,X4)) -> active#(U201(mark(X1),X2,X3,X4))
   mark#(U202(X1,X2)) -> mark#(X1)
   mark#(U202(X1,X2)) -> U202#(mark(X1),X2)
   mark#(U202(X1,X2)) -> active#(U202(mark(X1),X2))
   mark#(U21(X1,X2)) -> mark#(X1)
   mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
   mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
   mark#(U211(X1,X2)) -> mark#(X1)
   mark#(U211(X1,X2)) -> U211#(mark(X1),X2)
   mark#(U211(X1,X2)) -> active#(U211(mark(X1),X2))
   mark#(U221(X1,X2,X3)) -> mark#(X1)
   mark#(U221(X1,X2,X3)) -> U221#(mark(X1),X2,X3)
   mark#(U221(X1,X2,X3)) -> active#(U221(mark(X1),X2,X3))
   mark#(fst(X)) -> mark#(X)
   mark#(fst(X)) -> fst#(mark(X))
   mark#(fst(X)) -> active#(fst(mark(X)))
   mark#(U31(X1,X2)) -> mark#(X1)
   mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
   mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
   mark#(U41(X1,X2,X3)) -> mark#(X1)
   mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
   mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
   mark#(U42(X1,X2)) -> mark#(X1)
   mark#(U42(X1,X2)) -> U42#(mark(X1),X2)
   mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
   mark#(U43(X)) -> mark#(X)
   mark#(U43(X)) -> U43#(mark(X))
   mark#(U43(X)) -> active#(U43(mark(X)))
   mark#(U51(X1,X2,X3)) -> mark#(X1)
   mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
   mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
   mark#(U52(X1,X2)) -> mark#(X1)
   mark#(U52(X1,X2)) -> U52#(mark(X1),X2)
   mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
   mark#(U53(X)) -> mark#(X)
   mark#(U53(X)) -> U53#(mark(X))
   mark#(U53(X)) -> active#(U53(mark(X)))
   mark#(U61(X1,X2)) -> mark#(X1)
   mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
   mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
   mark#(U62(X)) -> mark#(X)
   mark#(U62(X)) -> U62#(mark(X))
   mark#(U62(X)) -> active#(U62(mark(X)))
   mark#(isPLNat(X)) -> active#(isPLNat(X))
   mark#(U71(X1,X2)) -> mark#(X1)
   mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
   mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
   mark#(U72(X)) -> mark#(X)
   mark#(U72(X)) -> U72#(mark(X))
   mark#(U72(X)) -> active#(U72(mark(X)))
   mark#(U81(X1,X2)) -> mark#(X1)
   mark#(U81(X1,X2)) -> U81#(mark(X1),X2)
   mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
   mark#(U82(X)) -> mark#(X)
   mark#(U82(X)) -> U82#(mark(X))
   mark#(U82(X)) -> active#(U82(mark(X)))
   mark#(U91(X1,X2)) -> mark#(X1)
   mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
   mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
   mark#(U92(X)) -> mark#(X)
   mark#(U92(X)) -> U92#(mark(X))
   mark#(U92(X)) -> active#(U92(mark(X)))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> and#(mark(X1),X2)
   mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
   mark#(isNaturalKind(X)) -> active#(isNaturalKind(X))
   mark#(isLNatKind(X)) -> active#(isLNatKind(X))
   mark#(isPLNatKind(X)) -> active#(isPLNatKind(X))
   mark#(tail(X)) -> mark#(X)
   mark#(tail(X)) -> tail#(mark(X))
   mark#(tail(X)) -> active#(tail(mark(X)))
   mark#(take(X1,X2)) -> mark#(X2)
   mark#(take(X1,X2)) -> mark#(X1)
   mark#(take(X1,X2)) -> take#(mark(X1),mark(X2))
   mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2)))
   mark#(0()) -> active#(0())
   mark#(sel(X1,X2)) -> mark#(X2)
   mark#(sel(X1,X2)) -> mark#(X1)
   mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2))
   mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2)))
   U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
   U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
   U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
   U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
   U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
   U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
   U102#(mark(X1),X2) -> U102#(X1,X2)
   U102#(X1,mark(X2)) -> U102#(X1,X2)
   U102#(active(X1),X2) -> U102#(X1,X2)
   U102#(X1,active(X2)) -> U102#(X1,X2)
   isNatural#(mark(X)) -> isNatural#(X)
   isNatural#(active(X)) -> isNatural#(X)
   U103#(mark(X)) -> U103#(X)
   U103#(active(X)) -> U103#(X)
   isLNat#(mark(X)) -> isLNat#(X)
   isLNat#(active(X)) -> isLNat#(X)
   U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
   U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
   U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
   U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
   U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
   U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
   snd#(mark(X)) -> snd#(X)
   snd#(active(X)) -> snd#(X)
   splitAt#(mark(X1),X2) -> splitAt#(X1,X2)
   splitAt#(X1,mark(X2)) -> splitAt#(X1,X2)
   splitAt#(active(X1),X2) -> splitAt#(X1,X2)
   splitAt#(X1,active(X2)) -> splitAt#(X1,X2)
   U111#(mark(X1),X2) -> U111#(X1,X2)
   U111#(X1,mark(X2)) -> U111#(X1,X2)
   U111#(active(X1),X2) -> U111#(X1,X2)
   U111#(X1,active(X2)) -> U111#(X1,X2)
   U112#(mark(X)) -> U112#(X)
   U112#(active(X)) -> U112#(X)
   U121#(mark(X1),X2) -> U121#(X1,X2)
   U121#(X1,mark(X2)) -> U121#(X1,X2)
   U121#(active(X1),X2) -> U121#(X1,X2)
   U121#(X1,active(X2)) -> U121#(X1,X2)
   U122#(mark(X)) -> U122#(X)
   U122#(active(X)) -> U122#(X)
   U131#(mark(X1),X2,X3) -> U131#(X1,X2,X3)
   U131#(X1,mark(X2),X3) -> U131#(X1,X2,X3)
   U131#(X1,X2,mark(X3)) -> U131#(X1,X2,X3)
   U131#(active(X1),X2,X3) -> U131#(X1,X2,X3)
   U131#(X1,active(X2),X3) -> U131#(X1,X2,X3)
   U131#(X1,X2,active(X3)) -> U131#(X1,X2,X3)
   U132#(mark(X1),X2) -> U132#(X1,X2)
   U132#(X1,mark(X2)) -> U132#(X1,X2)
   U132#(active(X1),X2) -> U132#(X1,X2)
   U132#(X1,active(X2)) -> U132#(X1,X2)
   U133#(mark(X)) -> U133#(X)
   U133#(active(X)) -> U133#(X)
   U141#(mark(X1),X2,X3) -> U141#(X1,X2,X3)
   U141#(X1,mark(X2),X3) -> U141#(X1,X2,X3)
   U141#(X1,X2,mark(X3)) -> U141#(X1,X2,X3)
   U141#(active(X1),X2,X3) -> U141#(X1,X2,X3)
   U141#(X1,active(X2),X3) -> U141#(X1,X2,X3)
   U141#(X1,X2,active(X3)) -> U141#(X1,X2,X3)
   U142#(mark(X1),X2) -> U142#(X1,X2)
   U142#(X1,mark(X2)) -> U142#(X1,X2)
   U142#(active(X1),X2) -> U142#(X1,X2)
   U142#(X1,active(X2)) -> U142#(X1,X2)
   U143#(mark(X)) -> U143#(X)
   U143#(active(X)) -> U143#(X)
   U151#(mark(X1),X2,X3) -> U151#(X1,X2,X3)
   U151#(X1,mark(X2),X3) -> U151#(X1,X2,X3)
   U151#(X1,X2,mark(X3)) -> U151#(X1,X2,X3)
   U151#(active(X1),X2,X3) -> U151#(X1,X2,X3)
   U151#(X1,active(X2),X3) -> U151#(X1,X2,X3)
   U151#(X1,X2,active(X3)) -> U151#(X1,X2,X3)
   U152#(mark(X1),X2) -> U152#(X1,X2)
   U152#(X1,mark(X2)) -> U152#(X1,X2)
   U152#(active(X1),X2) -> U152#(X1,X2)
   U152#(X1,active(X2)) -> U152#(X1,X2)
   U153#(mark(X)) -> U153#(X)
   U153#(active(X)) -> U153#(X)
   U161#(mark(X1),X2) -> U161#(X1,X2)
   U161#(X1,mark(X2)) -> U161#(X1,X2)
   U161#(active(X1),X2) -> U161#(X1,X2)
   U161#(X1,active(X2)) -> U161#(X1,X2)
   cons#(mark(X1),X2) -> cons#(X1,X2)
   cons#(X1,mark(X2)) -> cons#(X1,X2)
   cons#(active(X1),X2) -> cons#(X1,X2)
   cons#(X1,active(X2)) -> cons#(X1,X2)
   natsFrom#(mark(X)) -> natsFrom#(X)
   natsFrom#(active(X)) -> natsFrom#(X)
   s#(mark(X)) -> s#(X)
   s#(active(X)) -> s#(X)
   U171#(mark(X1),X2,X3) -> U171#(X1,X2,X3)
   U171#(X1,mark(X2),X3) -> U171#(X1,X2,X3)
   U171#(X1,X2,mark(X3)) -> U171#(X1,X2,X3)
   U171#(active(X1),X2,X3) -> U171#(X1,X2,X3)
   U171#(X1,active(X2),X3) -> U171#(X1,X2,X3)
   U171#(X1,X2,active(X3)) -> U171#(X1,X2,X3)
   head#(mark(X)) -> head#(X)
   head#(active(X)) -> head#(X)
   afterNth#(mark(X1),X2) -> afterNth#(X1,X2)
   afterNth#(X1,mark(X2)) -> afterNth#(X1,X2)
   afterNth#(active(X1),X2) -> afterNth#(X1,X2)
   afterNth#(X1,active(X2)) -> afterNth#(X1,X2)
   U181#(mark(X1),X2) -> U181#(X1,X2)
   U181#(X1,mark(X2)) -> U181#(X1,X2)
   U181#(active(X1),X2) -> U181#(X1,X2)
   U181#(X1,active(X2)) -> U181#(X1,X2)
   U191#(mark(X1),X2) -> U191#(X1,X2)
   U191#(X1,mark(X2)) -> U191#(X1,X2)
   U191#(active(X1),X2) -> U191#(X1,X2)
   U191#(X1,active(X2)) -> U191#(X1,X2)
   pair#(mark(X1),X2) -> pair#(X1,X2)
   pair#(X1,mark(X2)) -> pair#(X1,X2)
   pair#(active(X1),X2) -> pair#(X1,X2)
   pair#(X1,active(X2)) -> pair#(X1,X2)
   U201#(mark(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,mark(X2),X3,X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,X2,mark(X3),X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,X2,X3,mark(X4)) -> U201#(X1,X2,X3,X4)
   U201#(active(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,active(X2),X3,X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,X2,active(X3),X4) -> U201#(X1,X2,X3,X4)
   U201#(X1,X2,X3,active(X4)) -> U201#(X1,X2,X3,X4)
   U202#(mark(X1),X2) -> U202#(X1,X2)
   U202#(X1,mark(X2)) -> U202#(X1,X2)
   U202#(active(X1),X2) -> U202#(X1,X2)
   U202#(X1,active(X2)) -> U202#(X1,X2)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U21#(X1,mark(X2)) -> U21#(X1,X2)
   U21#(active(X1),X2) -> U21#(X1,X2)
   U21#(X1,active(X2)) -> U21#(X1,X2)
   U211#(mark(X1),X2) -> U211#(X1,X2)
   U211#(X1,mark(X2)) -> U211#(X1,X2)
   U211#(active(X1),X2) -> U211#(X1,X2)
   U211#(X1,active(X2)) -> U211#(X1,X2)
   U221#(mark(X1),X2,X3) -> U221#(X1,X2,X3)
   U221#(X1,mark(X2),X3) -> U221#(X1,X2,X3)
   U221#(X1,X2,mark(X3)) -> U221#(X1,X2,X3)
   U221#(active(X1),X2,X3) -> U221#(X1,X2,X3)
   U221#(X1,active(X2),X3) -> U221#(X1,X2,X3)
   U221#(X1,X2,active(X3)) -> U221#(X1,X2,X3)
   fst#(mark(X)) -> fst#(X)
   fst#(active(X)) -> fst#(X)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U31#(X1,mark(X2)) -> U31#(X1,X2)
   U31#(active(X1),X2) -> U31#(X1,X2)
   U31#(X1,active(X2)) -> U31#(X1,X2)
   U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
   U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
   U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
   U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
   U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
   U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
   U42#(mark(X1),X2) -> U42#(X1,X2)
   U42#(X1,mark(X2)) -> U42#(X1,X2)
   U42#(active(X1),X2) -> U42#(X1,X2)
   U42#(X1,active(X2)) -> U42#(X1,X2)
   U43#(mark(X)) -> U43#(X)
   U43#(active(X)) -> U43#(X)
   U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
   U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
   U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
   U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
   U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
   U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
   U52#(mark(X1),X2) -> U52#(X1,X2)
   U52#(X1,mark(X2)) -> U52#(X1,X2)
   U52#(active(X1),X2) -> U52#(X1,X2)
   U52#(X1,active(X2)) -> U52#(X1,X2)
   U53#(mark(X)) -> U53#(X)
   U53#(active(X)) -> U53#(X)
   U61#(mark(X1),X2) -> U61#(X1,X2)
   U61#(X1,mark(X2)) -> U61#(X1,X2)
   U61#(active(X1),X2) -> U61#(X1,X2)
   U61#(X1,active(X2)) -> U61#(X1,X2)
   U62#(mark(X)) -> U62#(X)
   U62#(active(X)) -> U62#(X)
   isPLNat#(mark(X)) -> isPLNat#(X)
   isPLNat#(active(X)) -> isPLNat#(X)
   U71#(mark(X1),X2) -> U71#(X1,X2)
   U71#(X1,mark(X2)) -> U71#(X1,X2)
   U71#(active(X1),X2) -> U71#(X1,X2)
   U71#(X1,active(X2)) -> U71#(X1,X2)
   U72#(mark(X)) -> U72#(X)
   U72#(active(X)) -> U72#(X)
   U81#(mark(X1),X2) -> U81#(X1,X2)
   U81#(X1,mark(X2)) -> U81#(X1,X2)
   U81#(active(X1),X2) -> U81#(X1,X2)
   U81#(X1,active(X2)) -> U81#(X1,X2)
   U82#(mark(X)) -> U82#(X)
   U82#(active(X)) -> U82#(X)
   U91#(mark(X1),X2) -> U91#(X1,X2)
   U91#(X1,mark(X2)) -> U91#(X1,X2)
   U91#(active(X1),X2) -> U91#(X1,X2)
   U91#(X1,active(X2)) -> U91#(X1,X2)
   U92#(mark(X)) -> U92#(X)
   U92#(active(X)) -> U92#(X)
   and#(mark(X1),X2) -> and#(X1,X2)
   and#(X1,mark(X2)) -> and#(X1,X2)
   and#(active(X1),X2) -> and#(X1,X2)
   and#(X1,active(X2)) -> and#(X1,X2)
   isNaturalKind#(mark(X)) -> isNaturalKind#(X)
   isNaturalKind#(active(X)) -> isNaturalKind#(X)
   isLNatKind#(mark(X)) -> isLNatKind#(X)
   isLNatKind#(active(X)) -> isLNatKind#(X)
   isPLNatKind#(mark(X)) -> isPLNatKind#(X)
   isPLNatKind#(active(X)) -> isPLNatKind#(X)
   tail#(mark(X)) -> tail#(X)
   tail#(active(X)) -> tail#(X)
   take#(mark(X1),X2) -> take#(X1,X2)
   take#(X1,mark(X2)) -> take#(X1,X2)
   take#(active(X1),X2) -> take#(X1,X2)
   take#(X1,active(X2)) -> take#(X1,X2)
   sel#(mark(X1),X2) -> sel#(X1,X2)
   sel#(X1,mark(X2)) -> sel#(X1,X2)
   sel#(active(X1),X2) -> sel#(X1,X2)
   sel#(X1,active(X2)) -> sel#(X1,X2)
  TRS:
   active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
   active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
   active(U103(tt())) -> mark(tt())
   active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
   active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
   active(U112(tt())) -> mark(tt())
   active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
   active(U122(tt())) -> mark(tt())
   active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
   active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
   active(U133(tt())) -> mark(tt())
   active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
   active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
   active(U143(tt())) -> mark(tt())
   active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
   active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
   active(U153(tt())) -> mark(tt())
   active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
   active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
   active(U181(tt(),Y)) -> mark(Y)
   active(U191(tt(),XS)) -> mark(pair(nil(),XS))
   active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
   active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
   active(U21(tt(),X)) -> mark(X)
   active(U211(tt(),XS)) -> mark(XS)
   active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
   active(U31(tt(),N)) -> mark(N)
   active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
   active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
   active(U43(tt())) -> mark(tt())
   active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
   active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
   active(U53(tt())) -> mark(tt())
   active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
   active(U62(tt())) -> mark(tt())
   active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
   active(U72(tt())) -> mark(tt())
   active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
   active(U82(tt())) -> mark(tt())
   active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
   active(U92(tt())) -> mark(tt())
   active(afterNth(N,XS)) ->
   mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   active(and(tt(),X)) -> mark(X)
   active(fst(pair(X,Y))) ->
   mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
   active(head(cons(N,XS))) ->
   mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
   active(isLNat(nil())) -> mark(tt())
   active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
   active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
   active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
   active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
   active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active(isLNatKind(nil())) -> mark(tt())
   active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
   active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
   active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
   active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
   active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
   active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
   active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
   active(isNatural(0())) -> mark(tt())
   active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
   active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
   active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active(isNaturalKind(0())) -> mark(tt())
   active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
   active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
   active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
   active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
   active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
   active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
   active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
   active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
   active(sel(N,XS)) ->
   mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   active(snd(pair(X,Y))) ->
   mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
   active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
   active(splitAt(s(N),cons(X,XS))) ->
   mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                        and(isLNat(XS),isLNatKind(XS)))),
             N,X,XS))
   active(tail(cons(N,XS))) ->
   mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
   active(take(N,XS)) ->
   mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
   mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
   mark(tt()) -> active(tt())
   mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
   mark(isNatural(X)) -> active(isNatural(X))
   mark(U103(X)) -> active(U103(mark(X)))
   mark(isLNat(X)) -> active(isLNat(X))
   mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
   mark(snd(X)) -> active(snd(mark(X)))
   mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
   mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
   mark(U112(X)) -> active(U112(mark(X)))
   mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
   mark(U122(X)) -> active(U122(mark(X)))
   mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
   mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
   mark(U133(X)) -> active(U133(mark(X)))
   mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
   mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
   mark(U143(X)) -> active(U143(mark(X)))
   mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
   mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
   mark(U153(X)) -> active(U153(mark(X)))
   mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
   mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
   mark(natsFrom(X)) -> active(natsFrom(mark(X)))
   mark(s(X)) -> active(s(mark(X)))
   mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
   mark(head(X)) -> active(head(mark(X)))
   mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
   mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
   mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
   mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
   mark(nil()) -> active(nil())
   mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
   mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
   mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
   mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
   mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
   mark(fst(X)) -> active(fst(mark(X)))
   mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
   mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
   mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
   mark(U43(X)) -> active(U43(mark(X)))
   mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
   mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
   mark(U53(X)) -> active(U53(mark(X)))
   mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
   mark(U62(X)) -> active(U62(mark(X)))
   mark(isPLNat(X)) -> active(isPLNat(X))
   mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
   mark(U72(X)) -> active(U72(mark(X)))
   mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
   mark(U82(X)) -> active(U82(mark(X)))
   mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
   mark(U92(X)) -> active(U92(mark(X)))
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(isNaturalKind(X)) -> active(isNaturalKind(X))
   mark(isLNatKind(X)) -> active(isLNatKind(X))
   mark(isPLNatKind(X)) -> active(isPLNatKind(X))
   mark(tail(X)) -> active(tail(mark(X)))
   mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
   mark(0()) -> active(0())
   mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
   U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
   U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
   U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
   U101(active(X1),X2,X3) -> U101(X1,X2,X3)
   U101(X1,active(X2),X3) -> U101(X1,X2,X3)
   U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
   U102(mark(X1),X2) -> U102(X1,X2)
   U102(X1,mark(X2)) -> U102(X1,X2)
   U102(active(X1),X2) -> U102(X1,X2)
   U102(X1,active(X2)) -> U102(X1,X2)
   isNatural(mark(X)) -> isNatural(X)
   isNatural(active(X)) -> isNatural(X)
   U103(mark(X)) -> U103(X)
   U103(active(X)) -> U103(X)
   isLNat(mark(X)) -> isLNat(X)
   isLNat(active(X)) -> isLNat(X)
   U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
   U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
   U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
   U11(active(X1),X2,X3) -> U11(X1,X2,X3)
   U11(X1,active(X2),X3) -> U11(X1,X2,X3)
   U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
   snd(mark(X)) -> snd(X)
   snd(active(X)) -> snd(X)
   splitAt(mark(X1),X2) -> splitAt(X1,X2)
   splitAt(X1,mark(X2)) -> splitAt(X1,X2)
   splitAt(active(X1),X2) -> splitAt(X1,X2)
   splitAt(X1,active(X2)) -> splitAt(X1,X2)
   U111(mark(X1),X2) -> U111(X1,X2)
   U111(X1,mark(X2)) -> U111(X1,X2)
   U111(active(X1),X2) -> U111(X1,X2)
   U111(X1,active(X2)) -> U111(X1,X2)
   U112(mark(X)) -> U112(X)
   U112(active(X)) -> U112(X)
   U121(mark(X1),X2) -> U121(X1,X2)
   U121(X1,mark(X2)) -> U121(X1,X2)
   U121(active(X1),X2) -> U121(X1,X2)
   U121(X1,active(X2)) -> U121(X1,X2)
   U122(mark(X)) -> U122(X)
   U122(active(X)) -> U122(X)
   U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
   U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
   U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
   U131(active(X1),X2,X3) -> U131(X1,X2,X3)
   U131(X1,active(X2),X3) -> U131(X1,X2,X3)
   U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
   U132(mark(X1),X2) -> U132(X1,X2)
   U132(X1,mark(X2)) -> U132(X1,X2)
   U132(active(X1),X2) -> U132(X1,X2)
   U132(X1,active(X2)) -> U132(X1,X2)
   U133(mark(X)) -> U133(X)
   U133(active(X)) -> U133(X)
   U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
   U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
   U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
   U141(active(X1),X2,X3) -> U141(X1,X2,X3)
   U141(X1,active(X2),X3) -> U141(X1,X2,X3)
   U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
   U142(mark(X1),X2) -> U142(X1,X2)
   U142(X1,mark(X2)) -> U142(X1,X2)
   U142(active(X1),X2) -> U142(X1,X2)
   U142(X1,active(X2)) -> U142(X1,X2)
   U143(mark(X)) -> U143(X)
   U143(active(X)) -> U143(X)
   U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
   U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
   U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
   U151(active(X1),X2,X3) -> U151(X1,X2,X3)
   U151(X1,active(X2),X3) -> U151(X1,X2,X3)
   U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
   U152(mark(X1),X2) -> U152(X1,X2)
   U152(X1,mark(X2)) -> U152(X1,X2)
   U152(active(X1),X2) -> U152(X1,X2)
   U152(X1,active(X2)) -> U152(X1,X2)
   U153(mark(X)) -> U153(X)
   U153(active(X)) -> U153(X)
   U161(mark(X1),X2) -> U161(X1,X2)
   U161(X1,mark(X2)) -> U161(X1,X2)
   U161(active(X1),X2) -> U161(X1,X2)
   U161(X1,active(X2)) -> U161(X1,X2)
   cons(mark(X1),X2) -> cons(X1,X2)
   cons(X1,mark(X2)) -> cons(X1,X2)
   cons(active(X1),X2) -> cons(X1,X2)
   cons(X1,active(X2)) -> cons(X1,X2)
   natsFrom(mark(X)) -> natsFrom(X)
   natsFrom(active(X)) -> natsFrom(X)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
   U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
   U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
   U171(active(X1),X2,X3) -> U171(X1,X2,X3)
   U171(X1,active(X2),X3) -> U171(X1,X2,X3)
   U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
   head(mark(X)) -> head(X)
   head(active(X)) -> head(X)
   afterNth(mark(X1),X2) -> afterNth(X1,X2)
   afterNth(X1,mark(X2)) -> afterNth(X1,X2)
   afterNth(active(X1),X2) -> afterNth(X1,X2)
   afterNth(X1,active(X2)) -> afterNth(X1,X2)
   U181(mark(X1),X2) -> U181(X1,X2)
   U181(X1,mark(X2)) -> U181(X1,X2)
   U181(active(X1),X2) -> U181(X1,X2)
   U181(X1,active(X2)) -> U181(X1,X2)
   U191(mark(X1),X2) -> U191(X1,X2)
   U191(X1,mark(X2)) -> U191(X1,X2)
   U191(active(X1),X2) -> U191(X1,X2)
   U191(X1,active(X2)) -> U191(X1,X2)
   pair(mark(X1),X2) -> pair(X1,X2)
   pair(X1,mark(X2)) -> pair(X1,X2)
   pair(active(X1),X2) -> pair(X1,X2)
   pair(X1,active(X2)) -> pair(X1,X2)
   U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
   U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
   U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
   U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
   U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
   U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
   U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
   U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
   U202(mark(X1),X2) -> U202(X1,X2)
   U202(X1,mark(X2)) -> U202(X1,X2)
   U202(active(X1),X2) -> U202(X1,X2)
   U202(X1,active(X2)) -> U202(X1,X2)
   U21(mark(X1),X2) -> U21(X1,X2)
   U21(X1,mark(X2)) -> U21(X1,X2)
   U21(active(X1),X2) -> U21(X1,X2)
   U21(X1,active(X2)) -> U21(X1,X2)
   U211(mark(X1),X2) -> U211(X1,X2)
   U211(X1,mark(X2)) -> U211(X1,X2)
   U211(active(X1),X2) -> U211(X1,X2)
   U211(X1,active(X2)) -> U211(X1,X2)
   U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
   U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
   U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
   U221(active(X1),X2,X3) -> U221(X1,X2,X3)
   U221(X1,active(X2),X3) -> U221(X1,X2,X3)
   U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
   fst(mark(X)) -> fst(X)
   fst(active(X)) -> fst(X)
   U31(mark(X1),X2) -> U31(X1,X2)
   U31(X1,mark(X2)) -> U31(X1,X2)
   U31(active(X1),X2) -> U31(X1,X2)
   U31(X1,active(X2)) -> U31(X1,X2)
   U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
   U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
   U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
   U41(active(X1),X2,X3) -> U41(X1,X2,X3)
   U41(X1,active(X2),X3) -> U41(X1,X2,X3)
   U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
   U42(mark(X1),X2) -> U42(X1,X2)
   U42(X1,mark(X2)) -> U42(X1,X2)
   U42(active(X1),X2) -> U42(X1,X2)
   U42(X1,active(X2)) -> U42(X1,X2)
   U43(mark(X)) -> U43(X)
   U43(active(X)) -> U43(X)
   U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
   U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
   U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
   U51(active(X1),X2,X3) -> U51(X1,X2,X3)
   U51(X1,active(X2),X3) -> U51(X1,X2,X3)
   U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
   U52(mark(X1),X2) -> U52(X1,X2)
   U52(X1,mark(X2)) -> U52(X1,X2)
   U52(active(X1),X2) -> U52(X1,X2)
   U52(X1,active(X2)) -> U52(X1,X2)
   U53(mark(X)) -> U53(X)
   U53(active(X)) -> U53(X)
   U61(mark(X1),X2) -> U61(X1,X2)
   U61(X1,mark(X2)) -> U61(X1,X2)
   U61(active(X1),X2) -> U61(X1,X2)
   U61(X1,active(X2)) -> U61(X1,X2)
   U62(mark(X)) -> U62(X)
   U62(active(X)) -> U62(X)
   isPLNat(mark(X)) -> isPLNat(X)
   isPLNat(active(X)) -> isPLNat(X)
   U71(mark(X1),X2) -> U71(X1,X2)
   U71(X1,mark(X2)) -> U71(X1,X2)
   U71(active(X1),X2) -> U71(X1,X2)
   U71(X1,active(X2)) -> U71(X1,X2)
   U72(mark(X)) -> U72(X)
   U72(active(X)) -> U72(X)
   U81(mark(X1),X2) -> U81(X1,X2)
   U81(X1,mark(X2)) -> U81(X1,X2)
   U81(active(X1),X2) -> U81(X1,X2)
   U81(X1,active(X2)) -> U81(X1,X2)
   U82(mark(X)) -> U82(X)
   U82(active(X)) -> U82(X)
   U91(mark(X1),X2) -> U91(X1,X2)
   U91(X1,mark(X2)) -> U91(X1,X2)
   U91(active(X1),X2) -> U91(X1,X2)
   U91(X1,active(X2)) -> U91(X1,X2)
   U92(mark(X)) -> U92(X)
   U92(active(X)) -> U92(X)
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   isNaturalKind(mark(X)) -> isNaturalKind(X)
   isNaturalKind(active(X)) -> isNaturalKind(X)
   isLNatKind(mark(X)) -> isLNatKind(X)
   isLNatKind(active(X)) -> isLNatKind(X)
   isPLNatKind(mark(X)) -> isPLNatKind(X)
   isPLNatKind(active(X)) -> isPLNatKind(X)
   tail(mark(X)) -> tail(X)
   tail(active(X)) -> tail(X)
   take(mark(X1),X2) -> take(X1,X2)
   take(X1,mark(X2)) -> take(X1,X2)
   take(active(X1),X2) -> take(X1,X2)
   take(X1,active(X2)) -> take(X1,X2)
   sel(mark(X1),X2) -> sel(X1,X2)
   sel(X1,mark(X2)) -> sel(X1,X2)
   sel(active(X1),X2) -> sel(X1,X2)
   sel(X1,active(X2)) -> sel(X1,X2)
  EDG Processor:
   DPs:
    active#(U101(tt(),V1,V2)) -> isNatural#(V1)
    active#(U101(tt(),V1,V2)) -> U102#(isNatural(V1),V2)
    active#(U101(tt(),V1,V2)) -> mark#(U102(isNatural(V1),V2))
    active#(U102(tt(),V2)) -> isLNat#(V2)
    active#(U102(tt(),V2)) -> U103#(isLNat(V2))
    active#(U102(tt(),V2)) -> mark#(U103(isLNat(V2)))
    active#(U103(tt())) -> mark#(tt())
    active#(U11(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U11(tt(),N,XS)) -> snd#(splitAt(N,XS))
    active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
    active#(U111(tt(),V1)) -> isLNat#(V1)
    active#(U111(tt(),V1)) -> U112#(isLNat(V1))
    active#(U111(tt(),V1)) -> mark#(U112(isLNat(V1)))
    active#(U112(tt())) -> mark#(tt())
    active#(U121(tt(),V1)) -> isNatural#(V1)
    active#(U121(tt(),V1)) -> U122#(isNatural(V1))
    active#(U121(tt(),V1)) -> mark#(U122(isNatural(V1)))
    active#(U122(tt())) -> mark#(tt())
    active#(U131(tt(),V1,V2)) -> isNatural#(V1)
    active#(U131(tt(),V1,V2)) -> U132#(isNatural(V1),V2)
    active#(U131(tt(),V1,V2)) -> mark#(U132(isNatural(V1),V2))
    active#(U132(tt(),V2)) -> isLNat#(V2)
    active#(U132(tt(),V2)) -> U133#(isLNat(V2))
    active#(U132(tt(),V2)) -> mark#(U133(isLNat(V2)))
    active#(U133(tt())) -> mark#(tt())
    active#(U141(tt(),V1,V2)) -> isLNat#(V1)
    active#(U141(tt(),V1,V2)) -> U142#(isLNat(V1),V2)
    active#(U141(tt(),V1,V2)) -> mark#(U142(isLNat(V1),V2))
    active#(U142(tt(),V2)) -> isLNat#(V2)
    active#(U142(tt(),V2)) -> U143#(isLNat(V2))
    active#(U142(tt(),V2)) -> mark#(U143(isLNat(V2)))
    active#(U143(tt())) -> mark#(tt())
    active#(U151(tt(),V1,V2)) -> isNatural#(V1)
    active#(U151(tt(),V1,V2)) -> U152#(isNatural(V1),V2)
    active#(U151(tt(),V1,V2)) -> mark#(U152(isNatural(V1),V2))
    active#(U152(tt(),V2)) -> isLNat#(V2)
    active#(U152(tt(),V2)) -> U153#(isLNat(V2))
    active#(U152(tt(),V2)) -> mark#(U153(isLNat(V2)))
    active#(U153(tt())) -> mark#(tt())
    active#(U161(tt(),N)) -> s#(N)
    active#(U161(tt(),N)) -> natsFrom#(s(N))
    active#(U161(tt(),N)) -> cons#(N,natsFrom(s(N)))
    active#(U161(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
    active#(U171(tt(),N,XS)) -> afterNth#(N,XS)
    active#(U171(tt(),N,XS)) -> head#(afterNth(N,XS))
    active#(U171(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
    active#(U181(tt(),Y)) -> mark#(Y)
    active#(U191(tt(),XS)) -> pair#(nil(),XS)
    active#(U191(tt(),XS)) -> mark#(pair(nil(),XS))
    active#(U201(tt(),N,X,XS)) -> splitAt#(N,XS)
    active#(U201(tt(),N,X,XS)) -> U202#(splitAt(N,XS),X)
    active#(U201(tt(),N,X,XS)) -> mark#(U202(splitAt(N,XS),X))
    active#(U202(pair(YS,ZS),X)) -> cons#(X,YS)
    active#(U202(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
    active#(U202(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
    active#(U21(tt(),X)) -> mark#(X)
    active#(U211(tt(),XS)) -> mark#(XS)
    active#(U221(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U221(tt(),N,XS)) -> fst#(splitAt(N,XS))
    active#(U221(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
    active#(U31(tt(),N)) -> mark#(N)
    active#(U41(tt(),V1,V2)) -> isNatural#(V1)
    active#(U41(tt(),V1,V2)) -> U42#(isNatural(V1),V2)
    active#(U41(tt(),V1,V2)) -> mark#(U42(isNatural(V1),V2))
    active#(U42(tt(),V2)) -> isLNat#(V2)
    active#(U42(tt(),V2)) -> U43#(isLNat(V2))
    active#(U42(tt(),V2)) -> mark#(U43(isLNat(V2)))
    active#(U43(tt())) -> mark#(tt())
    active#(U51(tt(),V1,V2)) -> isNatural#(V1)
    active#(U51(tt(),V1,V2)) -> U52#(isNatural(V1),V2)
    active#(U51(tt(),V1,V2)) -> mark#(U52(isNatural(V1),V2))
    active#(U52(tt(),V2)) -> isLNat#(V2)
    active#(U52(tt(),V2)) -> U53#(isLNat(V2))
    active#(U52(tt(),V2)) -> mark#(U53(isLNat(V2)))
    active#(U53(tt())) -> mark#(tt())
    active#(U61(tt(),V1)) -> isPLNat#(V1)
    active#(U61(tt(),V1)) -> U62#(isPLNat(V1))
    active#(U61(tt(),V1)) -> mark#(U62(isPLNat(V1)))
    active#(U62(tt())) -> mark#(tt())
    active#(U71(tt(),V1)) -> isNatural#(V1)
    active#(U71(tt(),V1)) -> U72#(isNatural(V1))
    active#(U71(tt(),V1)) -> mark#(U72(isNatural(V1)))
    active#(U72(tt())) -> mark#(tt())
    active#(U81(tt(),V1)) -> isPLNat#(V1)
    active#(U81(tt(),V1)) -> U82#(isPLNat(V1))
    active#(U81(tt(),V1)) -> mark#(U82(isPLNat(V1)))
    active#(U82(tt())) -> mark#(tt())
    active#(U91(tt(),V1)) -> isLNat#(V1)
    active#(U91(tt(),V1)) -> U92#(isLNat(V1))
    active#(U91(tt(),V1)) -> mark#(U92(isLNat(V1)))
    active#(U92(tt())) -> mark#(tt())
    active#(afterNth(N,XS)) -> isLNatKind#(XS)
    active#(afterNth(N,XS)) -> isLNat#(XS)
    active#(afterNth(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
    active#(afterNth(N,XS)) -> isNaturalKind#(N)
    active#(afterNth(N,XS)) -> isNatural#(N)
    active#(afterNth(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
    active#(afterNth(N,XS)) ->
    and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    active#(afterNth(N,XS)) ->
    U11#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    active#(afterNth(N,XS)) ->
    mark#(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    active#(and(tt(),X)) -> mark#(X)
    active#(fst(pair(X,Y))) -> isLNatKind#(Y)
    active#(fst(pair(X,Y))) -> isLNat#(Y)
    active#(fst(pair(X,Y))) -> and#(isLNat(Y),isLNatKind(Y))
    active#(fst(pair(X,Y))) -> isLNatKind#(X)
    active#(fst(pair(X,Y))) -> isLNat#(X)
    active#(fst(pair(X,Y))) -> and#(isLNat(X),isLNatKind(X))
    active#(fst(pair(X,Y))) -> and#(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
    active#(fst(pair(X,Y))) ->
    U21#(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
    active#(fst(pair(X,Y))) ->
    mark#(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
    active#(head(cons(N,XS))) -> isLNatKind#(XS)
    active#(head(cons(N,XS))) -> isLNat#(XS)
    active#(head(cons(N,XS))) -> and#(isLNat(XS),isLNatKind(XS))
    active#(head(cons(N,XS))) -> isNaturalKind#(N)
    active#(head(cons(N,XS))) -> isNatural#(N)
    active#(head(cons(N,XS))) -> and#(isNatural(N),isNaturalKind(N))
    active#(head(cons(N,XS))) ->
    and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    active#(head(cons(N,XS))) ->
    U31#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
    active#(head(cons(N,XS))) ->
    mark#(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
    active#(isLNat(nil())) -> mark#(tt())
    active#(isLNat(afterNth(V1,V2))) -> isLNatKind#(V2)
    active#(isLNat(afterNth(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNat(afterNth(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNat(afterNth(V1,V2))) -> U41#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    active#(isLNat(afterNth(V1,V2))) -> mark#(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active#(isLNat(cons(V1,V2))) -> isLNatKind#(V2)
    active#(isLNat(cons(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNat(cons(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNat(cons(V1,V2))) -> U51#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    active#(isLNat(cons(V1,V2))) -> mark#(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active#(isLNat(fst(V1))) -> isPLNatKind#(V1)
    active#(isLNat(fst(V1))) -> U61#(isPLNatKind(V1),V1)
    active#(isLNat(fst(V1))) -> mark#(U61(isPLNatKind(V1),V1))
    active#(isLNat(natsFrom(V1))) -> isNaturalKind#(V1)
    active#(isLNat(natsFrom(V1))) -> U71#(isNaturalKind(V1),V1)
    active#(isLNat(natsFrom(V1))) -> mark#(U71(isNaturalKind(V1),V1))
    active#(isLNat(snd(V1))) -> isPLNatKind#(V1)
    active#(isLNat(snd(V1))) -> U81#(isPLNatKind(V1),V1)
    active#(isLNat(snd(V1))) -> mark#(U81(isPLNatKind(V1),V1))
    active#(isLNat(tail(V1))) -> isLNatKind#(V1)
    active#(isLNat(tail(V1))) -> U91#(isLNatKind(V1),V1)
    active#(isLNat(tail(V1))) -> mark#(U91(isLNatKind(V1),V1))
    active#(isLNat(take(V1,V2))) -> isLNatKind#(V2)
    active#(isLNat(take(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNat(take(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNat(take(V1,V2))) -> U101#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    active#(isLNat(take(V1,V2))) -> mark#(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active#(isLNatKind(nil())) -> mark#(tt())
    active#(isLNatKind(afterNth(V1,V2))) -> isLNatKind#(V2)
    active#(isLNatKind(afterNth(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNatKind(afterNth(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNatKind(afterNth(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
    active#(isLNatKind(cons(V1,V2))) -> isLNatKind#(V2)
    active#(isLNatKind(cons(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNatKind(cons(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNatKind(cons(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
    active#(isLNatKind(fst(V1))) -> isPLNatKind#(V1)
    active#(isLNatKind(fst(V1))) -> mark#(isPLNatKind(V1))
    active#(isLNatKind(natsFrom(V1))) -> isNaturalKind#(V1)
    active#(isLNatKind(natsFrom(V1))) -> mark#(isNaturalKind(V1))
    active#(isLNatKind(snd(V1))) -> isPLNatKind#(V1)
    active#(isLNatKind(snd(V1))) -> mark#(isPLNatKind(V1))
    active#(isLNatKind(tail(V1))) -> isLNatKind#(V1)
    active#(isLNatKind(tail(V1))) -> mark#(isLNatKind(V1))
    active#(isLNatKind(take(V1,V2))) -> isLNatKind#(V2)
    active#(isLNatKind(take(V1,V2))) -> isNaturalKind#(V1)
    active#(isLNatKind(take(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isLNatKind(take(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
    active#(isNatural(0())) -> mark#(tt())
    active#(isNatural(head(V1))) -> isLNatKind#(V1)
    active#(isNatural(head(V1))) -> U111#(isLNatKind(V1),V1)
    active#(isNatural(head(V1))) -> mark#(U111(isLNatKind(V1),V1))
    active#(isNatural(s(V1))) -> isNaturalKind#(V1)
    active#(isNatural(s(V1))) -> U121#(isNaturalKind(V1),V1)
    active#(isNatural(s(V1))) -> mark#(U121(isNaturalKind(V1),V1))
    active#(isNatural(sel(V1,V2))) -> isLNatKind#(V2)
    active#(isNatural(sel(V1,V2))) -> isNaturalKind#(V1)
    active#(isNatural(sel(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isNatural(sel(V1,V2))) -> U131#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    active#(isNatural(sel(V1,V2))) -> mark#(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active#(isNaturalKind(0())) -> mark#(tt())
    active#(isNaturalKind(head(V1))) -> isLNatKind#(V1)
    active#(isNaturalKind(head(V1))) -> mark#(isLNatKind(V1))
    active#(isNaturalKind(s(V1))) -> isNaturalKind#(V1)
    active#(isNaturalKind(s(V1))) -> mark#(isNaturalKind(V1))
    active#(isNaturalKind(sel(V1,V2))) -> isLNatKind#(V2)
    active#(isNaturalKind(sel(V1,V2))) -> isNaturalKind#(V1)
    active#(isNaturalKind(sel(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isNaturalKind(sel(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
    active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V2)
    active#(isPLNat(pair(V1,V2))) -> isLNatKind#(V1)
    active#(isPLNat(pair(V1,V2))) -> and#(isLNatKind(V1),isLNatKind(V2))
    active#(isPLNat(pair(V1,V2))) -> U141#(and(isLNatKind(V1),isLNatKind(V2)),V1,V2)
    active#(isPLNat(pair(V1,V2))) -> mark#(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
    active#(isPLNat(splitAt(V1,V2))) -> isLNatKind#(V2)
    active#(isPLNat(splitAt(V1,V2))) -> isNaturalKind#(V1)
    active#(isPLNat(splitAt(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isPLNat(splitAt(V1,V2))) -> U151#(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V2)
    active#(isPLNatKind(pair(V1,V2))) -> isLNatKind#(V1)
    active#(isPLNatKind(pair(V1,V2))) -> and#(isLNatKind(V1),isLNatKind(V2))
    active#(isPLNatKind(pair(V1,V2))) -> mark#(and(isLNatKind(V1),isLNatKind(V2)))
    active#(isPLNatKind(splitAt(V1,V2))) -> isLNatKind#(V2)
    active#(isPLNatKind(splitAt(V1,V2))) -> isNaturalKind#(V1)
    active#(isPLNatKind(splitAt(V1,V2))) -> and#(isNaturalKind(V1),isLNatKind(V2))
    active#(isPLNatKind(splitAt(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
    active#(natsFrom(N)) -> isNaturalKind#(N)
    active#(natsFrom(N)) -> isNatural#(N)
    active#(natsFrom(N)) -> and#(isNatural(N),isNaturalKind(N))
    active#(natsFrom(N)) -> U161#(and(isNatural(N),isNaturalKind(N)),N)
    active#(natsFrom(N)) -> mark#(U161(and(isNatural(N),isNaturalKind(N)),N))
    active#(sel(N,XS)) -> isLNatKind#(XS)
    active#(sel(N,XS)) -> isLNat#(XS)
    active#(sel(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
    active#(sel(N,XS)) -> isNaturalKind#(N)
    active#(sel(N,XS)) -> isNatural#(N)
    active#(sel(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
    active#(sel(N,XS)) -> and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    active#(sel(N,XS)) ->
    U171#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    active#(sel(N,XS)) ->
    mark#(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    active#(snd(pair(X,Y))) -> isLNatKind#(Y)
    active#(snd(pair(X,Y))) -> isLNat#(Y)
    active#(snd(pair(X,Y))) -> and#(isLNat(Y),isLNatKind(Y))
    active#(snd(pair(X,Y))) -> isLNatKind#(X)
    active#(snd(pair(X,Y))) -> isLNat#(X)
    active#(snd(pair(X,Y))) -> and#(isLNat(X),isLNatKind(X))
    active#(snd(pair(X,Y))) -> and#(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
    active#(snd(pair(X,Y))) ->
    U181#(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
    active#(snd(pair(X,Y))) ->
    mark#(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
    active#(splitAt(0(),XS)) -> isLNatKind#(XS)
    active#(splitAt(0(),XS)) -> isLNat#(XS)
    active#(splitAt(0(),XS)) -> and#(isLNat(XS),isLNatKind(XS))
    active#(splitAt(0(),XS)) -> U191#(and(isLNat(XS),isLNatKind(XS)),XS)
    active#(splitAt(0(),XS)) -> mark#(U191(and(isLNat(XS),isLNatKind(XS)),XS))
    active#(splitAt(s(N),cons(X,XS))) -> isLNatKind#(XS)
    active#(splitAt(s(N),cons(X,XS))) -> isLNat#(XS)
    active#(splitAt(s(N),cons(X,XS))) -> and#(isLNat(XS),isLNatKind(XS))
    active#(splitAt(s(N),cons(X,XS))) -> isNaturalKind#(X)
    active#(splitAt(s(N),cons(X,XS))) -> isNatural#(X)
    active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(X),isNaturalKind(X))
    active#(splitAt(s(N),cons(X,XS))) ->
    and#(and(isNatural(X),isNaturalKind(X)),and(isLNat(XS),isLNatKind(XS)))
    active#(splitAt(s(N),cons(X,XS))) -> isNaturalKind#(N)
    active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
    active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(N),isNaturalKind(N))
    active#(splitAt(s(N),cons(X,XS))) ->
    and#(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                and(isLNat(XS),isLNatKind(XS))))
    active#(splitAt(s(N),cons(X,XS))) ->
    U201#(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                     and(isLNat(XS),isLNatKind(XS)))),
          N,X,XS)
    active#(splitAt(s(N),cons(X,XS))) ->
    mark#(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
    active#(tail(cons(N,XS))) -> isLNatKind#(XS)
    active#(tail(cons(N,XS))) -> isLNat#(XS)
    active#(tail(cons(N,XS))) -> and#(isLNat(XS),isLNatKind(XS))
    active#(tail(cons(N,XS))) -> isNaturalKind#(N)
    active#(tail(cons(N,XS))) -> isNatural#(N)
    active#(tail(cons(N,XS))) -> and#(isNatural(N),isNaturalKind(N))
    active#(tail(cons(N,XS))) ->
    and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    active#(tail(cons(N,XS))) ->
    U211#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
    active#(tail(cons(N,XS))) ->
    mark#(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
    active#(take(N,XS)) -> isLNatKind#(XS)
    active#(take(N,XS)) -> isLNat#(XS)
    active#(take(N,XS)) -> and#(isLNat(XS),isLNatKind(XS))
    active#(take(N,XS)) -> isNaturalKind#(N)
    active#(take(N,XS)) -> isNatural#(N)
    active#(take(N,XS)) -> and#(isNatural(N),isNaturalKind(N))
    active#(take(N,XS)) -> and#(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    active#(take(N,XS)) ->
    U221#(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    active#(take(N,XS)) ->
    mark#(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    mark#(U101(X1,X2,X3)) -> mark#(X1)
    mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3)
    mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
    mark#(tt()) -> active#(tt())
    mark#(U102(X1,X2)) -> mark#(X1)
    mark#(U102(X1,X2)) -> U102#(mark(X1),X2)
    mark#(U102(X1,X2)) -> active#(U102(mark(X1),X2))
    mark#(isNatural(X)) -> active#(isNatural(X))
    mark#(U103(X)) -> mark#(X)
    mark#(U103(X)) -> U103#(mark(X))
    mark#(U103(X)) -> active#(U103(mark(X)))
    mark#(isLNat(X)) -> active#(isLNat(X))
    mark#(U11(X1,X2,X3)) -> mark#(X1)
    mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3)
    mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
    mark#(snd(X)) -> mark#(X)
    mark#(snd(X)) -> snd#(mark(X))
    mark#(snd(X)) -> active#(snd(mark(X)))
    mark#(splitAt(X1,X2)) -> mark#(X2)
    mark#(splitAt(X1,X2)) -> mark#(X1)
    mark#(splitAt(X1,X2)) -> splitAt#(mark(X1),mark(X2))
    mark#(splitAt(X1,X2)) -> active#(splitAt(mark(X1),mark(X2)))
    mark#(U111(X1,X2)) -> mark#(X1)
    mark#(U111(X1,X2)) -> U111#(mark(X1),X2)
    mark#(U111(X1,X2)) -> active#(U111(mark(X1),X2))
    mark#(U112(X)) -> mark#(X)
    mark#(U112(X)) -> U112#(mark(X))
    mark#(U112(X)) -> active#(U112(mark(X)))
    mark#(U121(X1,X2)) -> mark#(X1)
    mark#(U121(X1,X2)) -> U121#(mark(X1),X2)
    mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2))
    mark#(U122(X)) -> mark#(X)
    mark#(U122(X)) -> U122#(mark(X))
    mark#(U122(X)) -> active#(U122(mark(X)))
    mark#(U131(X1,X2,X3)) -> mark#(X1)
    mark#(U131(X1,X2,X3)) -> U131#(mark(X1),X2,X3)
    mark#(U131(X1,X2,X3)) -> active#(U131(mark(X1),X2,X3))
    mark#(U132(X1,X2)) -> mark#(X1)
    mark#(U132(X1,X2)) -> U132#(mark(X1),X2)
    mark#(U132(X1,X2)) -> active#(U132(mark(X1),X2))
    mark#(U133(X)) -> mark#(X)
    mark#(U133(X)) -> U133#(mark(X))
    mark#(U133(X)) -> active#(U133(mark(X)))
    mark#(U141(X1,X2,X3)) -> mark#(X1)
    mark#(U141(X1,X2,X3)) -> U141#(mark(X1),X2,X3)
    mark#(U141(X1,X2,X3)) -> active#(U141(mark(X1),X2,X3))
    mark#(U142(X1,X2)) -> mark#(X1)
    mark#(U142(X1,X2)) -> U142#(mark(X1),X2)
    mark#(U142(X1,X2)) -> active#(U142(mark(X1),X2))
    mark#(U143(X)) -> mark#(X)
    mark#(U143(X)) -> U143#(mark(X))
    mark#(U143(X)) -> active#(U143(mark(X)))
    mark#(U151(X1,X2,X3)) -> mark#(X1)
    mark#(U151(X1,X2,X3)) -> U151#(mark(X1),X2,X3)
    mark#(U151(X1,X2,X3)) -> active#(U151(mark(X1),X2,X3))
    mark#(U152(X1,X2)) -> mark#(X1)
    mark#(U152(X1,X2)) -> U152#(mark(X1),X2)
    mark#(U152(X1,X2)) -> active#(U152(mark(X1),X2))
    mark#(U153(X)) -> mark#(X)
    mark#(U153(X)) -> U153#(mark(X))
    mark#(U153(X)) -> active#(U153(mark(X)))
    mark#(U161(X1,X2)) -> mark#(X1)
    mark#(U161(X1,X2)) -> U161#(mark(X1),X2)
    mark#(U161(X1,X2)) -> active#(U161(mark(X1),X2))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> cons#(mark(X1),X2)
    mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
    mark#(natsFrom(X)) -> mark#(X)
    mark#(natsFrom(X)) -> natsFrom#(mark(X))
    mark#(natsFrom(X)) -> active#(natsFrom(mark(X)))
    mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> s#(mark(X))
    mark#(s(X)) -> active#(s(mark(X)))
    mark#(U171(X1,X2,X3)) -> mark#(X1)
    mark#(U171(X1,X2,X3)) -> U171#(mark(X1),X2,X3)
    mark#(U171(X1,X2,X3)) -> active#(U171(mark(X1),X2,X3))
    mark#(head(X)) -> mark#(X)
    mark#(head(X)) -> head#(mark(X))
    mark#(head(X)) -> active#(head(mark(X)))
    mark#(afterNth(X1,X2)) -> mark#(X2)
    mark#(afterNth(X1,X2)) -> mark#(X1)
    mark#(afterNth(X1,X2)) -> afterNth#(mark(X1),mark(X2))
    mark#(afterNth(X1,X2)) -> active#(afterNth(mark(X1),mark(X2)))
    mark#(U181(X1,X2)) -> mark#(X1)
    mark#(U181(X1,X2)) -> U181#(mark(X1),X2)
    mark#(U181(X1,X2)) -> active#(U181(mark(X1),X2))
    mark#(U191(X1,X2)) -> mark#(X1)
    mark#(U191(X1,X2)) -> U191#(mark(X1),X2)
    mark#(U191(X1,X2)) -> active#(U191(mark(X1),X2))
    mark#(pair(X1,X2)) -> mark#(X2)
    mark#(pair(X1,X2)) -> mark#(X1)
    mark#(pair(X1,X2)) -> pair#(mark(X1),mark(X2))
    mark#(pair(X1,X2)) -> active#(pair(mark(X1),mark(X2)))
    mark#(nil()) -> active#(nil())
    mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U201(X1,X2,X3,X4)) -> U201#(mark(X1),X2,X3,X4)
    mark#(U201(X1,X2,X3,X4)) -> active#(U201(mark(X1),X2,X3,X4))
    mark#(U202(X1,X2)) -> mark#(X1)
    mark#(U202(X1,X2)) -> U202#(mark(X1),X2)
    mark#(U202(X1,X2)) -> active#(U202(mark(X1),X2))
    mark#(U21(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
    mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
    mark#(U211(X1,X2)) -> mark#(X1)
    mark#(U211(X1,X2)) -> U211#(mark(X1),X2)
    mark#(U211(X1,X2)) -> active#(U211(mark(X1),X2))
    mark#(U221(X1,X2,X3)) -> mark#(X1)
    mark#(U221(X1,X2,X3)) -> U221#(mark(X1),X2,X3)
    mark#(U221(X1,X2,X3)) -> active#(U221(mark(X1),X2,X3))
    mark#(fst(X)) -> mark#(X)
    mark#(fst(X)) -> fst#(mark(X))
    mark#(fst(X)) -> active#(fst(mark(X)))
    mark#(U31(X1,X2)) -> mark#(X1)
    mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
    mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
    mark#(U41(X1,X2,X3)) -> mark#(X1)
    mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
    mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
    mark#(U42(X1,X2)) -> mark#(X1)
    mark#(U42(X1,X2)) -> U42#(mark(X1),X2)
    mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
    mark#(U43(X)) -> mark#(X)
    mark#(U43(X)) -> U43#(mark(X))
    mark#(U43(X)) -> active#(U43(mark(X)))
    mark#(U51(X1,X2,X3)) -> mark#(X1)
    mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
    mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
    mark#(U52(X1,X2)) -> mark#(X1)
    mark#(U52(X1,X2)) -> U52#(mark(X1),X2)
    mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
    mark#(U53(X)) -> mark#(X)
    mark#(U53(X)) -> U53#(mark(X))
    mark#(U53(X)) -> active#(U53(mark(X)))
    mark#(U61(X1,X2)) -> mark#(X1)
    mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
    mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
    mark#(U62(X)) -> mark#(X)
    mark#(U62(X)) -> U62#(mark(X))
    mark#(U62(X)) -> active#(U62(mark(X)))
    mark#(isPLNat(X)) -> active#(isPLNat(X))
    mark#(U71(X1,X2)) -> mark#(X1)
    mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
    mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
    mark#(U72(X)) -> mark#(X)
    mark#(U72(X)) -> U72#(mark(X))
    mark#(U72(X)) -> active#(U72(mark(X)))
    mark#(U81(X1,X2)) -> mark#(X1)
    mark#(U81(X1,X2)) -> U81#(mark(X1),X2)
    mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
    mark#(U82(X)) -> mark#(X)
    mark#(U82(X)) -> U82#(mark(X))
    mark#(U82(X)) -> active#(U82(mark(X)))
    mark#(U91(X1,X2)) -> mark#(X1)
    mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
    mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
    mark#(U92(X)) -> mark#(X)
    mark#(U92(X)) -> U92#(mark(X))
    mark#(U92(X)) -> active#(U92(mark(X)))
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> and#(mark(X1),X2)
    mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
    mark#(isNaturalKind(X)) -> active#(isNaturalKind(X))
    mark#(isLNatKind(X)) -> active#(isLNatKind(X))
    mark#(isPLNatKind(X)) -> active#(isPLNatKind(X))
    mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> tail#(mark(X))
    mark#(tail(X)) -> active#(tail(mark(X)))
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> take#(mark(X1),mark(X2))
    mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2)))
    mark#(0()) -> active#(0())
    mark#(sel(X1,X2)) -> mark#(X2)
    mark#(sel(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> sel#(mark(X1),mark(X2))
    mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2)))
    U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
    U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
    U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
    U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
    U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
    U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
    U102#(mark(X1),X2) -> U102#(X1,X2)
    U102#(X1,mark(X2)) -> U102#(X1,X2)
    U102#(active(X1),X2) -> U102#(X1,X2)
    U102#(X1,active(X2)) -> U102#(X1,X2)
    isNatural#(mark(X)) -> isNatural#(X)
    isNatural#(active(X)) -> isNatural#(X)
    U103#(mark(X)) -> U103#(X)
    U103#(active(X)) -> U103#(X)
    isLNat#(mark(X)) -> isLNat#(X)
    isLNat#(active(X)) -> isLNat#(X)
    U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
    U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
    U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
    U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
    U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
    U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
    snd#(mark(X)) -> snd#(X)
    snd#(active(X)) -> snd#(X)
    splitAt#(mark(X1),X2) -> splitAt#(X1,X2)
    splitAt#(X1,mark(X2)) -> splitAt#(X1,X2)
    splitAt#(active(X1),X2) -> splitAt#(X1,X2)
    splitAt#(X1,active(X2)) -> splitAt#(X1,X2)
    U111#(mark(X1),X2) -> U111#(X1,X2)
    U111#(X1,mark(X2)) -> U111#(X1,X2)
    U111#(active(X1),X2) -> U111#(X1,X2)
    U111#(X1,active(X2)) -> U111#(X1,X2)
    U112#(mark(X)) -> U112#(X)
    U112#(active(X)) -> U112#(X)
    U121#(mark(X1),X2) -> U121#(X1,X2)
    U121#(X1,mark(X2)) -> U121#(X1,X2)
    U121#(active(X1),X2) -> U121#(X1,X2)
    U121#(X1,active(X2)) -> U121#(X1,X2)
    U122#(mark(X)) -> U122#(X)
    U122#(active(X)) -> U122#(X)
    U131#(mark(X1),X2,X3) -> U131#(X1,X2,X3)
    U131#(X1,mark(X2),X3) -> U131#(X1,X2,X3)
    U131#(X1,X2,mark(X3)) -> U131#(X1,X2,X3)
    U131#(active(X1),X2,X3) -> U131#(X1,X2,X3)
    U131#(X1,active(X2),X3) -> U131#(X1,X2,X3)
    U131#(X1,X2,active(X3)) -> U131#(X1,X2,X3)
    U132#(mark(X1),X2) -> U132#(X1,X2)
    U132#(X1,mark(X2)) -> U132#(X1,X2)
    U132#(active(X1),X2) -> U132#(X1,X2)
    U132#(X1,active(X2)) -> U132#(X1,X2)
    U133#(mark(X)) -> U133#(X)
    U133#(active(X)) -> U133#(X)
    U141#(mark(X1),X2,X3) -> U141#(X1,X2,X3)
    U141#(X1,mark(X2),X3) -> U141#(X1,X2,X3)
    U141#(X1,X2,mark(X3)) -> U141#(X1,X2,X3)
    U141#(active(X1),X2,X3) -> U141#(X1,X2,X3)
    U141#(X1,active(X2),X3) -> U141#(X1,X2,X3)
    U141#(X1,X2,active(X3)) -> U141#(X1,X2,X3)
    U142#(mark(X1),X2) -> U142#(X1,X2)
    U142#(X1,mark(X2)) -> U142#(X1,X2)
    U142#(active(X1),X2) -> U142#(X1,X2)
    U142#(X1,active(X2)) -> U142#(X1,X2)
    U143#(mark(X)) -> U143#(X)
    U143#(active(X)) -> U143#(X)
    U151#(mark(X1),X2,X3) -> U151#(X1,X2,X3)
    U151#(X1,mark(X2),X3) -> U151#(X1,X2,X3)
    U151#(X1,X2,mark(X3)) -> U151#(X1,X2,X3)
    U151#(active(X1),X2,X3) -> U151#(X1,X2,X3)
    U151#(X1,active(X2),X3) -> U151#(X1,X2,X3)
    U151#(X1,X2,active(X3)) -> U151#(X1,X2,X3)
    U152#(mark(X1),X2) -> U152#(X1,X2)
    U152#(X1,mark(X2)) -> U152#(X1,X2)
    U152#(active(X1),X2) -> U152#(X1,X2)
    U152#(X1,active(X2)) -> U152#(X1,X2)
    U153#(mark(X)) -> U153#(X)
    U153#(active(X)) -> U153#(X)
    U161#(mark(X1),X2) -> U161#(X1,X2)
    U161#(X1,mark(X2)) -> U161#(X1,X2)
    U161#(active(X1),X2) -> U161#(X1,X2)
    U161#(X1,active(X2)) -> U161#(X1,X2)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    cons#(X1,mark(X2)) -> cons#(X1,X2)
    cons#(active(X1),X2) -> cons#(X1,X2)
    cons#(X1,active(X2)) -> cons#(X1,X2)
    natsFrom#(mark(X)) -> natsFrom#(X)
    natsFrom#(active(X)) -> natsFrom#(X)
    s#(mark(X)) -> s#(X)
    s#(active(X)) -> s#(X)
    U171#(mark(X1),X2,X3) -> U171#(X1,X2,X3)
    U171#(X1,mark(X2),X3) -> U171#(X1,X2,X3)
    U171#(X1,X2,mark(X3)) -> U171#(X1,X2,X3)
    U171#(active(X1),X2,X3) -> U171#(X1,X2,X3)
    U171#(X1,active(X2),X3) -> U171#(X1,X2,X3)
    U171#(X1,X2,active(X3)) -> U171#(X1,X2,X3)
    head#(mark(X)) -> head#(X)
    head#(active(X)) -> head#(X)
    afterNth#(mark(X1),X2) -> afterNth#(X1,X2)
    afterNth#(X1,mark(X2)) -> afterNth#(X1,X2)
    afterNth#(active(X1),X2) -> afterNth#(X1,X2)
    afterNth#(X1,active(X2)) -> afterNth#(X1,X2)
    U181#(mark(X1),X2) -> U181#(X1,X2)
    U181#(X1,mark(X2)) -> U181#(X1,X2)
    U181#(active(X1),X2) -> U181#(X1,X2)
    U181#(X1,active(X2)) -> U181#(X1,X2)
    U191#(mark(X1),X2) -> U191#(X1,X2)
    U191#(X1,mark(X2)) -> U191#(X1,X2)
    U191#(active(X1),X2) -> U191#(X1,X2)
    U191#(X1,active(X2)) -> U191#(X1,X2)
    pair#(mark(X1),X2) -> pair#(X1,X2)
    pair#(X1,mark(X2)) -> pair#(X1,X2)
    pair#(active(X1),X2) -> pair#(X1,X2)
    pair#(X1,active(X2)) -> pair#(X1,X2)
    U201#(mark(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,mark(X2),X3,X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,X2,mark(X3),X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,X2,X3,mark(X4)) -> U201#(X1,X2,X3,X4)
    U201#(active(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,active(X2),X3,X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,X2,active(X3),X4) -> U201#(X1,X2,X3,X4)
    U201#(X1,X2,X3,active(X4)) -> U201#(X1,X2,X3,X4)
    U202#(mark(X1),X2) -> U202#(X1,X2)
    U202#(X1,mark(X2)) -> U202#(X1,X2)
    U202#(active(X1),X2) -> U202#(X1,X2)
    U202#(X1,active(X2)) -> U202#(X1,X2)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U21#(X1,mark(X2)) -> U21#(X1,X2)
    U21#(active(X1),X2) -> U21#(X1,X2)
    U21#(X1,active(X2)) -> U21#(X1,X2)
    U211#(mark(X1),X2) -> U211#(X1,X2)
    U211#(X1,mark(X2)) -> U211#(X1,X2)
    U211#(active(X1),X2) -> U211#(X1,X2)
    U211#(X1,active(X2)) -> U211#(X1,X2)
    U221#(mark(X1),X2,X3) -> U221#(X1,X2,X3)
    U221#(X1,mark(X2),X3) -> U221#(X1,X2,X3)
    U221#(X1,X2,mark(X3)) -> U221#(X1,X2,X3)
    U221#(active(X1),X2,X3) -> U221#(X1,X2,X3)
    U221#(X1,active(X2),X3) -> U221#(X1,X2,X3)
    U221#(X1,X2,active(X3)) -> U221#(X1,X2,X3)
    fst#(mark(X)) -> fst#(X)
    fst#(active(X)) -> fst#(X)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U31#(X1,mark(X2)) -> U31#(X1,X2)
    U31#(active(X1),X2) -> U31#(X1,X2)
    U31#(X1,active(X2)) -> U31#(X1,X2)
    U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
    U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
    U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
    U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
    U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
    U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
    U42#(mark(X1),X2) -> U42#(X1,X2)
    U42#(X1,mark(X2)) -> U42#(X1,X2)
    U42#(active(X1),X2) -> U42#(X1,X2)
    U42#(X1,active(X2)) -> U42#(X1,X2)
    U43#(mark(X)) -> U43#(X)
    U43#(active(X)) -> U43#(X)
    U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
    U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
    U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
    U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
    U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
    U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
    U52#(mark(X1),X2) -> U52#(X1,X2)
    U52#(X1,mark(X2)) -> U52#(X1,X2)
    U52#(active(X1),X2) -> U52#(X1,X2)
    U52#(X1,active(X2)) -> U52#(X1,X2)
    U53#(mark(X)) -> U53#(X)
    U53#(active(X)) -> U53#(X)
    U61#(mark(X1),X2) -> U61#(X1,X2)
    U61#(X1,mark(X2)) -> U61#(X1,X2)
    U61#(active(X1),X2) -> U61#(X1,X2)
    U61#(X1,active(X2)) -> U61#(X1,X2)
    U62#(mark(X)) -> U62#(X)
    U62#(active(X)) -> U62#(X)
    isPLNat#(mark(X)) -> isPLNat#(X)
    isPLNat#(active(X)) -> isPLNat#(X)
    U71#(mark(X1),X2) -> U71#(X1,X2)
    U71#(X1,mark(X2)) -> U71#(X1,X2)
    U71#(active(X1),X2) -> U71#(X1,X2)
    U71#(X1,active(X2)) -> U71#(X1,X2)
    U72#(mark(X)) -> U72#(X)
    U72#(active(X)) -> U72#(X)
    U81#(mark(X1),X2) -> U81#(X1,X2)
    U81#(X1,mark(X2)) -> U81#(X1,X2)
    U81#(active(X1),X2) -> U81#(X1,X2)
    U81#(X1,active(X2)) -> U81#(X1,X2)
    U82#(mark(X)) -> U82#(X)
    U82#(active(X)) -> U82#(X)
    U91#(mark(X1),X2) -> U91#(X1,X2)
    U91#(X1,mark(X2)) -> U91#(X1,X2)
    U91#(active(X1),X2) -> U91#(X1,X2)
    U91#(X1,active(X2)) -> U91#(X1,X2)
    U92#(mark(X)) -> U92#(X)
    U92#(active(X)) -> U92#(X)
    and#(mark(X1),X2) -> and#(X1,X2)
    and#(X1,mark(X2)) -> and#(X1,X2)
    and#(active(X1),X2) -> and#(X1,X2)
    and#(X1,active(X2)) -> and#(X1,X2)
    isNaturalKind#(mark(X)) -> isNaturalKind#(X)
    isNaturalKind#(active(X)) -> isNaturalKind#(X)
    isLNatKind#(mark(X)) -> isLNatKind#(X)
    isLNatKind#(active(X)) -> isLNatKind#(X)
    isPLNatKind#(mark(X)) -> isPLNatKind#(X)
    isPLNatKind#(active(X)) -> isPLNatKind#(X)
    tail#(mark(X)) -> tail#(X)
    tail#(active(X)) -> tail#(X)
    take#(mark(X1),X2) -> take#(X1,X2)
    take#(X1,mark(X2)) -> take#(X1,X2)
    take#(active(X1),X2) -> take#(X1,X2)
    take#(X1,active(X2)) -> take#(X1,X2)
    sel#(mark(X1),X2) -> sel#(X1,X2)
    sel#(X1,mark(X2)) -> sel#(X1,X2)
    sel#(active(X1),X2) -> sel#(X1,X2)
    sel#(X1,active(X2)) -> sel#(X1,X2)
   TRS:
    active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
    active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
    active(U103(tt())) -> mark(tt())
    active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
    active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
    active(U112(tt())) -> mark(tt())
    active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
    active(U122(tt())) -> mark(tt())
    active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
    active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
    active(U133(tt())) -> mark(tt())
    active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
    active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
    active(U143(tt())) -> mark(tt())
    active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
    active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
    active(U153(tt())) -> mark(tt())
    active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
    active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
    active(U181(tt(),Y)) -> mark(Y)
    active(U191(tt(),XS)) -> mark(pair(nil(),XS))
    active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
    active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
    active(U21(tt(),X)) -> mark(X)
    active(U211(tt(),XS)) -> mark(XS)
    active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
    active(U31(tt(),N)) -> mark(N)
    active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
    active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
    active(U43(tt())) -> mark(tt())
    active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
    active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
    active(U53(tt())) -> mark(tt())
    active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
    active(U62(tt())) -> mark(tt())
    active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
    active(U72(tt())) -> mark(tt())
    active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
    active(U82(tt())) -> mark(tt())
    active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
    active(U92(tt())) -> mark(tt())
    active(afterNth(N,XS)) ->
    mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    active(and(tt(),X)) -> mark(X)
    active(fst(pair(X,Y))) ->
    mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
    active(head(cons(N,XS))) ->
    mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
    active(isLNat(nil())) -> mark(tt())
    active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
    active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
    active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
    active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
    active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active(isLNatKind(nil())) -> mark(tt())
    active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
    active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
    active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
    active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
    active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
    active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
    active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
    active(isNatural(0())) -> mark(tt())
    active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
    active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
    active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active(isNaturalKind(0())) -> mark(tt())
    active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
    active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
    active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
    active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
    active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
    active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
    active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
    active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
    active(sel(N,XS)) ->
    mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    active(snd(pair(X,Y))) ->
    mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
    active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
    active(splitAt(s(N),cons(X,XS))) ->
    mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                         and(isLNat(XS),isLNatKind(XS)))),
              N,X,XS))
    active(tail(cons(N,XS))) ->
    mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
    active(take(N,XS)) ->
    mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
    mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
    mark(tt()) -> active(tt())
    mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
    mark(isNatural(X)) -> active(isNatural(X))
    mark(U103(X)) -> active(U103(mark(X)))
    mark(isLNat(X)) -> active(isLNat(X))
    mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
    mark(snd(X)) -> active(snd(mark(X)))
    mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
    mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
    mark(U112(X)) -> active(U112(mark(X)))
    mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
    mark(U122(X)) -> active(U122(mark(X)))
    mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
    mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
    mark(U133(X)) -> active(U133(mark(X)))
    mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
    mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
    mark(U143(X)) -> active(U143(mark(X)))
    mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
    mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
    mark(U153(X)) -> active(U153(mark(X)))
    mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
    mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    mark(natsFrom(X)) -> active(natsFrom(mark(X)))
    mark(s(X)) -> active(s(mark(X)))
    mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
    mark(head(X)) -> active(head(mark(X)))
    mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
    mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
    mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
    mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
    mark(nil()) -> active(nil())
    mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
    mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
    mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
    mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
    mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
    mark(fst(X)) -> active(fst(mark(X)))
    mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
    mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
    mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
    mark(U43(X)) -> active(U43(mark(X)))
    mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
    mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
    mark(U53(X)) -> active(U53(mark(X)))
    mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
    mark(U62(X)) -> active(U62(mark(X)))
    mark(isPLNat(X)) -> active(isPLNat(X))
    mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
    mark(U72(X)) -> active(U72(mark(X)))
    mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
    mark(U82(X)) -> active(U82(mark(X)))
    mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
    mark(U92(X)) -> active(U92(mark(X)))
    mark(and(X1,X2)) -> active(and(mark(X1),X2))
    mark(isNaturalKind(X)) -> active(isNaturalKind(X))
    mark(isLNatKind(X)) -> active(isLNatKind(X))
    mark(isPLNatKind(X)) -> active(isPLNatKind(X))
    mark(tail(X)) -> active(tail(mark(X)))
    mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
    mark(0()) -> active(0())
    mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
    U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
    U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
    U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
    U101(active(X1),X2,X3) -> U101(X1,X2,X3)
    U101(X1,active(X2),X3) -> U101(X1,X2,X3)
    U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
    U102(mark(X1),X2) -> U102(X1,X2)
    U102(X1,mark(X2)) -> U102(X1,X2)
    U102(active(X1),X2) -> U102(X1,X2)
    U102(X1,active(X2)) -> U102(X1,X2)
    isNatural(mark(X)) -> isNatural(X)
    isNatural(active(X)) -> isNatural(X)
    U103(mark(X)) -> U103(X)
    U103(active(X)) -> U103(X)
    isLNat(mark(X)) -> isLNat(X)
    isLNat(active(X)) -> isLNat(X)
    U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
    U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
    U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
    U11(active(X1),X2,X3) -> U11(X1,X2,X3)
    U11(X1,active(X2),X3) -> U11(X1,X2,X3)
    U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
    snd(mark(X)) -> snd(X)
    snd(active(X)) -> snd(X)
    splitAt(mark(X1),X2) -> splitAt(X1,X2)
    splitAt(X1,mark(X2)) -> splitAt(X1,X2)
    splitAt(active(X1),X2) -> splitAt(X1,X2)
    splitAt(X1,active(X2)) -> splitAt(X1,X2)
    U111(mark(X1),X2) -> U111(X1,X2)
    U111(X1,mark(X2)) -> U111(X1,X2)
    U111(active(X1),X2) -> U111(X1,X2)
    U111(X1,active(X2)) -> U111(X1,X2)
    U112(mark(X)) -> U112(X)
    U112(active(X)) -> U112(X)
    U121(mark(X1),X2) -> U121(X1,X2)
    U121(X1,mark(X2)) -> U121(X1,X2)
    U121(active(X1),X2) -> U121(X1,X2)
    U121(X1,active(X2)) -> U121(X1,X2)
    U122(mark(X)) -> U122(X)
    U122(active(X)) -> U122(X)
    U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
    U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
    U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
    U131(active(X1),X2,X3) -> U131(X1,X2,X3)
    U131(X1,active(X2),X3) -> U131(X1,X2,X3)
    U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
    U132(mark(X1),X2) -> U132(X1,X2)
    U132(X1,mark(X2)) -> U132(X1,X2)
    U132(active(X1),X2) -> U132(X1,X2)
    U132(X1,active(X2)) -> U132(X1,X2)
    U133(mark(X)) -> U133(X)
    U133(active(X)) -> U133(X)
    U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
    U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
    U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
    U141(active(X1),X2,X3) -> U141(X1,X2,X3)
    U141(X1,active(X2),X3) -> U141(X1,X2,X3)
    U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
    U142(mark(X1),X2) -> U142(X1,X2)
    U142(X1,mark(X2)) -> U142(X1,X2)
    U142(active(X1),X2) -> U142(X1,X2)
    U142(X1,active(X2)) -> U142(X1,X2)
    U143(mark(X)) -> U143(X)
    U143(active(X)) -> U143(X)
    U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
    U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
    U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
    U151(active(X1),X2,X3) -> U151(X1,X2,X3)
    U151(X1,active(X2),X3) -> U151(X1,X2,X3)
    U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
    U152(mark(X1),X2) -> U152(X1,X2)
    U152(X1,mark(X2)) -> U152(X1,X2)
    U152(active(X1),X2) -> U152(X1,X2)
    U152(X1,active(X2)) -> U152(X1,X2)
    U153(mark(X)) -> U153(X)
    U153(active(X)) -> U153(X)
    U161(mark(X1),X2) -> U161(X1,X2)
    U161(X1,mark(X2)) -> U161(X1,X2)
    U161(active(X1),X2) -> U161(X1,X2)
    U161(X1,active(X2)) -> U161(X1,X2)
    cons(mark(X1),X2) -> cons(X1,X2)
    cons(X1,mark(X2)) -> cons(X1,X2)
    cons(active(X1),X2) -> cons(X1,X2)
    cons(X1,active(X2)) -> cons(X1,X2)
    natsFrom(mark(X)) -> natsFrom(X)
    natsFrom(active(X)) -> natsFrom(X)
    s(mark(X)) -> s(X)
    s(active(X)) -> s(X)
    U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
    U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
    U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
    U171(active(X1),X2,X3) -> U171(X1,X2,X3)
    U171(X1,active(X2),X3) -> U171(X1,X2,X3)
    U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
    head(mark(X)) -> head(X)
    head(active(X)) -> head(X)
    afterNth(mark(X1),X2) -> afterNth(X1,X2)
    afterNth(X1,mark(X2)) -> afterNth(X1,X2)
    afterNth(active(X1),X2) -> afterNth(X1,X2)
    afterNth(X1,active(X2)) -> afterNth(X1,X2)
    U181(mark(X1),X2) -> U181(X1,X2)
    U181(X1,mark(X2)) -> U181(X1,X2)
    U181(active(X1),X2) -> U181(X1,X2)
    U181(X1,active(X2)) -> U181(X1,X2)
    U191(mark(X1),X2) -> U191(X1,X2)
    U191(X1,mark(X2)) -> U191(X1,X2)
    U191(active(X1),X2) -> U191(X1,X2)
    U191(X1,active(X2)) -> U191(X1,X2)
    pair(mark(X1),X2) -> pair(X1,X2)
    pair(X1,mark(X2)) -> pair(X1,X2)
    pair(active(X1),X2) -> pair(X1,X2)
    pair(X1,active(X2)) -> pair(X1,X2)
    U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
    U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
    U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
    U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
    U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
    U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
    U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
    U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
    U202(mark(X1),X2) -> U202(X1,X2)
    U202(X1,mark(X2)) -> U202(X1,X2)
    U202(active(X1),X2) -> U202(X1,X2)
    U202(X1,active(X2)) -> U202(X1,X2)
    U21(mark(X1),X2) -> U21(X1,X2)
    U21(X1,mark(X2)) -> U21(X1,X2)
    U21(active(X1),X2) -> U21(X1,X2)
    U21(X1,active(X2)) -> U21(X1,X2)
    U211(mark(X1),X2) -> U211(X1,X2)
    U211(X1,mark(X2)) -> U211(X1,X2)
    U211(active(X1),X2) -> U211(X1,X2)
    U211(X1,active(X2)) -> U211(X1,X2)
    U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
    U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
    U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
    U221(active(X1),X2,X3) -> U221(X1,X2,X3)
    U221(X1,active(X2),X3) -> U221(X1,X2,X3)
    U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
    fst(mark(X)) -> fst(X)
    fst(active(X)) -> fst(X)
    U31(mark(X1),X2) -> U31(X1,X2)
    U31(X1,mark(X2)) -> U31(X1,X2)
    U31(active(X1),X2) -> U31(X1,X2)
    U31(X1,active(X2)) -> U31(X1,X2)
    U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
    U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
    U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
    U41(active(X1),X2,X3) -> U41(X1,X2,X3)
    U41(X1,active(X2),X3) -> U41(X1,X2,X3)
    U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
    U42(mark(X1),X2) -> U42(X1,X2)
    U42(X1,mark(X2)) -> U42(X1,X2)
    U42(active(X1),X2) -> U42(X1,X2)
    U42(X1,active(X2)) -> U42(X1,X2)
    U43(mark(X)) -> U43(X)
    U43(active(X)) -> U43(X)
    U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
    U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
    U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
    U51(active(X1),X2,X3) -> U51(X1,X2,X3)
    U51(X1,active(X2),X3) -> U51(X1,X2,X3)
    U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
    U52(mark(X1),X2) -> U52(X1,X2)
    U52(X1,mark(X2)) -> U52(X1,X2)
    U52(active(X1),X2) -> U52(X1,X2)
    U52(X1,active(X2)) -> U52(X1,X2)
    U53(mark(X)) -> U53(X)
    U53(active(X)) -> U53(X)
    U61(mark(X1),X2) -> U61(X1,X2)
    U61(X1,mark(X2)) -> U61(X1,X2)
    U61(active(X1),X2) -> U61(X1,X2)
    U61(X1,active(X2)) -> U61(X1,X2)
    U62(mark(X)) -> U62(X)
    U62(active(X)) -> U62(X)
    isPLNat(mark(X)) -> isPLNat(X)
    isPLNat(active(X)) -> isPLNat(X)
    U71(mark(X1),X2) -> U71(X1,X2)
    U71(X1,mark(X2)) -> U71(X1,X2)
    U71(active(X1),X2) -> U71(X1,X2)
    U71(X1,active(X2)) -> U71(X1,X2)
    U72(mark(X)) -> U72(X)
    U72(active(X)) -> U72(X)
    U81(mark(X1),X2) -> U81(X1,X2)
    U81(X1,mark(X2)) -> U81(X1,X2)
    U81(active(X1),X2) -> U81(X1,X2)
    U81(X1,active(X2)) -> U81(X1,X2)
    U82(mark(X)) -> U82(X)
    U82(active(X)) -> U82(X)
    U91(mark(X1),X2) -> U91(X1,X2)
    U91(X1,mark(X2)) -> U91(X1,X2)
    U91(active(X1),X2) -> U91(X1,X2)
    U91(X1,active(X2)) -> U91(X1,X2)
    U92(mark(X)) -> U92(X)
    U92(active(X)) -> U92(X)
    and(mark(X1),X2) -> and(X1,X2)
    and(X1,mark(X2)) -> and(X1,X2)
    and(active(X1),X2) -> and(X1,X2)
    and(X1,active(X2)) -> and(X1,X2)
    isNaturalKind(mark(X)) -> isNaturalKind(X)
    isNaturalKind(active(X)) -> isNaturalKind(X)
    isLNatKind(mark(X)) -> isLNatKind(X)
    isLNatKind(active(X)) -> isLNatKind(X)
    isPLNatKind(mark(X)) -> isPLNatKind(X)
    isPLNatKind(active(X)) -> isPLNatKind(X)
    tail(mark(X)) -> tail(X)
    tail(active(X)) -> tail(X)
    take(mark(X1),X2) -> take(X1,X2)
    take(X1,mark(X2)) -> take(X1,X2)
    take(active(X1),X2) -> take(X1,X2)
    take(X1,active(X2)) -> take(X1,X2)
    sel(mark(X1),X2) -> sel(X1,X2)
    sel(X1,mark(X2)) -> sel(X1,X2)
    sel(active(X1),X2) -> sel(X1,X2)
    sel(X1,active(X2)) -> sel(X1,X2)
   graph:
    ...
   SCC Processor:
    #sccs: 61
    #rules: 397
    #arcs: 39095/430336
    DPs:
     mark#(sel(X1,X2)) -> mark#(X2)
     mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2)))
     active#(take(N,XS)) ->
     mark#(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark#(sel(X1,X2)) -> mark#(X1)
     mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2)))
     active#(tail(cons(N,XS))) ->
     mark#(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     mark#(take(X1,X2)) -> mark#(X1)
     mark#(take(X1,X2)) -> mark#(X2)
     mark#(tail(X)) -> active#(tail(mark(X)))
     active#(splitAt(s(N),cons(X,XS))) ->
     mark#(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                           and(isLNat(XS),isLNatKind(XS)))),
                N,X,XS))
     mark#(tail(X)) -> mark#(X)
     mark#(isPLNatKind(X)) -> active#(isPLNatKind(X))
     active#(splitAt(0(),XS)) -> mark#(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     mark#(isLNatKind(X)) -> active#(isLNatKind(X))
     active#(snd(pair(X,Y))) ->
     mark#(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     mark#(isNaturalKind(X)) -> active#(isNaturalKind(X))
     active#(sel(N,XS)) ->
     mark#(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
     active#(natsFrom(N)) -> mark#(U161(and(isNatural(N),isNaturalKind(N)),N))
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(U92(X)) -> active#(U92(mark(X)))
     active#(isPLNatKind(splitAt(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
     mark#(U92(X)) -> mark#(X)
     mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
     active#(isPLNatKind(pair(V1,V2))) -> mark#(and(isLNatKind(V1),isLNatKind(V2)))
     mark#(U91(X1,X2)) -> mark#(X1)
     mark#(U82(X)) -> active#(U82(mark(X)))
     active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     mark#(U82(X)) -> mark#(X)
     mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
     active#(isPLNat(pair(V1,V2))) -> mark#(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     mark#(U81(X1,X2)) -> mark#(X1)
     mark#(U72(X)) -> active#(U72(mark(X)))
     active#(isNaturalKind(sel(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
     mark#(U72(X)) -> mark#(X)
     mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
     active#(isNaturalKind(s(V1))) -> mark#(isNaturalKind(V1))
     mark#(U71(X1,X2)) -> mark#(X1)
     mark#(isPLNat(X)) -> active#(isPLNat(X))
     active#(isNaturalKind(head(V1))) -> mark#(isLNatKind(V1))
     mark#(U62(X)) -> active#(U62(mark(X)))
     active#(isNatural(sel(V1,V2))) -> mark#(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     mark#(U62(X)) -> mark#(X)
     mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
     active#(isNatural(s(V1))) -> mark#(U121(isNaturalKind(V1),V1))
     mark#(U61(X1,X2)) -> mark#(X1)
     mark#(U53(X)) -> active#(U53(mark(X)))
     active#(isNatural(head(V1))) -> mark#(U111(isLNatKind(V1),V1))
     mark#(U53(X)) -> mark#(X)
     mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
     active#(isLNatKind(take(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
     mark#(U52(X1,X2)) -> mark#(X1)
     mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
     active#(isLNatKind(tail(V1))) -> mark#(isLNatKind(V1))
     mark#(U51(X1,X2,X3)) -> mark#(X1)
     mark#(U43(X)) -> active#(U43(mark(X)))
     active#(isLNatKind(snd(V1))) -> mark#(isPLNatKind(V1))
     mark#(U43(X)) -> mark#(X)
     mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
     active#(isLNatKind(natsFrom(V1))) -> mark#(isNaturalKind(V1))
     mark#(U42(X1,X2)) -> mark#(X1)
     mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
     active#(isLNatKind(fst(V1))) -> mark#(isPLNatKind(V1))
     mark#(U41(X1,X2,X3)) -> mark#(X1)
     mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
     active#(isLNatKind(cons(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
     mark#(U31(X1,X2)) -> mark#(X1)
     mark#(fst(X)) -> active#(fst(mark(X)))
     active#(isLNatKind(afterNth(V1,V2))) -> mark#(and(isNaturalKind(V1),isLNatKind(V2)))
     mark#(fst(X)) -> mark#(X)
     mark#(U221(X1,X2,X3)) -> active#(U221(mark(X1),X2,X3))
     active#(isLNat(take(V1,V2))) -> mark#(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     mark#(U221(X1,X2,X3)) -> mark#(X1)
     mark#(U211(X1,X2)) -> active#(U211(mark(X1),X2))
     active#(isLNat(tail(V1))) -> mark#(U91(isLNatKind(V1),V1))
     mark#(U211(X1,X2)) -> mark#(X1)
     mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
     active#(isLNat(snd(V1))) -> mark#(U81(isPLNatKind(V1),V1))
     mark#(U21(X1,X2)) -> mark#(X1)
     mark#(U202(X1,X2)) -> active#(U202(mark(X1),X2))
     active#(isLNat(natsFrom(V1))) -> mark#(U71(isNaturalKind(V1),V1))
     mark#(U202(X1,X2)) -> mark#(X1)
     mark#(U201(X1,X2,X3,X4)) -> active#(U201(mark(X1),X2,X3,X4))
     active#(isLNat(fst(V1))) -> mark#(U61(isPLNatKind(V1),V1))
     mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
     mark#(pair(X1,X2)) -> active#(pair(mark(X1),mark(X2)))
     active#(isLNat(cons(V1,V2))) -> mark#(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     mark#(pair(X1,X2)) -> mark#(X1)
     mark#(pair(X1,X2)) -> mark#(X2)
     mark#(U191(X1,X2)) -> active#(U191(mark(X1),X2))
     active#(isLNat(afterNth(V1,V2))) -> mark#(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     mark#(U191(X1,X2)) -> mark#(X1)
     mark#(U181(X1,X2)) -> active#(U181(mark(X1),X2))
     active#(head(cons(N,XS))) ->
     mark#(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     mark#(U181(X1,X2)) -> mark#(X1)
     mark#(afterNth(X1,X2)) -> active#(afterNth(mark(X1),mark(X2)))
     active#(fst(pair(X,Y))) ->
     mark#(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     mark#(afterNth(X1,X2)) -> mark#(X1)
     mark#(afterNth(X1,X2)) -> mark#(X2)
     mark#(head(X)) -> active#(head(mark(X)))
     active#(and(tt(),X)) -> mark#(X)
     mark#(head(X)) -> mark#(X)
     mark#(U171(X1,X2,X3)) -> active#(U171(mark(X1),X2,X3))
     active#(afterNth(N,XS)) ->
     mark#(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark#(U171(X1,X2,X3)) -> mark#(X1)
     mark#(s(X)) -> active#(s(mark(X)))
     active#(U91(tt(),V1)) -> mark#(U92(isLNat(V1)))
     mark#(s(X)) -> mark#(X)
     mark#(natsFrom(X)) -> active#(natsFrom(mark(X)))
     active#(U81(tt(),V1)) -> mark#(U82(isPLNat(V1)))
     mark#(natsFrom(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
     active#(U71(tt(),V1)) -> mark#(U72(isNatural(V1)))
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(U161(X1,X2)) -> active#(U161(mark(X1),X2))
     active#(U61(tt(),V1)) -> mark#(U62(isPLNat(V1)))
     mark#(U161(X1,X2)) -> mark#(X1)
     mark#(U153(X)) -> active#(U153(mark(X)))
     active#(U52(tt(),V2)) -> mark#(U53(isLNat(V2)))
     mark#(U153(X)) -> mark#(X)
     mark#(U152(X1,X2)) -> active#(U152(mark(X1),X2))
     active#(U51(tt(),V1,V2)) -> mark#(U52(isNatural(V1),V2))
     mark#(U152(X1,X2)) -> mark#(X1)
     mark#(U151(X1,X2,X3)) -> active#(U151(mark(X1),X2,X3))
     active#(U42(tt(),V2)) -> mark#(U43(isLNat(V2)))
     mark#(U151(X1,X2,X3)) -> mark#(X1)
     mark#(U143(X)) -> active#(U143(mark(X)))
     active#(U41(tt(),V1,V2)) -> mark#(U42(isNatural(V1),V2))
     mark#(U143(X)) -> mark#(X)
     mark#(U142(X1,X2)) -> active#(U142(mark(X1),X2))
     active#(U31(tt(),N)) -> mark#(N)
     mark#(U142(X1,X2)) -> mark#(X1)
     mark#(U141(X1,X2,X3)) -> active#(U141(mark(X1),X2,X3))
     active#(U221(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
     mark#(U141(X1,X2,X3)) -> mark#(X1)
     mark#(U133(X)) -> active#(U133(mark(X)))
     active#(U211(tt(),XS)) -> mark#(XS)
     mark#(U133(X)) -> mark#(X)
     mark#(U132(X1,X2)) -> active#(U132(mark(X1),X2))
     active#(U21(tt(),X)) -> mark#(X)
     mark#(U132(X1,X2)) -> mark#(X1)
     mark#(U131(X1,X2,X3)) -> active#(U131(mark(X1),X2,X3))
     active#(U202(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
     mark#(U131(X1,X2,X3)) -> mark#(X1)
     mark#(U122(X)) -> active#(U122(mark(X)))
     active#(U201(tt(),N,X,XS)) -> mark#(U202(splitAt(N,XS),X))
     mark#(U122(X)) -> mark#(X)
     mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2))
     active#(U191(tt(),XS)) -> mark#(pair(nil(),XS))
     mark#(U121(X1,X2)) -> mark#(X1)
     mark#(U112(X)) -> active#(U112(mark(X)))
     active#(U181(tt(),Y)) -> mark#(Y)
     mark#(U112(X)) -> mark#(X)
     mark#(U111(X1,X2)) -> active#(U111(mark(X1),X2))
     active#(U171(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
     mark#(U111(X1,X2)) -> mark#(X1)
     mark#(splitAt(X1,X2)) -> active#(splitAt(mark(X1),mark(X2)))
     active#(U161(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
     mark#(splitAt(X1,X2)) -> mark#(X1)
     mark#(splitAt(X1,X2)) -> mark#(X2)
     mark#(snd(X)) -> active#(snd(mark(X)))
     active#(U152(tt(),V2)) -> mark#(U153(isLNat(V2)))
     mark#(snd(X)) -> mark#(X)
     mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
     active#(U151(tt(),V1,V2)) -> mark#(U152(isNatural(V1),V2))
     mark#(U11(X1,X2,X3)) -> mark#(X1)
     mark#(isLNat(X)) -> active#(isLNat(X))
     active#(U142(tt(),V2)) -> mark#(U143(isLNat(V2)))
     mark#(U103(X)) -> active#(U103(mark(X)))
     active#(U141(tt(),V1,V2)) -> mark#(U142(isLNat(V1),V2))
     mark#(U103(X)) -> mark#(X)
     mark#(isNatural(X)) -> active#(isNatural(X))
     active#(U132(tt(),V2)) -> mark#(U133(isLNat(V2)))
     mark#(U102(X1,X2)) -> active#(U102(mark(X1),X2))
     active#(U131(tt(),V1,V2)) -> mark#(U132(isNatural(V1),V2))
     mark#(U102(X1,X2)) -> mark#(X1)
     mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
     active#(U121(tt(),V1)) -> mark#(U122(isNatural(V1)))
     mark#(U101(X1,X2,X3)) -> mark#(X1)
     active#(U111(tt(),V1)) -> mark#(U112(isLNat(V1)))
     active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
     active#(U102(tt(),V2)) -> mark#(U103(isLNat(V2)))
     active#(U101(tt(),V1,V2)) -> mark#(U102(isNatural(V1),V2))
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U102#(X1,active(X2)) -> U102#(X1,X2)
     U102#(active(X1),X2) -> U102#(X1,X2)
     U102#(X1,mark(X2)) -> U102#(X1,X2)
     U102#(mark(X1),X2) -> U102#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isNatural#(active(X)) -> isNatural#(X)
     isNatural#(mark(X)) -> isNatural#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isLNat#(mark(X)) -> isLNat#(X)
     isLNat#(active(X)) -> isLNat#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U103#(mark(X)) -> U103#(X)
     U103#(active(X)) -> U103#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     splitAt#(mark(X1),X2) -> splitAt#(X1,X2)
     splitAt#(X1,active(X2)) -> splitAt#(X1,X2)
     splitAt#(active(X1),X2) -> splitAt#(X1,X2)
     splitAt#(X1,mark(X2)) -> splitAt#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     snd#(mark(X)) -> snd#(X)
     snd#(active(X)) -> snd#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U112#(mark(X)) -> U112#(X)
     U112#(active(X)) -> U112#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U122#(mark(X)) -> U122#(X)
     U122#(active(X)) -> U122#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U132#(mark(X1),X2) -> U132#(X1,X2)
     U132#(X1,active(X2)) -> U132#(X1,X2)
     U132#(active(X1),X2) -> U132#(X1,X2)
     U132#(X1,mark(X2)) -> U132#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U133#(mark(X)) -> U133#(X)
     U133#(active(X)) -> U133#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U142#(mark(X1),X2) -> U142#(X1,X2)
     U142#(X1,active(X2)) -> U142#(X1,X2)
     U142#(active(X1),X2) -> U142#(X1,X2)
     U142#(X1,mark(X2)) -> U142#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U143#(mark(X)) -> U143#(X)
     U143#(active(X)) -> U143#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U152#(mark(X1),X2) -> U152#(X1,X2)
     U152#(X1,active(X2)) -> U152#(X1,X2)
     U152#(active(X1),X2) -> U152#(X1,X2)
     U152#(X1,mark(X2)) -> U152#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U153#(mark(X)) -> U153#(X)
     U153#(active(X)) -> U153#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     s#(mark(X)) -> s#(X)
     s#(active(X)) -> s#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     natsFrom#(mark(X)) -> natsFrom#(X)
     natsFrom#(active(X)) -> natsFrom#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(X1,active(X2)) -> cons#(X1,X2)
     cons#(active(X1),X2) -> cons#(X1,X2)
     cons#(X1,mark(X2)) -> cons#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     afterNth#(mark(X1),X2) -> afterNth#(X1,X2)
     afterNth#(X1,active(X2)) -> afterNth#(X1,X2)
     afterNth#(active(X1),X2) -> afterNth#(X1,X2)
     afterNth#(X1,mark(X2)) -> afterNth#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     head#(mark(X)) -> head#(X)
     head#(active(X)) -> head#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     pair#(mark(X1),X2) -> pair#(X1,X2)
     pair#(X1,active(X2)) -> pair#(X1,X2)
     pair#(active(X1),X2) -> pair#(X1,X2)
     pair#(X1,mark(X2)) -> pair#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U202#(mark(X1),X2) -> U202#(X1,X2)
     U202#(X1,active(X2)) -> U202#(X1,X2)
     U202#(active(X1),X2) -> U202#(X1,X2)
     U202#(X1,mark(X2)) -> U202#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     fst#(mark(X)) -> fst#(X)
     fst#(active(X)) -> fst#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U42#(mark(X1),X2) -> U42#(X1,X2)
     U42#(X1,active(X2)) -> U42#(X1,X2)
     U42#(active(X1),X2) -> U42#(X1,X2)
     U42#(X1,mark(X2)) -> U42#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U43#(mark(X)) -> U43#(X)
     U43#(active(X)) -> U43#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U52#(mark(X1),X2) -> U52#(X1,X2)
     U52#(X1,active(X2)) -> U52#(X1,X2)
     U52#(active(X1),X2) -> U52#(X1,X2)
     U52#(X1,mark(X2)) -> U52#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U53#(mark(X)) -> U53#(X)
     U53#(active(X)) -> U53#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isPLNat#(mark(X)) -> isPLNat#(X)
     isPLNat#(active(X)) -> isPLNat#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U62#(mark(X)) -> U62#(X)
     U62#(active(X)) -> U62#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U72#(mark(X)) -> U72#(X)
     U72#(active(X)) -> U72#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U82#(mark(X)) -> U82#(X)
     U82#(active(X)) -> U82#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U92#(mark(X)) -> U92#(X)
     U92#(active(X)) -> U92#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isLNatKind#(mark(X)) -> isLNatKind#(X)
     isLNatKind#(active(X)) -> isLNatKind#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     and#(mark(X1),X2) -> and#(X1,X2)
     and#(X1,active(X2)) -> and#(X1,X2)
     and#(active(X1),X2) -> and#(X1,X2)
     and#(X1,mark(X2)) -> and#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isNaturalKind#(mark(X)) -> isNaturalKind#(X)
     isNaturalKind#(active(X)) -> isNaturalKind#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
     U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
     U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
     U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U21#(X1,active(X2)) -> U21#(X1,X2)
     U21#(active(X1),X2) -> U21#(X1,X2)
     U21#(X1,mark(X2)) -> U21#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U31#(X1,active(X2)) -> U31#(X1,X2)
     U31#(active(X1),X2) -> U31#(X1,X2)
     U31#(X1,mark(X2)) -> U31#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
     U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
     U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
     U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
     U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
     U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
     U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
     U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
     U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
     U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
     U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     isPLNatKind#(mark(X)) -> isPLNatKind#(X)
     isPLNatKind#(active(X)) -> isPLNatKind#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U61#(mark(X1),X2) -> U61#(X1,X2)
     U61#(X1,active(X2)) -> U61#(X1,X2)
     U61#(active(X1),X2) -> U61#(X1,X2)
     U61#(X1,mark(X2)) -> U61#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U71#(mark(X1),X2) -> U71#(X1,X2)
     U71#(X1,active(X2)) -> U71#(X1,X2)
     U71#(active(X1),X2) -> U71#(X1,X2)
     U71#(X1,mark(X2)) -> U71#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U81#(mark(X1),X2) -> U81#(X1,X2)
     U81#(X1,active(X2)) -> U81#(X1,X2)
     U81#(active(X1),X2) -> U81#(X1,X2)
     U81#(X1,mark(X2)) -> U81#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U91#(mark(X1),X2) -> U91#(X1,X2)
     U91#(X1,active(X2)) -> U91#(X1,X2)
     U91#(active(X1),X2) -> U91#(X1,X2)
     U91#(X1,mark(X2)) -> U91#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3)
     U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
     U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
     U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
     U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
     U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U111#(mark(X1),X2) -> U111#(X1,X2)
     U111#(X1,active(X2)) -> U111#(X1,X2)
     U111#(active(X1),X2) -> U111#(X1,X2)
     U111#(X1,mark(X2)) -> U111#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U121#(mark(X1),X2) -> U121#(X1,X2)
     U121#(X1,active(X2)) -> U121#(X1,X2)
     U121#(active(X1),X2) -> U121#(X1,X2)
     U121#(X1,mark(X2)) -> U121#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U131#(mark(X1),X2,X3) -> U131#(X1,X2,X3)
     U131#(X1,X2,active(X3)) -> U131#(X1,X2,X3)
     U131#(X1,active(X2),X3) -> U131#(X1,X2,X3)
     U131#(active(X1),X2,X3) -> U131#(X1,X2,X3)
     U131#(X1,X2,mark(X3)) -> U131#(X1,X2,X3)
     U131#(X1,mark(X2),X3) -> U131#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U141#(mark(X1),X2,X3) -> U141#(X1,X2,X3)
     U141#(X1,X2,active(X3)) -> U141#(X1,X2,X3)
     U141#(X1,active(X2),X3) -> U141#(X1,X2,X3)
     U141#(active(X1),X2,X3) -> U141#(X1,X2,X3)
     U141#(X1,X2,mark(X3)) -> U141#(X1,X2,X3)
     U141#(X1,mark(X2),X3) -> U141#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U151#(mark(X1),X2,X3) -> U151#(X1,X2,X3)
     U151#(X1,X2,active(X3)) -> U151#(X1,X2,X3)
     U151#(X1,active(X2),X3) -> U151#(X1,X2,X3)
     U151#(active(X1),X2,X3) -> U151#(X1,X2,X3)
     U151#(X1,X2,mark(X3)) -> U151#(X1,X2,X3)
     U151#(X1,mark(X2),X3) -> U151#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U161#(mark(X1),X2) -> U161#(X1,X2)
     U161#(X1,active(X2)) -> U161#(X1,X2)
     U161#(active(X1),X2) -> U161#(X1,X2)
     U161#(X1,mark(X2)) -> U161#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U171#(mark(X1),X2,X3) -> U171#(X1,X2,X3)
     U171#(X1,X2,active(X3)) -> U171#(X1,X2,X3)
     U171#(X1,active(X2),X3) -> U171#(X1,X2,X3)
     U171#(active(X1),X2,X3) -> U171#(X1,X2,X3)
     U171#(X1,X2,mark(X3)) -> U171#(X1,X2,X3)
     U171#(X1,mark(X2),X3) -> U171#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U181#(mark(X1),X2) -> U181#(X1,X2)
     U181#(X1,active(X2)) -> U181#(X1,X2)
     U181#(active(X1),X2) -> U181#(X1,X2)
     U181#(X1,mark(X2)) -> U181#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U191#(mark(X1),X2) -> U191#(X1,X2)
     U191#(X1,active(X2)) -> U191#(X1,X2)
     U191#(active(X1),X2) -> U191#(X1,X2)
     U191#(X1,mark(X2)) -> U191#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U201#(mark(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
     U201#(X1,X2,X3,active(X4)) -> U201#(X1,X2,X3,X4)
     U201#(X1,X2,active(X3),X4) -> U201#(X1,X2,X3,X4)
     U201#(X1,active(X2),X3,X4) -> U201#(X1,X2,X3,X4)
     U201#(active(X1),X2,X3,X4) -> U201#(X1,X2,X3,X4)
     U201#(X1,X2,X3,mark(X4)) -> U201#(X1,X2,X3,X4)
     U201#(X1,X2,mark(X3),X4) -> U201#(X1,X2,X3,X4)
     U201#(X1,mark(X2),X3,X4) -> U201#(X1,X2,X3,X4)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U211#(mark(X1),X2) -> U211#(X1,X2)
     U211#(X1,active(X2)) -> U211#(X1,X2)
     U211#(active(X1),X2) -> U211#(X1,X2)
     U211#(X1,mark(X2)) -> U211#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     U221#(mark(X1),X2,X3) -> U221#(X1,X2,X3)
     U221#(X1,X2,active(X3)) -> U221#(X1,X2,X3)
     U221#(X1,active(X2),X3) -> U221#(X1,X2,X3)
     U221#(active(X1),X2,X3) -> U221#(X1,X2,X3)
     U221#(X1,X2,mark(X3)) -> U221#(X1,X2,X3)
     U221#(X1,mark(X2),X3) -> U221#(X1,X2,X3)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     tail#(mark(X)) -> tail#(X)
     tail#(active(X)) -> tail#(X)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     take#(mark(X1),X2) -> take#(X1,X2)
     take#(X1,active(X2)) -> take#(X1,X2)
     take#(active(X1),X2) -> take#(X1,X2)
     take#(X1,mark(X2)) -> take#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open
    
    DPs:
     sel#(mark(X1),X2) -> sel#(X1,X2)
     sel#(X1,active(X2)) -> sel#(X1,X2)
     sel#(active(X1),X2) -> sel#(X1,X2)
     sel#(X1,mark(X2)) -> sel#(X1,X2)
    TRS:
     active(U101(tt(),V1,V2)) -> mark(U102(isNatural(V1),V2))
     active(U102(tt(),V2)) -> mark(U103(isLNat(V2)))
     active(U103(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U111(tt(),V1)) -> mark(U112(isLNat(V1)))
     active(U112(tt())) -> mark(tt())
     active(U121(tt(),V1)) -> mark(U122(isNatural(V1)))
     active(U122(tt())) -> mark(tt())
     active(U131(tt(),V1,V2)) -> mark(U132(isNatural(V1),V2))
     active(U132(tt(),V2)) -> mark(U133(isLNat(V2)))
     active(U133(tt())) -> mark(tt())
     active(U141(tt(),V1,V2)) -> mark(U142(isLNat(V1),V2))
     active(U142(tt(),V2)) -> mark(U143(isLNat(V2)))
     active(U143(tt())) -> mark(tt())
     active(U151(tt(),V1,V2)) -> mark(U152(isNatural(V1),V2))
     active(U152(tt(),V2)) -> mark(U153(isLNat(V2)))
     active(U153(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(splitAt(N,XS),X))
     active(U202(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X)) -> mark(X)
     active(U211(tt(),XS)) -> mark(XS)
     active(U221(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),V1,V2)) -> mark(U42(isNatural(V1),V2))
     active(U42(tt(),V2)) -> mark(U43(isLNat(V2)))
     active(U43(tt())) -> mark(tt())
     active(U51(tt(),V1,V2)) -> mark(U52(isNatural(V1),V2))
     active(U52(tt(),V2)) -> mark(U53(isLNat(V2)))
     active(U53(tt())) -> mark(tt())
     active(U61(tt(),V1)) -> mark(U62(isPLNat(V1)))
     active(U62(tt())) -> mark(tt())
     active(U71(tt(),V1)) -> mark(U72(isNatural(V1)))
     active(U72(tt())) -> mark(tt())
     active(U81(tt(),V1)) -> mark(U82(isPLNat(V1)))
     active(U82(tt())) -> mark(tt())
     active(U91(tt(),V1)) -> mark(U92(isLNat(V1)))
     active(U92(tt())) -> mark(tt())
     active(afterNth(N,XS)) ->
     mark(U11(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) ->
     mark(U21(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X))
     active(head(cons(N,XS))) ->
     mark(U31(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
     active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
     active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
     active(isLNat(take(V1,V2))) -> mark(U101(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isLNatKind(nil())) -> mark(tt())
     active(isLNatKind(afterNth(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(cons(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isLNatKind(fst(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(natsFrom(V1))) -> mark(isNaturalKind(V1))
     active(isLNatKind(snd(V1))) -> mark(isPLNatKind(V1))
     active(isLNatKind(tail(V1))) -> mark(isLNatKind(V1))
     active(isLNatKind(take(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNatKind(V1),V1))
     active(isNatural(s(V1))) -> mark(U121(isNaturalKind(V1),V1))
     active(isNatural(sel(V1,V2))) -> mark(U131(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isNaturalKind(0())) -> mark(tt())
     active(isNaturalKind(head(V1))) -> mark(isLNatKind(V1))
     active(isNaturalKind(s(V1))) -> mark(isNaturalKind(V1))
     active(isNaturalKind(sel(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(U141(and(isLNatKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(and(isNaturalKind(V1),isLNatKind(V2)),V1,V2))
     active(isPLNatKind(pair(V1,V2))) -> mark(and(isLNatKind(V1),isLNatKind(V2)))
     active(isPLNatKind(splitAt(V1,V2))) -> mark(and(isNaturalKind(V1),isLNatKind(V2)))
     active(natsFrom(N)) -> mark(U161(and(isNatural(N),isNaturalKind(N)),N))
     active(sel(N,XS)) ->
     mark(U171(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     active(snd(pair(X,Y))) ->
     mark(U181(and(and(isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y))
     active(splitAt(0(),XS)) -> mark(U191(and(isLNat(XS),isLNatKind(XS)),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U201(and(and(isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS)))),
               N,X,XS))
     active(tail(cons(N,XS))) ->
     mark(U211(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS))
     active(take(N,XS)) ->
     mark(U221(and(and(isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(U102(X1,X2)) -> active(U102(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U103(X)) -> active(U103(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U111(X1,X2)) -> active(U111(mark(X1),X2))
     mark(U112(X)) -> active(U112(mark(X)))
     mark(U121(X1,X2)) -> active(U121(mark(X1),X2))
     mark(U122(X)) -> active(U122(mark(X)))
     mark(U131(X1,X2,X3)) -> active(U131(mark(X1),X2,X3))
     mark(U132(X1,X2)) -> active(U132(mark(X1),X2))
     mark(U133(X)) -> active(U133(mark(X)))
     mark(U141(X1,X2,X3)) -> active(U141(mark(X1),X2,X3))
     mark(U142(X1,X2)) -> active(U142(mark(X1),X2))
     mark(U143(X)) -> active(U143(mark(X)))
     mark(U151(X1,X2,X3)) -> active(U151(mark(X1),X2,X3))
     mark(U152(X1,X2)) -> active(U152(mark(X1),X2))
     mark(U153(X)) -> active(U153(mark(X)))
     mark(U161(X1,X2)) -> active(U161(mark(X1),X2))
     mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
     mark(natsFrom(X)) -> active(natsFrom(mark(X)))
     mark(s(X)) -> active(s(mark(X)))
     mark(U171(X1,X2,X3)) -> active(U171(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U181(X1,X2)) -> active(U181(mark(X1),X2))
     mark(U191(X1,X2)) -> active(U191(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U201(X1,X2,X3,X4)) -> active(U201(mark(X1),X2,X3,X4))
     mark(U202(X1,X2)) -> active(U202(mark(X1),X2))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
     mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
     mark(U43(X)) -> active(U43(mark(X)))
     mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
     mark(U53(X)) -> active(U53(mark(X)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U62(X)) -> active(U62(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(X))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(U72(X)) -> active(U72(mark(X)))
     mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
     mark(U82(X)) -> active(U82(mark(X)))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(U92(X)) -> active(U92(mark(X)))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNaturalKind(X)) -> active(isNaturalKind(X))
     mark(isLNatKind(X)) -> active(isLNatKind(X))
     mark(isPLNatKind(X)) -> active(isPLNatKind(X))
     mark(tail(X)) -> active(tail(mark(X)))
     mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
     mark(0()) -> active(0())
     mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
     U101(mark(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     U102(mark(X1),X2) -> U102(X1,X2)
     U102(X1,mark(X2)) -> U102(X1,X2)
     U102(active(X1),X2) -> U102(X1,X2)
     U102(X1,active(X2)) -> U102(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U103(mark(X)) -> U103(X)
     U103(active(X)) -> U103(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(X)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     splitAt(mark(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,mark(X2)) -> splitAt(X1,X2)
     splitAt(active(X1),X2) -> splitAt(X1,X2)
     splitAt(X1,active(X2)) -> splitAt(X1,X2)
     U111(mark(X1),X2) -> U111(X1,X2)
     U111(X1,mark(X2)) -> U111(X1,X2)
     U111(active(X1),X2) -> U111(X1,X2)
     U111(X1,active(X2)) -> U111(X1,X2)
     U112(mark(X)) -> U112(X)
     U112(active(X)) -> U112(X)
     U121(mark(X1),X2) -> U121(X1,X2)
     U121(X1,mark(X2)) -> U121(X1,X2)
     U121(active(X1),X2) -> U121(X1,X2)
     U121(X1,active(X2)) -> U121(X1,X2)
     U122(mark(X)) -> U122(X)
     U122(active(X)) -> U122(X)
     U131(mark(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,mark(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,mark(X3)) -> U131(X1,X2,X3)
     U131(active(X1),X2,X3) -> U131(X1,X2,X3)
     U131(X1,active(X2),X3) -> U131(X1,X2,X3)
     U131(X1,X2,active(X3)) -> U131(X1,X2,X3)
     U132(mark(X1),X2) -> U132(X1,X2)
     U132(X1,mark(X2)) -> U132(X1,X2)
     U132(active(X1),X2) -> U132(X1,X2)
     U132(X1,active(X2)) -> U132(X1,X2)
     U133(mark(X)) -> U133(X)
     U133(active(X)) -> U133(X)
     U141(mark(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,mark(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,mark(X3)) -> U141(X1,X2,X3)
     U141(active(X1),X2,X3) -> U141(X1,X2,X3)
     U141(X1,active(X2),X3) -> U141(X1,X2,X3)
     U141(X1,X2,active(X3)) -> U141(X1,X2,X3)
     U142(mark(X1),X2) -> U142(X1,X2)
     U142(X1,mark(X2)) -> U142(X1,X2)
     U142(active(X1),X2) -> U142(X1,X2)
     U142(X1,active(X2)) -> U142(X1,X2)
     U143(mark(X)) -> U143(X)
     U143(active(X)) -> U143(X)
     U151(mark(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,mark(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,mark(X3)) -> U151(X1,X2,X3)
     U151(active(X1),X2,X3) -> U151(X1,X2,X3)
     U151(X1,active(X2),X3) -> U151(X1,X2,X3)
     U151(X1,X2,active(X3)) -> U151(X1,X2,X3)
     U152(mark(X1),X2) -> U152(X1,X2)
     U152(X1,mark(X2)) -> U152(X1,X2)
     U152(active(X1),X2) -> U152(X1,X2)
     U152(X1,active(X2)) -> U152(X1,X2)
     U153(mark(X)) -> U153(X)
     U153(active(X)) -> U153(X)
     U161(mark(X1),X2) -> U161(X1,X2)
     U161(X1,mark(X2)) -> U161(X1,X2)
     U161(active(X1),X2) -> U161(X1,X2)
     U161(X1,active(X2)) -> U161(X1,X2)
     cons(mark(X1),X2) -> cons(X1,X2)
     cons(X1,mark(X2)) -> cons(X1,X2)
     cons(active(X1),X2) -> cons(X1,X2)
     cons(X1,active(X2)) -> cons(X1,X2)
     natsFrom(mark(X)) -> natsFrom(X)
     natsFrom(active(X)) -> natsFrom(X)
     s(mark(X)) -> s(X)
     s(active(X)) -> s(X)
     U171(mark(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,mark(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,mark(X3)) -> U171(X1,X2,X3)
     U171(active(X1),X2,X3) -> U171(X1,X2,X3)
     U171(X1,active(X2),X3) -> U171(X1,X2,X3)
     U171(X1,X2,active(X3)) -> U171(X1,X2,X3)
     head(mark(X)) -> head(X)
     head(active(X)) -> head(X)
     afterNth(mark(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,mark(X2)) -> afterNth(X1,X2)
     afterNth(active(X1),X2) -> afterNth(X1,X2)
     afterNth(X1,active(X2)) -> afterNth(X1,X2)
     U181(mark(X1),X2) -> U181(X1,X2)
     U181(X1,mark(X2)) -> U181(X1,X2)
     U181(active(X1),X2) -> U181(X1,X2)
     U181(X1,active(X2)) -> U181(X1,X2)
     U191(mark(X1),X2) -> U191(X1,X2)
     U191(X1,mark(X2)) -> U191(X1,X2)
     U191(active(X1),X2) -> U191(X1,X2)
     U191(X1,active(X2)) -> U191(X1,X2)
     pair(mark(X1),X2) -> pair(X1,X2)
     pair(X1,mark(X2)) -> pair(X1,X2)
     pair(active(X1),X2) -> pair(X1,X2)
     pair(X1,active(X2)) -> pair(X1,X2)
     U201(mark(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,mark(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,mark(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,mark(X4)) -> U201(X1,X2,X3,X4)
     U201(active(X1),X2,X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,active(X2),X3,X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,active(X3),X4) -> U201(X1,X2,X3,X4)
     U201(X1,X2,X3,active(X4)) -> U201(X1,X2,X3,X4)
     U202(mark(X1),X2) -> U202(X1,X2)
     U202(X1,mark(X2)) -> U202(X1,X2)
     U202(active(X1),X2) -> U202(X1,X2)
     U202(X1,active(X2)) -> U202(X1,X2)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U211(mark(X1),X2) -> U211(X1,X2)
     U211(X1,mark(X2)) -> U211(X1,X2)
     U211(active(X1),X2) -> U211(X1,X2)
     U211(X1,active(X2)) -> U211(X1,X2)
     U221(mark(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,mark(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,mark(X3)) -> U221(X1,X2,X3)
     U221(active(X1),X2,X3) -> U221(X1,X2,X3)
     U221(X1,active(X2),X3) -> U221(X1,X2,X3)
     U221(X1,X2,active(X3)) -> U221(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
     U41(active(X1),X2,X3) -> U41(X1,X2,X3)
     U41(X1,active(X2),X3) -> U41(X1,X2,X3)
     U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
     U42(mark(X1),X2) -> U42(X1,X2)
     U42(X1,mark(X2)) -> U42(X1,X2)
     U42(active(X1),X2) -> U42(X1,X2)
     U42(X1,active(X2)) -> U42(X1,X2)
     U43(mark(X)) -> U43(X)
     U43(active(X)) -> U43(X)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     U52(mark(X1),X2) -> U52(X1,X2)
     U52(X1,mark(X2)) -> U52(X1,X2)
     U52(active(X1),X2) -> U52(X1,X2)
     U52(X1,active(X2)) -> U52(X1,X2)
     U53(mark(X)) -> U53(X)
     U53(active(X)) -> U53(X)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U62(mark(X)) -> U62(X)
     U62(active(X)) -> U62(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(X)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     U72(mark(X)) -> U72(X)
     U72(active(X)) -> U72(X)
     U81(mark(X1),X2) -> U81(X1,X2)
     U81(X1,mark(X2)) -> U81(X1,X2)
     U81(active(X1),X2) -> U81(X1,X2)
     U81(X1,active(X2)) -> U81(X1,X2)
     U82(mark(X)) -> U82(X)
     U82(active(X)) -> U82(X)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     U92(mark(X)) -> U92(X)
     U92(active(X)) -> U92(X)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNaturalKind(mark(X)) -> isNaturalKind(X)
     isNaturalKind(active(X)) -> isNaturalKind(X)
     isLNatKind(mark(X)) -> isLNatKind(X)
     isLNatKind(active(X)) -> isLNatKind(X)
     isPLNatKind(mark(X)) -> isPLNatKind(X)
     isPLNatKind(active(X)) -> isPLNatKind(X)
     tail(mark(X)) -> tail(X)
     tail(active(X)) -> tail(X)
     take(mark(X1),X2) -> take(X1,X2)
     take(X1,mark(X2)) -> take(X1,X2)
     take(active(X1),X2) -> take(X1,X2)
     take(X1,active(X2)) -> take(X1,X2)
     sel(mark(X1),X2) -> sel(X1,X2)
     sel(X1,mark(X2)) -> sel(X1,X2)
     sel(active(X1),X2) -> sel(X1,X2)
     sel(X1,active(X2)) -> sel(X1,X2)
    Open