MAYBE

Problem:
 a__U101(tt(),V1,V2) -> a__U102(a__isNatural(V1),V2)
 a__U102(tt(),V2) -> a__U103(a__isLNat(V2))
 a__U103(tt()) -> tt()
 a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
 a__U111(tt(),V1) -> a__U112(a__isLNat(V1))
 a__U112(tt()) -> tt()
 a__U121(tt(),V1) -> a__U122(a__isNatural(V1))
 a__U122(tt()) -> tt()
 a__U131(tt(),V1,V2) -> a__U132(a__isNatural(V1),V2)
 a__U132(tt(),V2) -> a__U133(a__isLNat(V2))
 a__U133(tt()) -> tt()
 a__U141(tt(),V1,V2) -> a__U142(a__isLNat(V1),V2)
 a__U142(tt(),V2) -> a__U143(a__isLNat(V2))
 a__U143(tt()) -> tt()
 a__U151(tt(),V1,V2) -> a__U152(a__isNatural(V1),V2)
 a__U152(tt(),V2) -> a__U153(a__isLNat(V2))
 a__U153(tt()) -> tt()
 a__U161(tt(),N) -> cons(mark(N),natsFrom(s(N)))
 a__U171(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
 a__U181(tt(),Y) -> mark(Y)
 a__U191(tt(),XS) -> pair(nil(),mark(XS))
 a__U201(tt(),N,X,XS) -> a__U202(a__splitAt(mark(N),mark(XS)),X)
 a__U202(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
 a__U21(tt(),X) -> mark(X)
 a__U211(tt(),XS) -> mark(XS)
 a__U221(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
 a__U31(tt(),N) -> mark(N)
 a__U41(tt(),V1,V2) -> a__U42(a__isNatural(V1),V2)
 a__U42(tt(),V2) -> a__U43(a__isLNat(V2))
 a__U43(tt()) -> tt()
 a__U51(tt(),V1,V2) -> a__U52(a__isNatural(V1),V2)
 a__U52(tt(),V2) -> a__U53(a__isLNat(V2))
 a__U53(tt()) -> tt()
 a__U61(tt(),V1) -> a__U62(a__isPLNat(V1))
 a__U62(tt()) -> tt()
 a__U71(tt(),V1) -> a__U72(a__isNatural(V1))
 a__U72(tt()) -> tt()
 a__U81(tt(),V1) -> a__U82(a__isPLNat(V1))
 a__U82(tt()) -> tt()
 a__U91(tt(),V1) -> a__U92(a__isLNat(V1))
 a__U92(tt()) -> tt()
 a__afterNth(N,XS) ->
 a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
 a__and(tt(),X) -> mark(X)
 a__fst(pair(X,Y)) ->
 a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
 a__head(cons(N,XS)) ->
 a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
 a__isLNat(nil()) -> tt()
 a__isLNat(afterNth(V1,V2)) -> a__U41(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
 a__isLNat(cons(V1,V2)) -> a__U51(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
 a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1),V1)
 a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1),V1)
 a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1),V1)
 a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1),V1)
 a__isLNat(take(V1,V2)) -> a__U101(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
 a__isLNatKind(nil()) -> tt()
 a__isLNatKind(afterNth(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
 a__isLNatKind(cons(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
 a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
 a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
 a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
 a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
 a__isLNatKind(take(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
 a__isNatural(0()) -> tt()
 a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1),V1)
 a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1),V1)
 a__isNatural(sel(V1,V2)) -> a__U131(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
 a__isNaturalKind(0()) -> tt()
 a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
 a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
 a__isNaturalKind(sel(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
 a__isPLNat(pair(V1,V2)) -> a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
 a__isPLNat(splitAt(V1,V2)) -> a__U151(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
 a__isPLNatKind(pair(V1,V2)) -> a__and(a__isLNatKind(V1),isLNatKind(V2))
 a__isPLNatKind(splitAt(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
 a__natsFrom(N) -> a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N)
 a__sel(N,XS) ->
 a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
 a__snd(pair(X,Y)) ->
 a__U181(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
 a__splitAt(0(),XS) -> a__U191(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
 a__splitAt(s(N),cons(X,XS)) ->
 a__U201(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                             and(isLNat(XS),isLNatKind(XS)))),
         N,X,XS)
 a__tail(cons(N,XS)) ->
 a__U211(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
 a__take(N,XS) ->
 a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
 mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
 mark(U102(X1,X2)) -> a__U102(mark(X1),X2)
 mark(isNatural(X)) -> a__isNatural(X)
 mark(U103(X)) -> a__U103(mark(X))
 mark(isLNat(X)) -> a__isLNat(X)
 mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
 mark(snd(X)) -> a__snd(mark(X))
 mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
 mark(U111(X1,X2)) -> a__U111(mark(X1),X2)
 mark(U112(X)) -> a__U112(mark(X))
 mark(U121(X1,X2)) -> a__U121(mark(X1),X2)
 mark(U122(X)) -> a__U122(mark(X))
 mark(U131(X1,X2,X3)) -> a__U131(mark(X1),X2,X3)
 mark(U132(X1,X2)) -> a__U132(mark(X1),X2)
 mark(U133(X)) -> a__U133(mark(X))
 mark(U141(X1,X2,X3)) -> a__U141(mark(X1),X2,X3)
 mark(U142(X1,X2)) -> a__U142(mark(X1),X2)
 mark(U143(X)) -> a__U143(mark(X))
 mark(U151(X1,X2,X3)) -> a__U151(mark(X1),X2,X3)
 mark(U152(X1,X2)) -> a__U152(mark(X1),X2)
 mark(U153(X)) -> a__U153(mark(X))
 mark(U161(X1,X2)) -> a__U161(mark(X1),X2)
 mark(natsFrom(X)) -> a__natsFrom(mark(X))
 mark(U171(X1,X2,X3)) -> a__U171(mark(X1),X2,X3)
 mark(head(X)) -> a__head(mark(X))
 mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
 mark(U181(X1,X2)) -> a__U181(mark(X1),X2)
 mark(U191(X1,X2)) -> a__U191(mark(X1),X2)
 mark(U201(X1,X2,X3,X4)) -> a__U201(mark(X1),X2,X3,X4)
 mark(U202(X1,X2)) -> a__U202(mark(X1),X2)
 mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
 mark(U211(X1,X2)) -> a__U211(mark(X1),X2)
 mark(U221(X1,X2,X3)) -> a__U221(mark(X1),X2,X3)
 mark(fst(X)) -> a__fst(mark(X))
 mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
 mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
 mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
 mark(U43(X)) -> a__U43(mark(X))
 mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
 mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
 mark(U53(X)) -> a__U53(mark(X))
 mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
 mark(U62(X)) -> a__U62(mark(X))
 mark(isPLNat(X)) -> a__isPLNat(X)
 mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
 mark(U72(X)) -> a__U72(mark(X))
 mark(U81(X1,X2)) -> a__U81(mark(X1),X2)
 mark(U82(X)) -> a__U82(mark(X))
 mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
 mark(U92(X)) -> a__U92(mark(X))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNaturalKind(X)) -> a__isNaturalKind(X)
 mark(isLNatKind(X)) -> a__isLNatKind(X)
 mark(isPLNatKind(X)) -> a__isPLNatKind(X)
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(nil()) -> nil()
 mark(0()) -> 0()
 a__U101(X1,X2,X3) -> U101(X1,X2,X3)
 a__U102(X1,X2) -> U102(X1,X2)
 a__isNatural(X) -> isNatural(X)
 a__U103(X) -> U103(X)
 a__isLNat(X) -> isLNat(X)
 a__U11(X1,X2,X3) -> U11(X1,X2,X3)
 a__snd(X) -> snd(X)
 a__splitAt(X1,X2) -> splitAt(X1,X2)
 a__U111(X1,X2) -> U111(X1,X2)
 a__U112(X) -> U112(X)
 a__U121(X1,X2) -> U121(X1,X2)
 a__U122(X) -> U122(X)
 a__U131(X1,X2,X3) -> U131(X1,X2,X3)
 a__U132(X1,X2) -> U132(X1,X2)
 a__U133(X) -> U133(X)
 a__U141(X1,X2,X3) -> U141(X1,X2,X3)
 a__U142(X1,X2) -> U142(X1,X2)
 a__U143(X) -> U143(X)
 a__U151(X1,X2,X3) -> U151(X1,X2,X3)
 a__U152(X1,X2) -> U152(X1,X2)
 a__U153(X) -> U153(X)
 a__U161(X1,X2) -> U161(X1,X2)
 a__natsFrom(X) -> natsFrom(X)
 a__U171(X1,X2,X3) -> U171(X1,X2,X3)
 a__head(X) -> head(X)
 a__afterNth(X1,X2) -> afterNth(X1,X2)
 a__U181(X1,X2) -> U181(X1,X2)
 a__U191(X1,X2) -> U191(X1,X2)
 a__U201(X1,X2,X3,X4) -> U201(X1,X2,X3,X4)
 a__U202(X1,X2) -> U202(X1,X2)
 a__U21(X1,X2) -> U21(X1,X2)
 a__U211(X1,X2) -> U211(X1,X2)
 a__U221(X1,X2,X3) -> U221(X1,X2,X3)
 a__fst(X) -> fst(X)
 a__U31(X1,X2) -> U31(X1,X2)
 a__U41(X1,X2,X3) -> U41(X1,X2,X3)
 a__U42(X1,X2) -> U42(X1,X2)
 a__U43(X) -> U43(X)
 a__U51(X1,X2,X3) -> U51(X1,X2,X3)
 a__U52(X1,X2) -> U52(X1,X2)
 a__U53(X) -> U53(X)
 a__U61(X1,X2) -> U61(X1,X2)
 a__U62(X) -> U62(X)
 a__isPLNat(X) -> isPLNat(X)
 a__U71(X1,X2) -> U71(X1,X2)
 a__U72(X) -> U72(X)
 a__U81(X1,X2) -> U81(X1,X2)
 a__U82(X) -> U82(X)
 a__U91(X1,X2) -> U91(X1,X2)
 a__U92(X) -> U92(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNaturalKind(X) -> isNaturalKind(X)
 a__isLNatKind(X) -> isLNatKind(X)
 a__isPLNatKind(X) -> isPLNatKind(X)
 a__tail(X) -> tail(X)
 a__take(X1,X2) -> take(X1,X2)
 a__sel(X1,X2) -> sel(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__U101#(tt(),V1,V2) -> a__isNatural#(V1)
   a__U101#(tt(),V1,V2) -> a__U102#(a__isNatural(V1),V2)
   a__U102#(tt(),V2) -> a__isLNat#(V2)
   a__U102#(tt(),V2) -> a__U103#(a__isLNat(V2))
   a__U11#(tt(),N,XS) -> mark#(XS)
   a__U11#(tt(),N,XS) -> mark#(N)
   a__U11#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
   a__U11#(tt(),N,XS) -> a__snd#(a__splitAt(mark(N),mark(XS)))
   a__U111#(tt(),V1) -> a__isLNat#(V1)
   a__U111#(tt(),V1) -> a__U112#(a__isLNat(V1))
   a__U121#(tt(),V1) -> a__isNatural#(V1)
   a__U121#(tt(),V1) -> a__U122#(a__isNatural(V1))
   a__U131#(tt(),V1,V2) -> a__isNatural#(V1)
   a__U131#(tt(),V1,V2) -> a__U132#(a__isNatural(V1),V2)
   a__U132#(tt(),V2) -> a__isLNat#(V2)
   a__U132#(tt(),V2) -> a__U133#(a__isLNat(V2))
   a__U141#(tt(),V1,V2) -> a__isLNat#(V1)
   a__U141#(tt(),V1,V2) -> a__U142#(a__isLNat(V1),V2)
   a__U142#(tt(),V2) -> a__isLNat#(V2)
   a__U142#(tt(),V2) -> a__U143#(a__isLNat(V2))
   a__U151#(tt(),V1,V2) -> a__isNatural#(V1)
   a__U151#(tt(),V1,V2) -> a__U152#(a__isNatural(V1),V2)
   a__U152#(tt(),V2) -> a__isLNat#(V2)
   a__U152#(tt(),V2) -> a__U153#(a__isLNat(V2))
   a__U161#(tt(),N) -> mark#(N)
   a__U171#(tt(),N,XS) -> mark#(XS)
   a__U171#(tt(),N,XS) -> mark#(N)
   a__U171#(tt(),N,XS) -> a__afterNth#(mark(N),mark(XS))
   a__U171#(tt(),N,XS) -> a__head#(a__afterNth(mark(N),mark(XS)))
   a__U181#(tt(),Y) -> mark#(Y)
   a__U191#(tt(),XS) -> mark#(XS)
   a__U201#(tt(),N,X,XS) -> mark#(XS)
   a__U201#(tt(),N,X,XS) -> mark#(N)
   a__U201#(tt(),N,X,XS) -> a__splitAt#(mark(N),mark(XS))
   a__U201#(tt(),N,X,XS) -> a__U202#(a__splitAt(mark(N),mark(XS)),X)
   a__U202#(pair(YS,ZS),X) -> mark#(ZS)
   a__U202#(pair(YS,ZS),X) -> mark#(X)
   a__U21#(tt(),X) -> mark#(X)
   a__U211#(tt(),XS) -> mark#(XS)
   a__U221#(tt(),N,XS) -> mark#(XS)
   a__U221#(tt(),N,XS) -> mark#(N)
   a__U221#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
   a__U221#(tt(),N,XS) -> a__fst#(a__splitAt(mark(N),mark(XS)))
   a__U31#(tt(),N) -> mark#(N)
   a__U41#(tt(),V1,V2) -> a__isNatural#(V1)
   a__U41#(tt(),V1,V2) -> a__U42#(a__isNatural(V1),V2)
   a__U42#(tt(),V2) -> a__isLNat#(V2)
   a__U42#(tt(),V2) -> a__U43#(a__isLNat(V2))
   a__U51#(tt(),V1,V2) -> a__isNatural#(V1)
   a__U51#(tt(),V1,V2) -> a__U52#(a__isNatural(V1),V2)
   a__U52#(tt(),V2) -> a__isLNat#(V2)
   a__U52#(tt(),V2) -> a__U53#(a__isLNat(V2))
   a__U61#(tt(),V1) -> a__isPLNat#(V1)
   a__U61#(tt(),V1) -> a__U62#(a__isPLNat(V1))
   a__U71#(tt(),V1) -> a__isNatural#(V1)
   a__U71#(tt(),V1) -> a__U72#(a__isNatural(V1))
   a__U81#(tt(),V1) -> a__isPLNat#(V1)
   a__U81#(tt(),V1) -> a__U82#(a__isPLNat(V1))
   a__U91#(tt(),V1) -> a__isLNat#(V1)
   a__U91#(tt(),V1) -> a__U92#(a__isLNat(V1))
   a__afterNth#(N,XS) -> a__isNatural#(N)
   a__afterNth#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__afterNth#(N,XS) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   a__afterNth#(N,XS) ->
   a__U11#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   a__and#(tt(),X) -> mark#(X)
   a__fst#(pair(X,Y)) -> a__isLNat#(X)
   a__fst#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
   a__fst#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
   a__fst#(pair(X,Y)) ->
   a__U21#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
   a__head#(cons(N,XS)) -> a__isNatural#(N)
   a__head#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__head#(cons(N,XS)) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   a__head#(cons(N,XS)) ->
   a__U31#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
   a__isLNat#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNat#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNat#(afterNth(V1,V2)) -> a__U41#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNat#(cons(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNat#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNat#(cons(V1,V2)) -> a__U51#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNat#(fst(V1)) -> a__isPLNatKind#(V1)
   a__isLNat#(fst(V1)) -> a__U61#(a__isPLNatKind(V1),V1)
   a__isLNat#(natsFrom(V1)) -> a__isNaturalKind#(V1)
   a__isLNat#(natsFrom(V1)) -> a__U71#(a__isNaturalKind(V1),V1)
   a__isLNat#(snd(V1)) -> a__isPLNatKind#(V1)
   a__isLNat#(snd(V1)) -> a__U81#(a__isPLNatKind(V1),V1)
   a__isLNat#(tail(V1)) -> a__isLNatKind#(V1)
   a__isLNat#(tail(V1)) -> a__U91#(a__isLNatKind(V1),V1)
   a__isLNat#(take(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNat#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNat#(take(V1,V2)) -> a__U101#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNatKind#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNatKind#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNatKind#(cons(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNatKind#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNatKind#(fst(V1)) -> a__isPLNatKind#(V1)
   a__isLNatKind#(natsFrom(V1)) -> a__isNaturalKind#(V1)
   a__isLNatKind#(snd(V1)) -> a__isPLNatKind#(V1)
   a__isLNatKind#(tail(V1)) -> a__isLNatKind#(V1)
   a__isLNatKind#(take(V1,V2)) -> a__isNaturalKind#(V1)
   a__isLNatKind#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isNatural#(head(V1)) -> a__isLNatKind#(V1)
   a__isNatural#(head(V1)) -> a__U111#(a__isLNatKind(V1),V1)
   a__isNatural#(s(V1)) -> a__isNaturalKind#(V1)
   a__isNatural#(s(V1)) -> a__U121#(a__isNaturalKind(V1),V1)
   a__isNatural#(sel(V1,V2)) -> a__isNaturalKind#(V1)
   a__isNatural#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isNatural#(sel(V1,V2)) -> a__U131#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isNaturalKind#(head(V1)) -> a__isLNatKind#(V1)
   a__isNaturalKind#(s(V1)) -> a__isNaturalKind#(V1)
   a__isNaturalKind#(sel(V1,V2)) -> a__isNaturalKind#(V1)
   a__isNaturalKind#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isPLNat#(pair(V1,V2)) -> a__isLNatKind#(V1)
   a__isPLNat#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
   a__isPLNat#(pair(V1,V2)) -> a__U141#(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
   a__isPLNat#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
   a__isPLNat#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__isPLNat#(splitAt(V1,V2)) -> a__U151#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isPLNatKind#(pair(V1,V2)) -> a__isLNatKind#(V1)
   a__isPLNatKind#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
   a__isPLNatKind#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
   a__isPLNatKind#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
   a__natsFrom#(N) -> a__isNatural#(N)
   a__natsFrom#(N) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__natsFrom#(N) -> a__U161#(a__and(a__isNatural(N),isNaturalKind(N)),N)
   a__sel#(N,XS) -> a__isNatural#(N)
   a__sel#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__sel#(N,XS) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   a__sel#(N,XS) ->
   a__U171#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   a__snd#(pair(X,Y)) -> a__isLNat#(X)
   a__snd#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
   a__snd#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
   a__snd#(pair(X,Y)) ->
   a__U181#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
   a__splitAt#(0(),XS) -> a__isLNat#(XS)
   a__splitAt#(0(),XS) -> a__and#(a__isLNat(XS),isLNatKind(XS))
   a__splitAt#(0(),XS) -> a__U191#(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
   a__splitAt#(s(N),cons(X,XS)) -> a__isNatural#(N)
   a__splitAt#(s(N),cons(X,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__splitAt#(s(N),cons(X,XS)) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                        and(isLNat(XS),isLNatKind(XS))))
   a__splitAt#(s(N),cons(X,XS)) ->
   a__U201#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                                and(isLNat(XS),isLNatKind(XS)))),
            N,X,XS)
   a__tail#(cons(N,XS)) -> a__isNatural#(N)
   a__tail#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__tail#(cons(N,XS)) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   a__tail#(cons(N,XS)) ->
   a__U211#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
   a__take#(N,XS) -> a__isNatural#(N)
   a__take#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
   a__take#(N,XS) ->
   a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
   a__take#(N,XS) ->
   a__U221#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   mark#(U101(X1,X2,X3)) -> mark#(X1)
   mark#(U101(X1,X2,X3)) -> a__U101#(mark(X1),X2,X3)
   mark#(U102(X1,X2)) -> mark#(X1)
   mark#(U102(X1,X2)) -> a__U102#(mark(X1),X2)
   mark#(isNatural(X)) -> a__isNatural#(X)
   mark#(U103(X)) -> mark#(X)
   mark#(U103(X)) -> a__U103#(mark(X))
   mark#(isLNat(X)) -> a__isLNat#(X)
   mark#(U11(X1,X2,X3)) -> mark#(X1)
   mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3)
   mark#(snd(X)) -> mark#(X)
   mark#(snd(X)) -> a__snd#(mark(X))
   mark#(splitAt(X1,X2)) -> mark#(X2)
   mark#(splitAt(X1,X2)) -> mark#(X1)
   mark#(splitAt(X1,X2)) -> a__splitAt#(mark(X1),mark(X2))
   mark#(U111(X1,X2)) -> mark#(X1)
   mark#(U111(X1,X2)) -> a__U111#(mark(X1),X2)
   mark#(U112(X)) -> mark#(X)
   mark#(U112(X)) -> a__U112#(mark(X))
   mark#(U121(X1,X2)) -> mark#(X1)
   mark#(U121(X1,X2)) -> a__U121#(mark(X1),X2)
   mark#(U122(X)) -> mark#(X)
   mark#(U122(X)) -> a__U122#(mark(X))
   mark#(U131(X1,X2,X3)) -> mark#(X1)
   mark#(U131(X1,X2,X3)) -> a__U131#(mark(X1),X2,X3)
   mark#(U132(X1,X2)) -> mark#(X1)
   mark#(U132(X1,X2)) -> a__U132#(mark(X1),X2)
   mark#(U133(X)) -> mark#(X)
   mark#(U133(X)) -> a__U133#(mark(X))
   mark#(U141(X1,X2,X3)) -> mark#(X1)
   mark#(U141(X1,X2,X3)) -> a__U141#(mark(X1),X2,X3)
   mark#(U142(X1,X2)) -> mark#(X1)
   mark#(U142(X1,X2)) -> a__U142#(mark(X1),X2)
   mark#(U143(X)) -> mark#(X)
   mark#(U143(X)) -> a__U143#(mark(X))
   mark#(U151(X1,X2,X3)) -> mark#(X1)
   mark#(U151(X1,X2,X3)) -> a__U151#(mark(X1),X2,X3)
   mark#(U152(X1,X2)) -> mark#(X1)
   mark#(U152(X1,X2)) -> a__U152#(mark(X1),X2)
   mark#(U153(X)) -> mark#(X)
   mark#(U153(X)) -> a__U153#(mark(X))
   mark#(U161(X1,X2)) -> mark#(X1)
   mark#(U161(X1,X2)) -> a__U161#(mark(X1),X2)
   mark#(natsFrom(X)) -> mark#(X)
   mark#(natsFrom(X)) -> a__natsFrom#(mark(X))
   mark#(U171(X1,X2,X3)) -> mark#(X1)
   mark#(U171(X1,X2,X3)) -> a__U171#(mark(X1),X2,X3)
   mark#(head(X)) -> mark#(X)
   mark#(head(X)) -> a__head#(mark(X))
   mark#(afterNth(X1,X2)) -> mark#(X2)
   mark#(afterNth(X1,X2)) -> mark#(X1)
   mark#(afterNth(X1,X2)) -> a__afterNth#(mark(X1),mark(X2))
   mark#(U181(X1,X2)) -> mark#(X1)
   mark#(U181(X1,X2)) -> a__U181#(mark(X1),X2)
   mark#(U191(X1,X2)) -> mark#(X1)
   mark#(U191(X1,X2)) -> a__U191#(mark(X1),X2)
   mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U201(X1,X2,X3,X4)) -> a__U201#(mark(X1),X2,X3,X4)
   mark#(U202(X1,X2)) -> mark#(X1)
   mark#(U202(X1,X2)) -> a__U202#(mark(X1),X2)
   mark#(U21(X1,X2)) -> mark#(X1)
   mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2)
   mark#(U211(X1,X2)) -> mark#(X1)
   mark#(U211(X1,X2)) -> a__U211#(mark(X1),X2)
   mark#(U221(X1,X2,X3)) -> mark#(X1)
   mark#(U221(X1,X2,X3)) -> a__U221#(mark(X1),X2,X3)
   mark#(fst(X)) -> mark#(X)
   mark#(fst(X)) -> a__fst#(mark(X))
   mark#(U31(X1,X2)) -> mark#(X1)
   mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2)
   mark#(U41(X1,X2,X3)) -> mark#(X1)
   mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3)
   mark#(U42(X1,X2)) -> mark#(X1)
   mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2)
   mark#(U43(X)) -> mark#(X)
   mark#(U43(X)) -> a__U43#(mark(X))
   mark#(U51(X1,X2,X3)) -> mark#(X1)
   mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3)
   mark#(U52(X1,X2)) -> mark#(X1)
   mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2)
   mark#(U53(X)) -> mark#(X)
   mark#(U53(X)) -> a__U53#(mark(X))
   mark#(U61(X1,X2)) -> mark#(X1)
   mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2)
   mark#(U62(X)) -> mark#(X)
   mark#(U62(X)) -> a__U62#(mark(X))
   mark#(isPLNat(X)) -> a__isPLNat#(X)
   mark#(U71(X1,X2)) -> mark#(X1)
   mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2)
   mark#(U72(X)) -> mark#(X)
   mark#(U72(X)) -> a__U72#(mark(X))
   mark#(U81(X1,X2)) -> mark#(X1)
   mark#(U81(X1,X2)) -> a__U81#(mark(X1),X2)
   mark#(U82(X)) -> mark#(X)
   mark#(U82(X)) -> a__U82#(mark(X))
   mark#(U91(X1,X2)) -> mark#(X1)
   mark#(U91(X1,X2)) -> a__U91#(mark(X1),X2)
   mark#(U92(X)) -> mark#(X)
   mark#(U92(X)) -> a__U92#(mark(X))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(isNaturalKind(X)) -> a__isNaturalKind#(X)
   mark#(isLNatKind(X)) -> a__isLNatKind#(X)
   mark#(isPLNatKind(X)) -> a__isPLNatKind#(X)
   mark#(tail(X)) -> mark#(X)
   mark#(tail(X)) -> a__tail#(mark(X))
   mark#(take(X1,X2)) -> mark#(X2)
   mark#(take(X1,X2)) -> mark#(X1)
   mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
   mark#(sel(X1,X2)) -> mark#(X2)
   mark#(sel(X1,X2)) -> mark#(X1)
   mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
   mark#(pair(X1,X2)) -> mark#(X2)
   mark#(pair(X1,X2)) -> mark#(X1)
  TRS:
   a__U101(tt(),V1,V2) -> a__U102(a__isNatural(V1),V2)
   a__U102(tt(),V2) -> a__U103(a__isLNat(V2))
   a__U103(tt()) -> tt()
   a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
   a__U111(tt(),V1) -> a__U112(a__isLNat(V1))
   a__U112(tt()) -> tt()
   a__U121(tt(),V1) -> a__U122(a__isNatural(V1))
   a__U122(tt()) -> tt()
   a__U131(tt(),V1,V2) -> a__U132(a__isNatural(V1),V2)
   a__U132(tt(),V2) -> a__U133(a__isLNat(V2))
   a__U133(tt()) -> tt()
   a__U141(tt(),V1,V2) -> a__U142(a__isLNat(V1),V2)
   a__U142(tt(),V2) -> a__U143(a__isLNat(V2))
   a__U143(tt()) -> tt()
   a__U151(tt(),V1,V2) -> a__U152(a__isNatural(V1),V2)
   a__U152(tt(),V2) -> a__U153(a__isLNat(V2))
   a__U153(tt()) -> tt()
   a__U161(tt(),N) -> cons(mark(N),natsFrom(s(N)))
   a__U171(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
   a__U181(tt(),Y) -> mark(Y)
   a__U191(tt(),XS) -> pair(nil(),mark(XS))
   a__U201(tt(),N,X,XS) -> a__U202(a__splitAt(mark(N),mark(XS)),X)
   a__U202(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
   a__U21(tt(),X) -> mark(X)
   a__U211(tt(),XS) -> mark(XS)
   a__U221(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
   a__U31(tt(),N) -> mark(N)
   a__U41(tt(),V1,V2) -> a__U42(a__isNatural(V1),V2)
   a__U42(tt(),V2) -> a__U43(a__isLNat(V2))
   a__U43(tt()) -> tt()
   a__U51(tt(),V1,V2) -> a__U52(a__isNatural(V1),V2)
   a__U52(tt(),V2) -> a__U53(a__isLNat(V2))
   a__U53(tt()) -> tt()
   a__U61(tt(),V1) -> a__U62(a__isPLNat(V1))
   a__U62(tt()) -> tt()
   a__U71(tt(),V1) -> a__U72(a__isNatural(V1))
   a__U72(tt()) -> tt()
   a__U81(tt(),V1) -> a__U82(a__isPLNat(V1))
   a__U82(tt()) -> tt()
   a__U91(tt(),V1) -> a__U92(a__isLNat(V1))
   a__U92(tt()) -> tt()
   a__afterNth(N,XS) ->
   a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   a__and(tt(),X) -> mark(X)
   a__fst(pair(X,Y)) ->
   a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
   a__head(cons(N,XS)) ->
   a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
   a__isLNat(nil()) -> tt()
   a__isLNat(afterNth(V1,V2)) -> a__U41(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNat(cons(V1,V2)) -> a__U51(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1),V1)
   a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1),V1)
   a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1),V1)
   a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1),V1)
   a__isLNat(take(V1,V2)) -> a__U101(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isLNatKind(nil()) -> tt()
   a__isLNatKind(afterNth(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNatKind(cons(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
   a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
   a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
   a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
   a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
   a__isLNatKind(take(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
   a__isNatural(0()) -> tt()
   a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1),V1)
   a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1),V1)
   a__isNatural(sel(V1,V2)) -> a__U131(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isNaturalKind(0()) -> tt()
   a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
   a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
   a__isNaturalKind(sel(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
   a__isPLNat(pair(V1,V2)) -> a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
   a__isPLNat(splitAt(V1,V2)) -> a__U151(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
   a__isPLNatKind(pair(V1,V2)) -> a__and(a__isLNatKind(V1),isLNatKind(V2))
   a__isPLNatKind(splitAt(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
   a__natsFrom(N) -> a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N)
   a__sel(N,XS) ->
   a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   a__snd(pair(X,Y)) ->
   a__U181(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
   a__splitAt(0(),XS) -> a__U191(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
   a__splitAt(s(N),cons(X,XS)) ->
   a__U201(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                               and(isLNat(XS),isLNatKind(XS)))),
           N,X,XS)
   a__tail(cons(N,XS)) ->
   a__U211(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
   a__take(N,XS) ->
   a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
   mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
   mark(U102(X1,X2)) -> a__U102(mark(X1),X2)
   mark(isNatural(X)) -> a__isNatural(X)
   mark(U103(X)) -> a__U103(mark(X))
   mark(isLNat(X)) -> a__isLNat(X)
   mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
   mark(snd(X)) -> a__snd(mark(X))
   mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
   mark(U111(X1,X2)) -> a__U111(mark(X1),X2)
   mark(U112(X)) -> a__U112(mark(X))
   mark(U121(X1,X2)) -> a__U121(mark(X1),X2)
   mark(U122(X)) -> a__U122(mark(X))
   mark(U131(X1,X2,X3)) -> a__U131(mark(X1),X2,X3)
   mark(U132(X1,X2)) -> a__U132(mark(X1),X2)
   mark(U133(X)) -> a__U133(mark(X))
   mark(U141(X1,X2,X3)) -> a__U141(mark(X1),X2,X3)
   mark(U142(X1,X2)) -> a__U142(mark(X1),X2)
   mark(U143(X)) -> a__U143(mark(X))
   mark(U151(X1,X2,X3)) -> a__U151(mark(X1),X2,X3)
   mark(U152(X1,X2)) -> a__U152(mark(X1),X2)
   mark(U153(X)) -> a__U153(mark(X))
   mark(U161(X1,X2)) -> a__U161(mark(X1),X2)
   mark(natsFrom(X)) -> a__natsFrom(mark(X))
   mark(U171(X1,X2,X3)) -> a__U171(mark(X1),X2,X3)
   mark(head(X)) -> a__head(mark(X))
   mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
   mark(U181(X1,X2)) -> a__U181(mark(X1),X2)
   mark(U191(X1,X2)) -> a__U191(mark(X1),X2)
   mark(U201(X1,X2,X3,X4)) -> a__U201(mark(X1),X2,X3,X4)
   mark(U202(X1,X2)) -> a__U202(mark(X1),X2)
   mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
   mark(U211(X1,X2)) -> a__U211(mark(X1),X2)
   mark(U221(X1,X2,X3)) -> a__U221(mark(X1),X2,X3)
   mark(fst(X)) -> a__fst(mark(X))
   mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
   mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
   mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
   mark(U43(X)) -> a__U43(mark(X))
   mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
   mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
   mark(U53(X)) -> a__U53(mark(X))
   mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
   mark(U62(X)) -> a__U62(mark(X))
   mark(isPLNat(X)) -> a__isPLNat(X)
   mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
   mark(U72(X)) -> a__U72(mark(X))
   mark(U81(X1,X2)) -> a__U81(mark(X1),X2)
   mark(U82(X)) -> a__U82(mark(X))
   mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
   mark(U92(X)) -> a__U92(mark(X))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(isNaturalKind(X)) -> a__isNaturalKind(X)
   mark(isLNatKind(X)) -> a__isLNatKind(X)
   mark(isPLNatKind(X)) -> a__isPLNatKind(X)
   mark(tail(X)) -> a__tail(mark(X))
   mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
   mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
   mark(tt()) -> tt()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
   mark(nil()) -> nil()
   mark(0()) -> 0()
   a__U101(X1,X2,X3) -> U101(X1,X2,X3)
   a__U102(X1,X2) -> U102(X1,X2)
   a__isNatural(X) -> isNatural(X)
   a__U103(X) -> U103(X)
   a__isLNat(X) -> isLNat(X)
   a__U11(X1,X2,X3) -> U11(X1,X2,X3)
   a__snd(X) -> snd(X)
   a__splitAt(X1,X2) -> splitAt(X1,X2)
   a__U111(X1,X2) -> U111(X1,X2)
   a__U112(X) -> U112(X)
   a__U121(X1,X2) -> U121(X1,X2)
   a__U122(X) -> U122(X)
   a__U131(X1,X2,X3) -> U131(X1,X2,X3)
   a__U132(X1,X2) -> U132(X1,X2)
   a__U133(X) -> U133(X)
   a__U141(X1,X2,X3) -> U141(X1,X2,X3)
   a__U142(X1,X2) -> U142(X1,X2)
   a__U143(X) -> U143(X)
   a__U151(X1,X2,X3) -> U151(X1,X2,X3)
   a__U152(X1,X2) -> U152(X1,X2)
   a__U153(X) -> U153(X)
   a__U161(X1,X2) -> U161(X1,X2)
   a__natsFrom(X) -> natsFrom(X)
   a__U171(X1,X2,X3) -> U171(X1,X2,X3)
   a__head(X) -> head(X)
   a__afterNth(X1,X2) -> afterNth(X1,X2)
   a__U181(X1,X2) -> U181(X1,X2)
   a__U191(X1,X2) -> U191(X1,X2)
   a__U201(X1,X2,X3,X4) -> U201(X1,X2,X3,X4)
   a__U202(X1,X2) -> U202(X1,X2)
   a__U21(X1,X2) -> U21(X1,X2)
   a__U211(X1,X2) -> U211(X1,X2)
   a__U221(X1,X2,X3) -> U221(X1,X2,X3)
   a__fst(X) -> fst(X)
   a__U31(X1,X2) -> U31(X1,X2)
   a__U41(X1,X2,X3) -> U41(X1,X2,X3)
   a__U42(X1,X2) -> U42(X1,X2)
   a__U43(X) -> U43(X)
   a__U51(X1,X2,X3) -> U51(X1,X2,X3)
   a__U52(X1,X2) -> U52(X1,X2)
   a__U53(X) -> U53(X)
   a__U61(X1,X2) -> U61(X1,X2)
   a__U62(X) -> U62(X)
   a__isPLNat(X) -> isPLNat(X)
   a__U71(X1,X2) -> U71(X1,X2)
   a__U72(X) -> U72(X)
   a__U81(X1,X2) -> U81(X1,X2)
   a__U82(X) -> U82(X)
   a__U91(X1,X2) -> U91(X1,X2)
   a__U92(X) -> U92(X)
   a__and(X1,X2) -> and(X1,X2)
   a__isNaturalKind(X) -> isNaturalKind(X)
   a__isLNatKind(X) -> isLNatKind(X)
   a__isPLNatKind(X) -> isPLNatKind(X)
   a__tail(X) -> tail(X)
   a__take(X1,X2) -> take(X1,X2)
   a__sel(X1,X2) -> sel(X1,X2)
  TDG Processor:
   DPs:
    a__U101#(tt(),V1,V2) -> a__isNatural#(V1)
    a__U101#(tt(),V1,V2) -> a__U102#(a__isNatural(V1),V2)
    a__U102#(tt(),V2) -> a__isLNat#(V2)
    a__U102#(tt(),V2) -> a__U103#(a__isLNat(V2))
    a__U11#(tt(),N,XS) -> mark#(XS)
    a__U11#(tt(),N,XS) -> mark#(N)
    a__U11#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
    a__U11#(tt(),N,XS) -> a__snd#(a__splitAt(mark(N),mark(XS)))
    a__U111#(tt(),V1) -> a__isLNat#(V1)
    a__U111#(tt(),V1) -> a__U112#(a__isLNat(V1))
    a__U121#(tt(),V1) -> a__isNatural#(V1)
    a__U121#(tt(),V1) -> a__U122#(a__isNatural(V1))
    a__U131#(tt(),V1,V2) -> a__isNatural#(V1)
    a__U131#(tt(),V1,V2) -> a__U132#(a__isNatural(V1),V2)
    a__U132#(tt(),V2) -> a__isLNat#(V2)
    a__U132#(tt(),V2) -> a__U133#(a__isLNat(V2))
    a__U141#(tt(),V1,V2) -> a__isLNat#(V1)
    a__U141#(tt(),V1,V2) -> a__U142#(a__isLNat(V1),V2)
    a__U142#(tt(),V2) -> a__isLNat#(V2)
    a__U142#(tt(),V2) -> a__U143#(a__isLNat(V2))
    a__U151#(tt(),V1,V2) -> a__isNatural#(V1)
    a__U151#(tt(),V1,V2) -> a__U152#(a__isNatural(V1),V2)
    a__U152#(tt(),V2) -> a__isLNat#(V2)
    a__U152#(tt(),V2) -> a__U153#(a__isLNat(V2))
    a__U161#(tt(),N) -> mark#(N)
    a__U171#(tt(),N,XS) -> mark#(XS)
    a__U171#(tt(),N,XS) -> mark#(N)
    a__U171#(tt(),N,XS) -> a__afterNth#(mark(N),mark(XS))
    a__U171#(tt(),N,XS) -> a__head#(a__afterNth(mark(N),mark(XS)))
    a__U181#(tt(),Y) -> mark#(Y)
    a__U191#(tt(),XS) -> mark#(XS)
    a__U201#(tt(),N,X,XS) -> mark#(XS)
    a__U201#(tt(),N,X,XS) -> mark#(N)
    a__U201#(tt(),N,X,XS) -> a__splitAt#(mark(N),mark(XS))
    a__U201#(tt(),N,X,XS) -> a__U202#(a__splitAt(mark(N),mark(XS)),X)
    a__U202#(pair(YS,ZS),X) -> mark#(ZS)
    a__U202#(pair(YS,ZS),X) -> mark#(X)
    a__U21#(tt(),X) -> mark#(X)
    a__U211#(tt(),XS) -> mark#(XS)
    a__U221#(tt(),N,XS) -> mark#(XS)
    a__U221#(tt(),N,XS) -> mark#(N)
    a__U221#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
    a__U221#(tt(),N,XS) -> a__fst#(a__splitAt(mark(N),mark(XS)))
    a__U31#(tt(),N) -> mark#(N)
    a__U41#(tt(),V1,V2) -> a__isNatural#(V1)
    a__U41#(tt(),V1,V2) -> a__U42#(a__isNatural(V1),V2)
    a__U42#(tt(),V2) -> a__isLNat#(V2)
    a__U42#(tt(),V2) -> a__U43#(a__isLNat(V2))
    a__U51#(tt(),V1,V2) -> a__isNatural#(V1)
    a__U51#(tt(),V1,V2) -> a__U52#(a__isNatural(V1),V2)
    a__U52#(tt(),V2) -> a__isLNat#(V2)
    a__U52#(tt(),V2) -> a__U53#(a__isLNat(V2))
    a__U61#(tt(),V1) -> a__isPLNat#(V1)
    a__U61#(tt(),V1) -> a__U62#(a__isPLNat(V1))
    a__U71#(tt(),V1) -> a__isNatural#(V1)
    a__U71#(tt(),V1) -> a__U72#(a__isNatural(V1))
    a__U81#(tt(),V1) -> a__isPLNat#(V1)
    a__U81#(tt(),V1) -> a__U82#(a__isPLNat(V1))
    a__U91#(tt(),V1) -> a__isLNat#(V1)
    a__U91#(tt(),V1) -> a__U92#(a__isLNat(V1))
    a__afterNth#(N,XS) -> a__isNatural#(N)
    a__afterNth#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__afterNth#(N,XS) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    a__afterNth#(N,XS) ->
    a__U11#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    a__and#(tt(),X) -> mark#(X)
    a__fst#(pair(X,Y)) -> a__isLNat#(X)
    a__fst#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
    a__fst#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
    a__fst#(pair(X,Y)) ->
    a__U21#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
    a__head#(cons(N,XS)) -> a__isNatural#(N)
    a__head#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__head#(cons(N,XS)) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    a__head#(cons(N,XS)) ->
    a__U31#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
    a__isLNat#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNat#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNat#(afterNth(V1,V2)) -> a__U41#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNat#(cons(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNat#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNat#(cons(V1,V2)) -> a__U51#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNat#(fst(V1)) -> a__isPLNatKind#(V1)
    a__isLNat#(fst(V1)) -> a__U61#(a__isPLNatKind(V1),V1)
    a__isLNat#(natsFrom(V1)) -> a__isNaturalKind#(V1)
    a__isLNat#(natsFrom(V1)) -> a__U71#(a__isNaturalKind(V1),V1)
    a__isLNat#(snd(V1)) -> a__isPLNatKind#(V1)
    a__isLNat#(snd(V1)) -> a__U81#(a__isPLNatKind(V1),V1)
    a__isLNat#(tail(V1)) -> a__isLNatKind#(V1)
    a__isLNat#(tail(V1)) -> a__U91#(a__isLNatKind(V1),V1)
    a__isLNat#(take(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNat#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNat#(take(V1,V2)) -> a__U101#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNatKind#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNatKind#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNatKind#(cons(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNatKind#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNatKind#(fst(V1)) -> a__isPLNatKind#(V1)
    a__isLNatKind#(natsFrom(V1)) -> a__isNaturalKind#(V1)
    a__isLNatKind#(snd(V1)) -> a__isPLNatKind#(V1)
    a__isLNatKind#(tail(V1)) -> a__isLNatKind#(V1)
    a__isLNatKind#(take(V1,V2)) -> a__isNaturalKind#(V1)
    a__isLNatKind#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isNatural#(head(V1)) -> a__isLNatKind#(V1)
    a__isNatural#(head(V1)) -> a__U111#(a__isLNatKind(V1),V1)
    a__isNatural#(s(V1)) -> a__isNaturalKind#(V1)
    a__isNatural#(s(V1)) -> a__U121#(a__isNaturalKind(V1),V1)
    a__isNatural#(sel(V1,V2)) -> a__isNaturalKind#(V1)
    a__isNatural#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isNatural#(sel(V1,V2)) -> a__U131#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isNaturalKind#(head(V1)) -> a__isLNatKind#(V1)
    a__isNaturalKind#(s(V1)) -> a__isNaturalKind#(V1)
    a__isNaturalKind#(sel(V1,V2)) -> a__isNaturalKind#(V1)
    a__isNaturalKind#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isPLNat#(pair(V1,V2)) -> a__isLNatKind#(V1)
    a__isPLNat#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
    a__isPLNat#(pair(V1,V2)) -> a__U141#(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
    a__isPLNat#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
    a__isPLNat#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__isPLNat#(splitAt(V1,V2)) -> a__U151#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isPLNatKind#(pair(V1,V2)) -> a__isLNatKind#(V1)
    a__isPLNatKind#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
    a__isPLNatKind#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
    a__isPLNatKind#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
    a__natsFrom#(N) -> a__isNatural#(N)
    a__natsFrom#(N) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__natsFrom#(N) -> a__U161#(a__and(a__isNatural(N),isNaturalKind(N)),N)
    a__sel#(N,XS) -> a__isNatural#(N)
    a__sel#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__sel#(N,XS) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    a__sel#(N,XS) ->
    a__U171#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    a__snd#(pair(X,Y)) -> a__isLNat#(X)
    a__snd#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
    a__snd#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
    a__snd#(pair(X,Y)) ->
    a__U181#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
    a__splitAt#(0(),XS) -> a__isLNat#(XS)
    a__splitAt#(0(),XS) -> a__and#(a__isLNat(XS),isLNatKind(XS))
    a__splitAt#(0(),XS) -> a__U191#(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
    a__splitAt#(s(N),cons(X,XS)) -> a__isNatural#(N)
    a__splitAt#(s(N),cons(X,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__splitAt#(s(N),cons(X,XS)) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                         and(isLNat(XS),isLNatKind(XS))))
    a__splitAt#(s(N),cons(X,XS)) ->
    a__U201#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                                 and(isLNat(XS),isLNatKind(XS)))),
             N,X,XS)
    a__tail#(cons(N,XS)) -> a__isNatural#(N)
    a__tail#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__tail#(cons(N,XS)) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    a__tail#(cons(N,XS)) ->
    a__U211#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
    a__take#(N,XS) -> a__isNatural#(N)
    a__take#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
    a__take#(N,XS) ->
    a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
    a__take#(N,XS) ->
    a__U221#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    mark#(U101(X1,X2,X3)) -> mark#(X1)
    mark#(U101(X1,X2,X3)) -> a__U101#(mark(X1),X2,X3)
    mark#(U102(X1,X2)) -> mark#(X1)
    mark#(U102(X1,X2)) -> a__U102#(mark(X1),X2)
    mark#(isNatural(X)) -> a__isNatural#(X)
    mark#(U103(X)) -> mark#(X)
    mark#(U103(X)) -> a__U103#(mark(X))
    mark#(isLNat(X)) -> a__isLNat#(X)
    mark#(U11(X1,X2,X3)) -> mark#(X1)
    mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3)
    mark#(snd(X)) -> mark#(X)
    mark#(snd(X)) -> a__snd#(mark(X))
    mark#(splitAt(X1,X2)) -> mark#(X2)
    mark#(splitAt(X1,X2)) -> mark#(X1)
    mark#(splitAt(X1,X2)) -> a__splitAt#(mark(X1),mark(X2))
    mark#(U111(X1,X2)) -> mark#(X1)
    mark#(U111(X1,X2)) -> a__U111#(mark(X1),X2)
    mark#(U112(X)) -> mark#(X)
    mark#(U112(X)) -> a__U112#(mark(X))
    mark#(U121(X1,X2)) -> mark#(X1)
    mark#(U121(X1,X2)) -> a__U121#(mark(X1),X2)
    mark#(U122(X)) -> mark#(X)
    mark#(U122(X)) -> a__U122#(mark(X))
    mark#(U131(X1,X2,X3)) -> mark#(X1)
    mark#(U131(X1,X2,X3)) -> a__U131#(mark(X1),X2,X3)
    mark#(U132(X1,X2)) -> mark#(X1)
    mark#(U132(X1,X2)) -> a__U132#(mark(X1),X2)
    mark#(U133(X)) -> mark#(X)
    mark#(U133(X)) -> a__U133#(mark(X))
    mark#(U141(X1,X2,X3)) -> mark#(X1)
    mark#(U141(X1,X2,X3)) -> a__U141#(mark(X1),X2,X3)
    mark#(U142(X1,X2)) -> mark#(X1)
    mark#(U142(X1,X2)) -> a__U142#(mark(X1),X2)
    mark#(U143(X)) -> mark#(X)
    mark#(U143(X)) -> a__U143#(mark(X))
    mark#(U151(X1,X2,X3)) -> mark#(X1)
    mark#(U151(X1,X2,X3)) -> a__U151#(mark(X1),X2,X3)
    mark#(U152(X1,X2)) -> mark#(X1)
    mark#(U152(X1,X2)) -> a__U152#(mark(X1),X2)
    mark#(U153(X)) -> mark#(X)
    mark#(U153(X)) -> a__U153#(mark(X))
    mark#(U161(X1,X2)) -> mark#(X1)
    mark#(U161(X1,X2)) -> a__U161#(mark(X1),X2)
    mark#(natsFrom(X)) -> mark#(X)
    mark#(natsFrom(X)) -> a__natsFrom#(mark(X))
    mark#(U171(X1,X2,X3)) -> mark#(X1)
    mark#(U171(X1,X2,X3)) -> a__U171#(mark(X1),X2,X3)
    mark#(head(X)) -> mark#(X)
    mark#(head(X)) -> a__head#(mark(X))
    mark#(afterNth(X1,X2)) -> mark#(X2)
    mark#(afterNth(X1,X2)) -> mark#(X1)
    mark#(afterNth(X1,X2)) -> a__afterNth#(mark(X1),mark(X2))
    mark#(U181(X1,X2)) -> mark#(X1)
    mark#(U181(X1,X2)) -> a__U181#(mark(X1),X2)
    mark#(U191(X1,X2)) -> mark#(X1)
    mark#(U191(X1,X2)) -> a__U191#(mark(X1),X2)
    mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U201(X1,X2,X3,X4)) -> a__U201#(mark(X1),X2,X3,X4)
    mark#(U202(X1,X2)) -> mark#(X1)
    mark#(U202(X1,X2)) -> a__U202#(mark(X1),X2)
    mark#(U21(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2)
    mark#(U211(X1,X2)) -> mark#(X1)
    mark#(U211(X1,X2)) -> a__U211#(mark(X1),X2)
    mark#(U221(X1,X2,X3)) -> mark#(X1)
    mark#(U221(X1,X2,X3)) -> a__U221#(mark(X1),X2,X3)
    mark#(fst(X)) -> mark#(X)
    mark#(fst(X)) -> a__fst#(mark(X))
    mark#(U31(X1,X2)) -> mark#(X1)
    mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2)
    mark#(U41(X1,X2,X3)) -> mark#(X1)
    mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3)
    mark#(U42(X1,X2)) -> mark#(X1)
    mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2)
    mark#(U43(X)) -> mark#(X)
    mark#(U43(X)) -> a__U43#(mark(X))
    mark#(U51(X1,X2,X3)) -> mark#(X1)
    mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3)
    mark#(U52(X1,X2)) -> mark#(X1)
    mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2)
    mark#(U53(X)) -> mark#(X)
    mark#(U53(X)) -> a__U53#(mark(X))
    mark#(U61(X1,X2)) -> mark#(X1)
    mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2)
    mark#(U62(X)) -> mark#(X)
    mark#(U62(X)) -> a__U62#(mark(X))
    mark#(isPLNat(X)) -> a__isPLNat#(X)
    mark#(U71(X1,X2)) -> mark#(X1)
    mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2)
    mark#(U72(X)) -> mark#(X)
    mark#(U72(X)) -> a__U72#(mark(X))
    mark#(U81(X1,X2)) -> mark#(X1)
    mark#(U81(X1,X2)) -> a__U81#(mark(X1),X2)
    mark#(U82(X)) -> mark#(X)
    mark#(U82(X)) -> a__U82#(mark(X))
    mark#(U91(X1,X2)) -> mark#(X1)
    mark#(U91(X1,X2)) -> a__U91#(mark(X1),X2)
    mark#(U92(X)) -> mark#(X)
    mark#(U92(X)) -> a__U92#(mark(X))
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(isNaturalKind(X)) -> a__isNaturalKind#(X)
    mark#(isLNatKind(X)) -> a__isLNatKind#(X)
    mark#(isPLNatKind(X)) -> a__isPLNatKind#(X)
    mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(take(X1,X2)) -> mark#(X2)
    mark#(take(X1,X2)) -> mark#(X1)
    mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
    mark#(sel(X1,X2)) -> mark#(X2)
    mark#(sel(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
    mark#(pair(X1,X2)) -> mark#(X2)
    mark#(pair(X1,X2)) -> mark#(X1)
   TRS:
    a__U101(tt(),V1,V2) -> a__U102(a__isNatural(V1),V2)
    a__U102(tt(),V2) -> a__U103(a__isLNat(V2))
    a__U103(tt()) -> tt()
    a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
    a__U111(tt(),V1) -> a__U112(a__isLNat(V1))
    a__U112(tt()) -> tt()
    a__U121(tt(),V1) -> a__U122(a__isNatural(V1))
    a__U122(tt()) -> tt()
    a__U131(tt(),V1,V2) -> a__U132(a__isNatural(V1),V2)
    a__U132(tt(),V2) -> a__U133(a__isLNat(V2))
    a__U133(tt()) -> tt()
    a__U141(tt(),V1,V2) -> a__U142(a__isLNat(V1),V2)
    a__U142(tt(),V2) -> a__U143(a__isLNat(V2))
    a__U143(tt()) -> tt()
    a__U151(tt(),V1,V2) -> a__U152(a__isNatural(V1),V2)
    a__U152(tt(),V2) -> a__U153(a__isLNat(V2))
    a__U153(tt()) -> tt()
    a__U161(tt(),N) -> cons(mark(N),natsFrom(s(N)))
    a__U171(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
    a__U181(tt(),Y) -> mark(Y)
    a__U191(tt(),XS) -> pair(nil(),mark(XS))
    a__U201(tt(),N,X,XS) -> a__U202(a__splitAt(mark(N),mark(XS)),X)
    a__U202(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
    a__U21(tt(),X) -> mark(X)
    a__U211(tt(),XS) -> mark(XS)
    a__U221(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
    a__U31(tt(),N) -> mark(N)
    a__U41(tt(),V1,V2) -> a__U42(a__isNatural(V1),V2)
    a__U42(tt(),V2) -> a__U43(a__isLNat(V2))
    a__U43(tt()) -> tt()
    a__U51(tt(),V1,V2) -> a__U52(a__isNatural(V1),V2)
    a__U52(tt(),V2) -> a__U53(a__isLNat(V2))
    a__U53(tt()) -> tt()
    a__U61(tt(),V1) -> a__U62(a__isPLNat(V1))
    a__U62(tt()) -> tt()
    a__U71(tt(),V1) -> a__U72(a__isNatural(V1))
    a__U72(tt()) -> tt()
    a__U81(tt(),V1) -> a__U82(a__isPLNat(V1))
    a__U82(tt()) -> tt()
    a__U91(tt(),V1) -> a__U92(a__isLNat(V1))
    a__U92(tt()) -> tt()
    a__afterNth(N,XS) ->
    a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    a__and(tt(),X) -> mark(X)
    a__fst(pair(X,Y)) ->
    a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
    a__head(cons(N,XS)) ->
    a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
    a__isLNat(nil()) -> tt()
    a__isLNat(afterNth(V1,V2)) -> a__U41(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNat(cons(V1,V2)) -> a__U51(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1),V1)
    a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1),V1)
    a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1),V1)
    a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1),V1)
    a__isLNat(take(V1,V2)) -> a__U101(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isLNatKind(nil()) -> tt()
    a__isLNatKind(afterNth(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNatKind(cons(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
    a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
    a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
    a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
    a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
    a__isLNatKind(take(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
    a__isNatural(0()) -> tt()
    a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1),V1)
    a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1),V1)
    a__isNatural(sel(V1,V2)) -> a__U131(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isNaturalKind(0()) -> tt()
    a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
    a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
    a__isNaturalKind(sel(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
    a__isPLNat(pair(V1,V2)) -> a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
    a__isPLNat(splitAt(V1,V2)) -> a__U151(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
    a__isPLNatKind(pair(V1,V2)) -> a__and(a__isLNatKind(V1),isLNatKind(V2))
    a__isPLNatKind(splitAt(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
    a__natsFrom(N) -> a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N)
    a__sel(N,XS) ->
    a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    a__snd(pair(X,Y)) ->
    a__U181(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
    a__splitAt(0(),XS) -> a__U191(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
    a__splitAt(s(N),cons(X,XS)) ->
    a__U201(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                                and(isLNat(XS),isLNatKind(XS)))),
            N,X,XS)
    a__tail(cons(N,XS)) ->
    a__U211(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
    a__take(N,XS) ->
    a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
    mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
    mark(U102(X1,X2)) -> a__U102(mark(X1),X2)
    mark(isNatural(X)) -> a__isNatural(X)
    mark(U103(X)) -> a__U103(mark(X))
    mark(isLNat(X)) -> a__isLNat(X)
    mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    mark(snd(X)) -> a__snd(mark(X))
    mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
    mark(U111(X1,X2)) -> a__U111(mark(X1),X2)
    mark(U112(X)) -> a__U112(mark(X))
    mark(U121(X1,X2)) -> a__U121(mark(X1),X2)
    mark(U122(X)) -> a__U122(mark(X))
    mark(U131(X1,X2,X3)) -> a__U131(mark(X1),X2,X3)
    mark(U132(X1,X2)) -> a__U132(mark(X1),X2)
    mark(U133(X)) -> a__U133(mark(X))
    mark(U141(X1,X2,X3)) -> a__U141(mark(X1),X2,X3)
    mark(U142(X1,X2)) -> a__U142(mark(X1),X2)
    mark(U143(X)) -> a__U143(mark(X))
    mark(U151(X1,X2,X3)) -> a__U151(mark(X1),X2,X3)
    mark(U152(X1,X2)) -> a__U152(mark(X1),X2)
    mark(U153(X)) -> a__U153(mark(X))
    mark(U161(X1,X2)) -> a__U161(mark(X1),X2)
    mark(natsFrom(X)) -> a__natsFrom(mark(X))
    mark(U171(X1,X2,X3)) -> a__U171(mark(X1),X2,X3)
    mark(head(X)) -> a__head(mark(X))
    mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
    mark(U181(X1,X2)) -> a__U181(mark(X1),X2)
    mark(U191(X1,X2)) -> a__U191(mark(X1),X2)
    mark(U201(X1,X2,X3,X4)) -> a__U201(mark(X1),X2,X3,X4)
    mark(U202(X1,X2)) -> a__U202(mark(X1),X2)
    mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
    mark(U211(X1,X2)) -> a__U211(mark(X1),X2)
    mark(U221(X1,X2,X3)) -> a__U221(mark(X1),X2,X3)
    mark(fst(X)) -> a__fst(mark(X))
    mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
    mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
    mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
    mark(U43(X)) -> a__U43(mark(X))
    mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
    mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
    mark(U53(X)) -> a__U53(mark(X))
    mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
    mark(U62(X)) -> a__U62(mark(X))
    mark(isPLNat(X)) -> a__isPLNat(X)
    mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
    mark(U72(X)) -> a__U72(mark(X))
    mark(U81(X1,X2)) -> a__U81(mark(X1),X2)
    mark(U82(X)) -> a__U82(mark(X))
    mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
    mark(U92(X)) -> a__U92(mark(X))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(isNaturalKind(X)) -> a__isNaturalKind(X)
    mark(isLNatKind(X)) -> a__isLNatKind(X)
    mark(isPLNatKind(X)) -> a__isPLNatKind(X)
    mark(tail(X)) -> a__tail(mark(X))
    mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    mark(tt()) -> tt()
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    mark(nil()) -> nil()
    mark(0()) -> 0()
    a__U101(X1,X2,X3) -> U101(X1,X2,X3)
    a__U102(X1,X2) -> U102(X1,X2)
    a__isNatural(X) -> isNatural(X)
    a__U103(X) -> U103(X)
    a__isLNat(X) -> isLNat(X)
    a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    a__snd(X) -> snd(X)
    a__splitAt(X1,X2) -> splitAt(X1,X2)
    a__U111(X1,X2) -> U111(X1,X2)
    a__U112(X) -> U112(X)
    a__U121(X1,X2) -> U121(X1,X2)
    a__U122(X) -> U122(X)
    a__U131(X1,X2,X3) -> U131(X1,X2,X3)
    a__U132(X1,X2) -> U132(X1,X2)
    a__U133(X) -> U133(X)
    a__U141(X1,X2,X3) -> U141(X1,X2,X3)
    a__U142(X1,X2) -> U142(X1,X2)
    a__U143(X) -> U143(X)
    a__U151(X1,X2,X3) -> U151(X1,X2,X3)
    a__U152(X1,X2) -> U152(X1,X2)
    a__U153(X) -> U153(X)
    a__U161(X1,X2) -> U161(X1,X2)
    a__natsFrom(X) -> natsFrom(X)
    a__U171(X1,X2,X3) -> U171(X1,X2,X3)
    a__head(X) -> head(X)
    a__afterNth(X1,X2) -> afterNth(X1,X2)
    a__U181(X1,X2) -> U181(X1,X2)
    a__U191(X1,X2) -> U191(X1,X2)
    a__U201(X1,X2,X3,X4) -> U201(X1,X2,X3,X4)
    a__U202(X1,X2) -> U202(X1,X2)
    a__U21(X1,X2) -> U21(X1,X2)
    a__U211(X1,X2) -> U211(X1,X2)
    a__U221(X1,X2,X3) -> U221(X1,X2,X3)
    a__fst(X) -> fst(X)
    a__U31(X1,X2) -> U31(X1,X2)
    a__U41(X1,X2,X3) -> U41(X1,X2,X3)
    a__U42(X1,X2) -> U42(X1,X2)
    a__U43(X) -> U43(X)
    a__U51(X1,X2,X3) -> U51(X1,X2,X3)
    a__U52(X1,X2) -> U52(X1,X2)
    a__U53(X) -> U53(X)
    a__U61(X1,X2) -> U61(X1,X2)
    a__U62(X) -> U62(X)
    a__isPLNat(X) -> isPLNat(X)
    a__U71(X1,X2) -> U71(X1,X2)
    a__U72(X) -> U72(X)
    a__U81(X1,X2) -> U81(X1,X2)
    a__U82(X) -> U82(X)
    a__U91(X1,X2) -> U91(X1,X2)
    a__U92(X) -> U92(X)
    a__and(X1,X2) -> and(X1,X2)
    a__isNaturalKind(X) -> isNaturalKind(X)
    a__isLNatKind(X) -> isLNatKind(X)
    a__isPLNatKind(X) -> isPLNatKind(X)
    a__tail(X) -> tail(X)
    a__take(X1,X2) -> take(X1,X2)
    a__sel(X1,X2) -> sel(X1,X2)
   graph:
    ...
   SCC Processor:
    #sccs: 1
    #rules: 239
    #arcs: 9536/69169
    DPs:
     a__take#(N,XS) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
     a__and#(tt(),X) -> mark#(X)
     mark#(U101(X1,X2,X3)) -> mark#(X1)
     mark#(U101(X1,X2,X3)) -> a__U101#(mark(X1),X2,X3)
     a__U101#(tt(),V1,V2) -> a__isNatural#(V1)
     a__isNatural#(head(V1)) -> a__isLNatKind#(V1)
     a__isLNatKind#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
     a__isNaturalKind#(head(V1)) -> a__isLNatKind#(V1)
     a__isLNatKind#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind#(cons(V1,V2)) -> a__isNaturalKind#(V1)
     a__isNaturalKind#(s(V1)) -> a__isNaturalKind#(V1)
     a__isNaturalKind#(sel(V1,V2)) -> a__isNaturalKind#(V1)
     a__isNaturalKind#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind#(fst(V1)) -> a__isPLNatKind#(V1)
     a__isPLNatKind#(pair(V1,V2)) -> a__isLNatKind#(V1)
     a__isLNatKind#(natsFrom(V1)) -> a__isNaturalKind#(V1)
     a__isLNatKind#(snd(V1)) -> a__isPLNatKind#(V1)
     a__isPLNatKind#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
     a__isPLNatKind#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
     a__isPLNatKind#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind#(tail(V1)) -> a__isLNatKind#(V1)
     a__isLNatKind#(take(V1,V2)) -> a__isNaturalKind#(V1)
     a__isLNatKind#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isNatural#(head(V1)) -> a__U111#(a__isLNatKind(V1),V1)
     a__U111#(tt(),V1) -> a__isLNat#(V1)
     a__isLNat#(afterNth(V1,V2)) -> a__isNaturalKind#(V1)
     a__isLNat#(afterNth(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNat#(afterNth(V1,V2)) -> a__U41#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__U41#(tt(),V1,V2) -> a__isNatural#(V1)
     a__isNatural#(s(V1)) -> a__isNaturalKind#(V1)
     a__isNatural#(s(V1)) -> a__U121#(a__isNaturalKind(V1),V1)
     a__U121#(tt(),V1) -> a__isNatural#(V1)
     a__isNatural#(sel(V1,V2)) -> a__isNaturalKind#(V1)
     a__isNatural#(sel(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isNatural#(sel(V1,V2)) -> a__U131#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__U131#(tt(),V1,V2) -> a__isNatural#(V1)
     a__U131#(tt(),V1,V2) -> a__U132#(a__isNatural(V1),V2)
     a__U132#(tt(),V2) -> a__isLNat#(V2)
     a__isLNat#(cons(V1,V2)) -> a__isNaturalKind#(V1)
     a__isLNat#(cons(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNat#(cons(V1,V2)) -> a__U51#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__U51#(tt(),V1,V2) -> a__isNatural#(V1)
     a__U51#(tt(),V1,V2) -> a__U52#(a__isNatural(V1),V2)
     a__U52#(tt(),V2) -> a__isLNat#(V2)
     a__isLNat#(fst(V1)) -> a__isPLNatKind#(V1)
     a__isLNat#(fst(V1)) -> a__U61#(a__isPLNatKind(V1),V1)
     a__U61#(tt(),V1) -> a__isPLNat#(V1)
     a__isPLNat#(pair(V1,V2)) -> a__isLNatKind#(V1)
     a__isPLNat#(pair(V1,V2)) -> a__and#(a__isLNatKind(V1),isLNatKind(V2))
     a__isPLNat#(pair(V1,V2)) -> a__U141#(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
     a__U141#(tt(),V1,V2) -> a__isLNat#(V1)
     a__isLNat#(natsFrom(V1)) -> a__isNaturalKind#(V1)
     a__isLNat#(natsFrom(V1)) -> a__U71#(a__isNaturalKind(V1),V1)
     a__U71#(tt(),V1) -> a__isNatural#(V1)
     a__isLNat#(snd(V1)) -> a__isPLNatKind#(V1)
     a__isLNat#(snd(V1)) -> a__U81#(a__isPLNatKind(V1),V1)
     a__U81#(tt(),V1) -> a__isPLNat#(V1)
     a__isPLNat#(splitAt(V1,V2)) -> a__isNaturalKind#(V1)
     a__isPLNat#(splitAt(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isPLNat#(splitAt(V1,V2)) -> a__U151#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__U151#(tt(),V1,V2) -> a__isNatural#(V1)
     a__U151#(tt(),V1,V2) -> a__U152#(a__isNatural(V1),V2)
     a__U152#(tt(),V2) -> a__isLNat#(V2)
     a__isLNat#(tail(V1)) -> a__isLNatKind#(V1)
     a__isLNat#(tail(V1)) -> a__U91#(a__isLNatKind(V1),V1)
     a__U91#(tt(),V1) -> a__isLNat#(V1)
     a__isLNat#(take(V1,V2)) -> a__isNaturalKind#(V1)
     a__isLNat#(take(V1,V2)) -> a__and#(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNat#(take(V1,V2)) -> a__U101#(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__U101#(tt(),V1,V2) -> a__U102#(a__isNatural(V1),V2)
     a__U102#(tt(),V2) -> a__isLNat#(V2)
     a__U141#(tt(),V1,V2) -> a__U142#(a__isLNat(V1),V2)
     a__U142#(tt(),V2) -> a__isLNat#(V2)
     a__U41#(tt(),V1,V2) -> a__U42#(a__isNatural(V1),V2)
     a__U42#(tt(),V2) -> a__isLNat#(V2)
     mark#(U102(X1,X2)) -> mark#(X1)
     mark#(U102(X1,X2)) -> a__U102#(mark(X1),X2)
     mark#(isNatural(X)) -> a__isNatural#(X)
     mark#(U103(X)) -> mark#(X)
     mark#(isLNat(X)) -> a__isLNat#(X)
     mark#(U11(X1,X2,X3)) -> mark#(X1)
     mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3)
     a__U11#(tt(),N,XS) -> mark#(XS)
     mark#(snd(X)) -> mark#(X)
     mark#(snd(X)) -> a__snd#(mark(X))
     a__snd#(pair(X,Y)) -> a__isLNat#(X)
     a__snd#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
     a__snd#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
     a__snd#(pair(X,Y)) ->
     a__U181#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
     a__U181#(tt(),Y) -> mark#(Y)
     mark#(splitAt(X1,X2)) -> mark#(X2)
     mark#(splitAt(X1,X2)) -> mark#(X1)
     mark#(splitAt(X1,X2)) -> a__splitAt#(mark(X1),mark(X2))
     a__splitAt#(0(),XS) -> a__isLNat#(XS)
     a__splitAt#(0(),XS) -> a__and#(a__isLNat(XS),isLNatKind(XS))
     a__splitAt#(0(),XS) -> a__U191#(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
     a__U191#(tt(),XS) -> mark#(XS)
     mark#(U111(X1,X2)) -> mark#(X1)
     mark#(U111(X1,X2)) -> a__U111#(mark(X1),X2)
     mark#(U112(X)) -> mark#(X)
     mark#(U121(X1,X2)) -> mark#(X1)
     mark#(U121(X1,X2)) -> a__U121#(mark(X1),X2)
     mark#(U122(X)) -> mark#(X)
     mark#(U131(X1,X2,X3)) -> mark#(X1)
     mark#(U131(X1,X2,X3)) -> a__U131#(mark(X1),X2,X3)
     mark#(U132(X1,X2)) -> mark#(X1)
     mark#(U132(X1,X2)) -> a__U132#(mark(X1),X2)
     mark#(U133(X)) -> mark#(X)
     mark#(U141(X1,X2,X3)) -> mark#(X1)
     mark#(U141(X1,X2,X3)) -> a__U141#(mark(X1),X2,X3)
     mark#(U142(X1,X2)) -> mark#(X1)
     mark#(U142(X1,X2)) -> a__U142#(mark(X1),X2)
     mark#(U143(X)) -> mark#(X)
     mark#(U151(X1,X2,X3)) -> mark#(X1)
     mark#(U151(X1,X2,X3)) -> a__U151#(mark(X1),X2,X3)
     mark#(U152(X1,X2)) -> mark#(X1)
     mark#(U152(X1,X2)) -> a__U152#(mark(X1),X2)
     mark#(U153(X)) -> mark#(X)
     mark#(U161(X1,X2)) -> mark#(X1)
     mark#(U161(X1,X2)) -> a__U161#(mark(X1),X2)
     a__U161#(tt(),N) -> mark#(N)
     mark#(natsFrom(X)) -> mark#(X)
     mark#(natsFrom(X)) -> a__natsFrom#(mark(X))
     a__natsFrom#(N) -> a__isNatural#(N)
     a__natsFrom#(N) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__natsFrom#(N) -> a__U161#(a__and(a__isNatural(N),isNaturalKind(N)),N)
     mark#(U171(X1,X2,X3)) -> mark#(X1)
     mark#(U171(X1,X2,X3)) -> a__U171#(mark(X1),X2,X3)
     a__U171#(tt(),N,XS) -> mark#(XS)
     mark#(head(X)) -> mark#(X)
     mark#(head(X)) -> a__head#(mark(X))
     a__head#(cons(N,XS)) -> a__isNatural#(N)
     a__head#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__head#(cons(N,XS)) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
     a__head#(cons(N,XS)) ->
     a__U31#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
     a__U31#(tt(),N) -> mark#(N)
     mark#(afterNth(X1,X2)) -> mark#(X2)
     mark#(afterNth(X1,X2)) -> mark#(X1)
     mark#(afterNth(X1,X2)) -> a__afterNth#(mark(X1),mark(X2))
     a__afterNth#(N,XS) -> a__isNatural#(N)
     a__afterNth#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__afterNth#(N,XS) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
     a__afterNth#(N,XS) ->
     a__U11#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     a__U11#(tt(),N,XS) -> mark#(N)
     mark#(U181(X1,X2)) -> mark#(X1)
     mark#(U181(X1,X2)) -> a__U181#(mark(X1),X2)
     mark#(U191(X1,X2)) -> mark#(X1)
     mark#(U191(X1,X2)) -> a__U191#(mark(X1),X2)
     mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U201(X1,X2,X3,X4)) -> a__U201#(mark(X1),X2,X3,X4)
     a__U201#(tt(),N,X,XS) -> mark#(XS)
     mark#(U202(X1,X2)) -> mark#(X1)
     mark#(U202(X1,X2)) -> a__U202#(mark(X1),X2)
     a__U202#(pair(YS,ZS),X) -> mark#(ZS)
     mark#(U21(X1,X2)) -> mark#(X1)
     mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2)
     a__U21#(tt(),X) -> mark#(X)
     mark#(U211(X1,X2)) -> mark#(X1)
     mark#(U211(X1,X2)) -> a__U211#(mark(X1),X2)
     a__U211#(tt(),XS) -> mark#(XS)
     mark#(U221(X1,X2,X3)) -> mark#(X1)
     mark#(U221(X1,X2,X3)) -> a__U221#(mark(X1),X2,X3)
     a__U221#(tt(),N,XS) -> mark#(XS)
     mark#(fst(X)) -> mark#(X)
     mark#(fst(X)) -> a__fst#(mark(X))
     a__fst#(pair(X,Y)) -> a__isLNat#(X)
     a__fst#(pair(X,Y)) -> a__and#(a__isLNat(X),isLNatKind(X))
     a__fst#(pair(X,Y)) -> a__and#(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y)))
     a__fst#(pair(X,Y)) ->
     a__U21#(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
     mark#(U31(X1,X2)) -> mark#(X1)
     mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2)
     mark#(U41(X1,X2,X3)) -> mark#(X1)
     mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3)
     mark#(U42(X1,X2)) -> mark#(X1)
     mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2)
     mark#(U43(X)) -> mark#(X)
     mark#(U51(X1,X2,X3)) -> mark#(X1)
     mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3)
     mark#(U52(X1,X2)) -> mark#(X1)
     mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2)
     mark#(U53(X)) -> mark#(X)
     mark#(U61(X1,X2)) -> mark#(X1)
     mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2)
     mark#(U62(X)) -> mark#(X)
     mark#(isPLNat(X)) -> a__isPLNat#(X)
     mark#(U71(X1,X2)) -> mark#(X1)
     mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2)
     mark#(U72(X)) -> mark#(X)
     mark#(U81(X1,X2)) -> mark#(X1)
     mark#(U81(X1,X2)) -> a__U81#(mark(X1),X2)
     mark#(U82(X)) -> mark#(X)
     mark#(U91(X1,X2)) -> mark#(X1)
     mark#(U91(X1,X2)) -> a__U91#(mark(X1),X2)
     mark#(U92(X)) -> mark#(X)
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
     mark#(isNaturalKind(X)) -> a__isNaturalKind#(X)
     mark#(isLNatKind(X)) -> a__isLNatKind#(X)
     mark#(isPLNatKind(X)) -> a__isPLNatKind#(X)
     mark#(tail(X)) -> mark#(X)
     mark#(tail(X)) -> a__tail#(mark(X))
     a__tail#(cons(N,XS)) -> a__isNatural#(N)
     a__tail#(cons(N,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__tail#(cons(N,XS)) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
     a__tail#(cons(N,XS)) ->
     a__U211#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
     mark#(take(X1,X2)) -> mark#(X2)
     mark#(take(X1,X2)) -> mark#(X1)
     mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2))
     a__take#(N,XS) -> a__isNatural#(N)
     a__take#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__take#(N,XS) ->
     a__U221#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     a__U221#(tt(),N,XS) -> mark#(N)
     mark#(sel(X1,X2)) -> mark#(X2)
     mark#(sel(X1,X2)) -> mark#(X1)
     mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
     a__sel#(N,XS) -> a__isNatural#(N)
     a__sel#(N,XS) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__sel#(N,XS) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS)))
     a__sel#(N,XS) ->
     a__U171#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     a__U171#(tt(),N,XS) -> mark#(N)
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(s(X)) -> mark#(X)
     mark#(pair(X1,X2)) -> mark#(X2)
     mark#(pair(X1,X2)) -> mark#(X1)
     a__U171#(tt(),N,XS) -> a__afterNth#(mark(N),mark(XS))
     a__U171#(tt(),N,XS) -> a__head#(a__afterNth(mark(N),mark(XS)))
     a__U221#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
     a__splitAt#(s(N),cons(X,XS)) -> a__isNatural#(N)
     a__splitAt#(s(N),cons(X,XS)) -> a__and#(a__isNatural(N),isNaturalKind(N))
     a__splitAt#(s(N),cons(X,XS)) ->
     a__and#(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                          and(isLNat(XS),isLNatKind(XS))))
     a__splitAt#(s(N),cons(X,XS)) ->
     a__U201#(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and
                                                                  (isNatural(X),isNaturalKind(X)),
                                                                  and
                                                                  (isLNat(XS),isLNatKind(XS)))),
              N,X,XS)
     a__U201#(tt(),N,X,XS) -> mark#(N)
     a__U201#(tt(),N,X,XS) -> a__splitAt#(mark(N),mark(XS))
     a__U201#(tt(),N,X,XS) -> a__U202#(a__splitAt(mark(N),mark(XS)),X)
     a__U202#(pair(YS,ZS),X) -> mark#(X)
     a__U221#(tt(),N,XS) -> a__fst#(a__splitAt(mark(N),mark(XS)))
     a__U11#(tt(),N,XS) -> a__splitAt#(mark(N),mark(XS))
     a__U11#(tt(),N,XS) -> a__snd#(a__splitAt(mark(N),mark(XS)))
    TRS:
     a__U101(tt(),V1,V2) -> a__U102(a__isNatural(V1),V2)
     a__U102(tt(),V2) -> a__U103(a__isLNat(V2))
     a__U103(tt()) -> tt()
     a__U11(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
     a__U111(tt(),V1) -> a__U112(a__isLNat(V1))
     a__U112(tt()) -> tt()
     a__U121(tt(),V1) -> a__U122(a__isNatural(V1))
     a__U122(tt()) -> tt()
     a__U131(tt(),V1,V2) -> a__U132(a__isNatural(V1),V2)
     a__U132(tt(),V2) -> a__U133(a__isLNat(V2))
     a__U133(tt()) -> tt()
     a__U141(tt(),V1,V2) -> a__U142(a__isLNat(V1),V2)
     a__U142(tt(),V2) -> a__U143(a__isLNat(V2))
     a__U143(tt()) -> tt()
     a__U151(tt(),V1,V2) -> a__U152(a__isNatural(V1),V2)
     a__U152(tt(),V2) -> a__U153(a__isLNat(V2))
     a__U153(tt()) -> tt()
     a__U161(tt(),N) -> cons(mark(N),natsFrom(s(N)))
     a__U171(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
     a__U181(tt(),Y) -> mark(Y)
     a__U191(tt(),XS) -> pair(nil(),mark(XS))
     a__U201(tt(),N,X,XS) -> a__U202(a__splitAt(mark(N),mark(XS)),X)
     a__U202(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
     a__U21(tt(),X) -> mark(X)
     a__U211(tt(),XS) -> mark(XS)
     a__U221(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
     a__U31(tt(),N) -> mark(N)
     a__U41(tt(),V1,V2) -> a__U42(a__isNatural(V1),V2)
     a__U42(tt(),V2) -> a__U43(a__isLNat(V2))
     a__U43(tt()) -> tt()
     a__U51(tt(),V1,V2) -> a__U52(a__isNatural(V1),V2)
     a__U52(tt(),V2) -> a__U53(a__isLNat(V2))
     a__U53(tt()) -> tt()
     a__U61(tt(),V1) -> a__U62(a__isPLNat(V1))
     a__U62(tt()) -> tt()
     a__U71(tt(),V1) -> a__U72(a__isNatural(V1))
     a__U72(tt()) -> tt()
     a__U81(tt(),V1) -> a__U82(a__isPLNat(V1))
     a__U82(tt()) -> tt()
     a__U91(tt(),V1) -> a__U92(a__isLNat(V1))
     a__U92(tt()) -> tt()
     a__afterNth(N,XS) ->
     a__U11(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     a__and(tt(),X) -> mark(X)
     a__fst(pair(X,Y)) ->
     a__U21(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),X)
     a__head(cons(N,XS)) ->
     a__U31(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N)
     a__isLNat(nil()) -> tt()
     a__isLNat(afterNth(V1,V2)) -> a__U41(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__isLNat(cons(V1,V2)) -> a__U51(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1),V1)
     a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1),V1)
     a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1),V1)
     a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1),V1)
     a__isLNat(take(V1,V2)) -> a__U101(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__isLNatKind(nil()) -> tt()
     a__isLNatKind(afterNth(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind(cons(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
     a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
     a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
     a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
     a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
     a__isLNatKind(take(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
     a__isNatural(0()) -> tt()
     a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1),V1)
     a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1),V1)
     a__isNatural(sel(V1,V2)) -> a__U131(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__isNaturalKind(0()) -> tt()
     a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
     a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
     a__isNaturalKind(sel(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
     a__isPLNat(pair(V1,V2)) -> a__U141(a__and(a__isLNatKind(V1),isLNatKind(V2)),V1,V2)
     a__isPLNat(splitAt(V1,V2)) -> a__U151(a__and(a__isNaturalKind(V1),isLNatKind(V2)),V1,V2)
     a__isPLNatKind(pair(V1,V2)) -> a__and(a__isLNatKind(V1),isLNatKind(V2))
     a__isPLNatKind(splitAt(V1,V2)) -> a__and(a__isNaturalKind(V1),isLNatKind(V2))
     a__natsFrom(N) -> a__U161(a__and(a__isNatural(N),isNaturalKind(N)),N)
     a__sel(N,XS) ->
     a__U171(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     a__snd(pair(X,Y)) ->
     a__U181(a__and(a__and(a__isLNat(X),isLNatKind(X)),and(isLNat(Y),isLNatKind(Y))),Y)
     a__splitAt(0(),XS) -> a__U191(a__and(a__isLNat(XS),isLNatKind(XS)),XS)
     a__splitAt(s(N),cons(X,XS)) ->
     a__U201(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(and(isNatural(X),isNaturalKind(X)),
                                                                 and(isLNat(XS),isLNatKind(XS)))),
             N,X,XS)
     a__tail(cons(N,XS)) ->
     a__U211(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),XS)
     a__take(N,XS) ->
     a__U221(a__and(a__and(a__isNatural(N),isNaturalKind(N)),and(isLNat(XS),isLNatKind(XS))),N,XS)
     mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
     mark(U102(X1,X2)) -> a__U102(mark(X1),X2)
     mark(isNatural(X)) -> a__isNatural(X)
     mark(U103(X)) -> a__U103(mark(X))
     mark(isLNat(X)) -> a__isLNat(X)
     mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
     mark(snd(X)) -> a__snd(mark(X))
     mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
     mark(U111(X1,X2)) -> a__U111(mark(X1),X2)
     mark(U112(X)) -> a__U112(mark(X))
     mark(U121(X1,X2)) -> a__U121(mark(X1),X2)
     mark(U122(X)) -> a__U122(mark(X))
     mark(U131(X1,X2,X3)) -> a__U131(mark(X1),X2,X3)
     mark(U132(X1,X2)) -> a__U132(mark(X1),X2)
     mark(U133(X)) -> a__U133(mark(X))
     mark(U141(X1,X2,X3)) -> a__U141(mark(X1),X2,X3)
     mark(U142(X1,X2)) -> a__U142(mark(X1),X2)
     mark(U143(X)) -> a__U143(mark(X))
     mark(U151(X1,X2,X3)) -> a__U151(mark(X1),X2,X3)
     mark(U152(X1,X2)) -> a__U152(mark(X1),X2)
     mark(U153(X)) -> a__U153(mark(X))
     mark(U161(X1,X2)) -> a__U161(mark(X1),X2)
     mark(natsFrom(X)) -> a__natsFrom(mark(X))
     mark(U171(X1,X2,X3)) -> a__U171(mark(X1),X2,X3)
     mark(head(X)) -> a__head(mark(X))
     mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
     mark(U181(X1,X2)) -> a__U181(mark(X1),X2)
     mark(U191(X1,X2)) -> a__U191(mark(X1),X2)
     mark(U201(X1,X2,X3,X4)) -> a__U201(mark(X1),X2,X3,X4)
     mark(U202(X1,X2)) -> a__U202(mark(X1),X2)
     mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
     mark(U211(X1,X2)) -> a__U211(mark(X1),X2)
     mark(U221(X1,X2,X3)) -> a__U221(mark(X1),X2,X3)
     mark(fst(X)) -> a__fst(mark(X))
     mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
     mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
     mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
     mark(U43(X)) -> a__U43(mark(X))
     mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
     mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
     mark(U53(X)) -> a__U53(mark(X))
     mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
     mark(U62(X)) -> a__U62(mark(X))
     mark(isPLNat(X)) -> a__isPLNat(X)
     mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
     mark(U72(X)) -> a__U72(mark(X))
     mark(U81(X1,X2)) -> a__U81(mark(X1),X2)
     mark(U82(X)) -> a__U82(mark(X))
     mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
     mark(U92(X)) -> a__U92(mark(X))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(isNaturalKind(X)) -> a__isNaturalKind(X)
     mark(isLNatKind(X)) -> a__isLNatKind(X)
     mark(isPLNatKind(X)) -> a__isPLNatKind(X)
     mark(tail(X)) -> a__tail(mark(X))
     mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
     mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
     mark(tt()) -> tt()
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__U101(X1,X2,X3) -> U101(X1,X2,X3)
     a__U102(X1,X2) -> U102(X1,X2)
     a__isNatural(X) -> isNatural(X)
     a__U103(X) -> U103(X)
     a__isLNat(X) -> isLNat(X)
     a__U11(X1,X2,X3) -> U11(X1,X2,X3)
     a__snd(X) -> snd(X)
     a__splitAt(X1,X2) -> splitAt(X1,X2)
     a__U111(X1,X2) -> U111(X1,X2)
     a__U112(X) -> U112(X)
     a__U121(X1,X2) -> U121(X1,X2)
     a__U122(X) -> U122(X)
     a__U131(X1,X2,X3) -> U131(X1,X2,X3)
     a__U132(X1,X2) -> U132(X1,X2)
     a__U133(X) -> U133(X)
     a__U141(X1,X2,X3) -> U141(X1,X2,X3)
     a__U142(X1,X2) -> U142(X1,X2)
     a__U143(X) -> U143(X)
     a__U151(X1,X2,X3) -> U151(X1,X2,X3)
     a__U152(X1,X2) -> U152(X1,X2)
     a__U153(X) -> U153(X)
     a__U161(X1,X2) -> U161(X1,X2)
     a__natsFrom(X) -> natsFrom(X)
     a__U171(X1,X2,X3) -> U171(X1,X2,X3)
     a__head(X) -> head(X)
     a__afterNth(X1,X2) -> afterNth(X1,X2)
     a__U181(X1,X2) -> U181(X1,X2)
     a__U191(X1,X2) -> U191(X1,X2)
     a__U201(X1,X2,X3,X4) -> U201(X1,X2,X3,X4)
     a__U202(X1,X2) -> U202(X1,X2)
     a__U21(X1,X2) -> U21(X1,X2)
     a__U211(X1,X2) -> U211(X1,X2)
     a__U221(X1,X2,X3) -> U221(X1,X2,X3)
     a__fst(X) -> fst(X)
     a__U31(X1,X2) -> U31(X1,X2)
     a__U41(X1,X2,X3) -> U41(X1,X2,X3)
     a__U42(X1,X2) -> U42(X1,X2)
     a__U43(X) -> U43(X)
     a__U51(X1,X2,X3) -> U51(X1,X2,X3)
     a__U52(X1,X2) -> U52(X1,X2)
     a__U53(X) -> U53(X)
     a__U61(X1,X2) -> U61(X1,X2)
     a__U62(X) -> U62(X)
     a__isPLNat(X) -> isPLNat(X)
     a__U71(X1,X2) -> U71(X1,X2)
     a__U72(X) -> U72(X)
     a__U81(X1,X2) -> U81(X1,X2)
     a__U82(X) -> U82(X)
     a__U91(X1,X2) -> U91(X1,X2)
     a__U92(X) -> U92(X)
     a__and(X1,X2) -> and(X1,X2)
     a__isNaturalKind(X) -> isNaturalKind(X)
     a__isLNatKind(X) -> isLNatKind(X)
     a__isPLNatKind(X) -> isPLNatKind(X)
     a__tail(X) -> tail(X)
     a__take(X1,X2) -> take(X1,X2)
     a__sel(X1,X2) -> sel(X1,X2)
    Open