MAYBE

Problem:
 active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
 active(U102(tt())) -> mark(tt())
 active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
 active(U111(tt())) -> mark(tt())
 active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
 active(U121(tt())) -> mark(tt())
 active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
 active(U132(tt())) -> mark(tt())
 active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
 active(U142(tt())) -> mark(tt())
 active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
 active(U152(tt())) -> mark(tt())
 active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
 active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
 active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
 active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
 active(U182(tt(),Y)) -> mark(Y)
 active(U191(tt(),XS)) -> mark(pair(nil(),XS))
 active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
 active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
 active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
 active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
 active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
 active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
 active(U212(tt(),XS)) -> mark(XS)
 active(U22(tt(),X)) -> mark(X)
 active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
 active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
 active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
 active(U32(tt(),N)) -> mark(N)
 active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
 active(U42(tt())) -> mark(tt())
 active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
 active(U52(tt())) -> mark(tt())
 active(U61(tt())) -> mark(tt())
 active(U71(tt())) -> mark(tt())
 active(U81(tt())) -> mark(tt())
 active(U91(tt())) -> mark(tt())
 active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
 active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
 active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
 active(isLNat(nil())) -> mark(tt())
 active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
 active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
 active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
 active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
 active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
 active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
 active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
 active(isNatural(0())) -> mark(tt())
 active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
 active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
 active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
 active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
 active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
 active(natsFrom(N)) -> mark(U161(isNatural(N),N))
 active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
 active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
 active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
 active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
 active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
 active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
 mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(U102(X)) -> active(U102(mark(X)))
 mark(isLNat(X)) -> active(isLNat(X))
 mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
 mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
 mark(U111(X)) -> active(U111(mark(X)))
 mark(snd(X)) -> active(snd(mark(X)))
 mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
 mark(U121(X)) -> active(U121(mark(X)))
 mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
 mark(U132(X)) -> active(U132(mark(X)))
 mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
 mark(U142(X)) -> active(U142(mark(X)))
 mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
 mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
 mark(isNatural(X)) -> active(isNatural(X))
 mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
 mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
 mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
 mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
 mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
 mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
 mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
 mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
 mark(fst(X)) -> active(fst(mark(X)))
 mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
 mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
 mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
 mark(U42(X)) -> active(U42(mark(X)))
 mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
 mark(U52(X)) -> active(U52(mark(X)))
 mark(U61(X)) -> active(U61(mark(X)))
 mark(U71(X)) -> active(U71(mark(X)))
 mark(U81(X)) -> active(U81(mark(X)))
 mark(U91(X)) -> active(U91(mark(X)))
 mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
 U101(X1,mark(X2)) -> U101(X1,X2)
 U101(active(X1),X2) -> U101(X1,X2)
 U101(X1,active(X2)) -> U101(X1,X2)
 U102(mark(X)) -> U102(X)
 U102(active(X)) -> U102(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)
 U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
 U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
 U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
 U12(active(X1),X2,X3) -> U12(X1,X2,X3)
 U12(X1,active(X2),X3) -> U12(X1,X2,X3)
 U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
 U111(mark(X)) -> U111(X)
 U111(active(X)) -> U111(X)
 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)
 U121(mark(X)) -> U121(X)
 U121(active(X)) -> U121(X)
 U131(mark(X1),X2) -> U131(X1,X2)
 U131(X1,mark(X2)) -> U131(X1,X2)
 U131(active(X1),X2) -> U131(X1,X2)
 U131(X1,active(X2)) -> U131(X1,X2)
 U132(mark(X)) -> U132(X)
 U132(active(X)) -> U132(X)
 U141(mark(X1),X2) -> U141(X1,X2)
 U141(X1,mark(X2)) -> U141(X1,X2)
 U141(active(X1),X2) -> U141(X1,X2)
 U141(X1,active(X2)) -> U141(X1,X2)
 U142(mark(X)) -> U142(X)
 U142(active(X)) -> U142(X)
 U151(mark(X1),X2) -> U151(X1,X2)
 U151(X1,mark(X2)) -> U151(X1,X2)
 U151(active(X1),X2) -> U151(X1,X2)
 U151(X1,active(X2)) -> U151(X1,X2)
 U152(mark(X)) -> U152(X)
 U152(active(X)) -> U152(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)
 U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
 U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
 U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
 U172(active(X1),X2,X3) -> U172(X1,X2,X3)
 U172(X1,active(X2),X3) -> U172(X1,X2,X3)
 U172(X1,X2,active(X3)) -> U172(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)
 U182(mark(X1),X2) -> U182(X1,X2)
 U182(X1,mark(X2)) -> U182(X1,X2)
 U182(active(X1),X2) -> U182(X1,X2)
 U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
 U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
 U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
 U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
 U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
 U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
 U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
 U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
 isNatural(mark(X)) -> isNatural(X)
 isNatural(active(X)) -> isNatural(X)
 U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
 U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
 U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
 U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
 U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
 U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
 U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
 U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
 U204(mark(X1),X2) -> U204(X1,X2)
 U204(X1,mark(X2)) -> U204(X1,X2)
 U204(active(X1),X2) -> U204(X1,X2)
 U204(X1,active(X2)) -> U204(X1,X2)
 U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
 U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
 U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
 U21(active(X1),X2,X3) -> U21(X1,X2,X3)
 U21(X1,active(X2),X3) -> U21(X1,X2,X3)
 U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
 U22(mark(X1),X2) -> U22(X1,X2)
 U22(X1,mark(X2)) -> U22(X1,X2)
 U22(active(X1),X2) -> U22(X1,X2)
 U22(X1,active(X2)) -> U22(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)
 U212(mark(X1),X2) -> U212(X1,X2)
 U212(X1,mark(X2)) -> U212(X1,X2)
 U212(active(X1),X2) -> U212(X1,X2)
 U212(X1,active(X2)) -> U212(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)
 U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
 U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
 U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
 U222(active(X1),X2,X3) -> U222(X1,X2,X3)
 U222(X1,active(X2),X3) -> U222(X1,X2,X3)
 U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
 fst(mark(X)) -> fst(X)
 fst(active(X)) -> fst(X)
 U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
 U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
 U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
 U31(active(X1),X2,X3) -> U31(X1,X2,X3)
 U31(X1,active(X2),X3) -> U31(X1,X2,X3)
 U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
 U32(mark(X1),X2) -> U32(X1,X2)
 U32(X1,mark(X2)) -> U32(X1,X2)
 U32(active(X1),X2) -> U32(X1,X2)
 U32(X1,active(X2)) -> U32(X1,X2)
 U41(mark(X1),X2) -> U41(X1,X2)
 U41(X1,mark(X2)) -> U41(X1,X2)
 U41(active(X1),X2) -> U41(X1,X2)
 U41(X1,active(X2)) -> U41(X1,X2)
 U42(mark(X)) -> U42(X)
 U42(active(X)) -> U42(X)
 U51(mark(X1),X2) -> U51(X1,X2)
 U51(X1,mark(X2)) -> U51(X1,X2)
 U51(active(X1),X2) -> U51(X1,X2)
 U51(X1,active(X2)) -> U51(X1,X2)
 U52(mark(X)) -> U52(X)
 U52(active(X)) -> U52(X)
 U61(mark(X)) -> U61(X)
 U61(active(X)) -> U61(X)
 U71(mark(X)) -> U71(X)
 U71(active(X)) -> U71(X)
 U81(mark(X)) -> U81(X)
 U81(active(X)) -> U81(X)
 U91(mark(X)) -> U91(X)
 U91(active(X)) -> U91(X)
 isPLNat(mark(X)) -> isPLNat(X)
 isPLNat(active(X)) -> isPLNat(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(),V2)) -> isLNat#(V2)
   active#(U101(tt(),V2)) -> U102#(isLNat(V2))
   active#(U101(tt(),V2)) -> mark#(U102(isLNat(V2)))
   active#(U102(tt())) -> mark#(tt())
   active#(U11(tt(),N,XS)) -> isLNat#(XS)
   active#(U11(tt(),N,XS)) -> U12#(isLNat(XS),N,XS)
   active#(U11(tt(),N,XS)) -> mark#(U12(isLNat(XS),N,XS))
   active#(U111(tt())) -> mark#(tt())
   active#(U12(tt(),N,XS)) -> splitAt#(N,XS)
   active#(U12(tt(),N,XS)) -> snd#(splitAt(N,XS))
   active#(U12(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
   active#(U121(tt())) -> mark#(tt())
   active#(U131(tt(),V2)) -> isLNat#(V2)
   active#(U131(tt(),V2)) -> U132#(isLNat(V2))
   active#(U131(tt(),V2)) -> mark#(U132(isLNat(V2)))
   active#(U132(tt())) -> mark#(tt())
   active#(U141(tt(),V2)) -> isLNat#(V2)
   active#(U141(tt(),V2)) -> U142#(isLNat(V2))
   active#(U141(tt(),V2)) -> mark#(U142(isLNat(V2)))
   active#(U142(tt())) -> mark#(tt())
   active#(U151(tt(),V2)) -> isLNat#(V2)
   active#(U151(tt(),V2)) -> U152#(isLNat(V2))
   active#(U151(tt(),V2)) -> mark#(U152(isLNat(V2)))
   active#(U152(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)) -> isLNat#(XS)
   active#(U171(tt(),N,XS)) -> U172#(isLNat(XS),N,XS)
   active#(U171(tt(),N,XS)) -> mark#(U172(isLNat(XS),N,XS))
   active#(U172(tt(),N,XS)) -> afterNth#(N,XS)
   active#(U172(tt(),N,XS)) -> head#(afterNth(N,XS))
   active#(U172(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
   active#(U181(tt(),Y)) -> isLNat#(Y)
   active#(U181(tt(),Y)) -> U182#(isLNat(Y),Y)
   active#(U181(tt(),Y)) -> mark#(U182(isLNat(Y),Y))
   active#(U182(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)) -> isNatural#(X)
   active#(U201(tt(),N,X,XS)) -> U202#(isNatural(X),N,X,XS)
   active#(U201(tt(),N,X,XS)) -> mark#(U202(isNatural(X),N,X,XS))
   active#(U202(tt(),N,X,XS)) -> isLNat#(XS)
   active#(U202(tt(),N,X,XS)) -> U203#(isLNat(XS),N,X,XS)
   active#(U202(tt(),N,X,XS)) -> mark#(U203(isLNat(XS),N,X,XS))
   active#(U203(tt(),N,X,XS)) -> splitAt#(N,XS)
   active#(U203(tt(),N,X,XS)) -> U204#(splitAt(N,XS),X)
   active#(U203(tt(),N,X,XS)) -> mark#(U204(splitAt(N,XS),X))
   active#(U204(pair(YS,ZS),X)) -> cons#(X,YS)
   active#(U204(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
   active#(U204(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
   active#(U21(tt(),X,Y)) -> isLNat#(Y)
   active#(U21(tt(),X,Y)) -> U22#(isLNat(Y),X)
   active#(U21(tt(),X,Y)) -> mark#(U22(isLNat(Y),X))
   active#(U211(tt(),XS)) -> isLNat#(XS)
   active#(U211(tt(),XS)) -> U212#(isLNat(XS),XS)
   active#(U211(tt(),XS)) -> mark#(U212(isLNat(XS),XS))
   active#(U212(tt(),XS)) -> mark#(XS)
   active#(U22(tt(),X)) -> mark#(X)
   active#(U221(tt(),N,XS)) -> isLNat#(XS)
   active#(U221(tt(),N,XS)) -> U222#(isLNat(XS),N,XS)
   active#(U221(tt(),N,XS)) -> mark#(U222(isLNat(XS),N,XS))
   active#(U222(tt(),N,XS)) -> splitAt#(N,XS)
   active#(U222(tt(),N,XS)) -> fst#(splitAt(N,XS))
   active#(U222(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
   active#(U31(tt(),N,XS)) -> isLNat#(XS)
   active#(U31(tt(),N,XS)) -> U32#(isLNat(XS),N)
   active#(U31(tt(),N,XS)) -> mark#(U32(isLNat(XS),N))
   active#(U32(tt(),N)) -> mark#(N)
   active#(U41(tt(),V2)) -> isLNat#(V2)
   active#(U41(tt(),V2)) -> U42#(isLNat(V2))
   active#(U41(tt(),V2)) -> mark#(U42(isLNat(V2)))
   active#(U42(tt())) -> mark#(tt())
   active#(U51(tt(),V2)) -> isLNat#(V2)
   active#(U51(tt(),V2)) -> U52#(isLNat(V2))
   active#(U51(tt(),V2)) -> mark#(U52(isLNat(V2)))
   active#(U52(tt())) -> mark#(tt())
   active#(U61(tt())) -> mark#(tt())
   active#(U71(tt())) -> mark#(tt())
   active#(U81(tt())) -> mark#(tt())
   active#(U91(tt())) -> mark#(tt())
   active#(afterNth(N,XS)) -> isNatural#(N)
   active#(afterNth(N,XS)) -> U11#(isNatural(N),N,XS)
   active#(afterNth(N,XS)) -> mark#(U11(isNatural(N),N,XS))
   active#(fst(pair(X,Y))) -> isLNat#(X)
   active#(fst(pair(X,Y))) -> U21#(isLNat(X),X,Y)
   active#(fst(pair(X,Y))) -> mark#(U21(isLNat(X),X,Y))
   active#(head(cons(N,XS))) -> isNatural#(N)
   active#(head(cons(N,XS))) -> U31#(isNatural(N),N,XS)
   active#(head(cons(N,XS))) -> mark#(U31(isNatural(N),N,XS))
   active#(isLNat(nil())) -> mark#(tt())
   active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
   active#(isLNat(afterNth(V1,V2))) -> U41#(isNatural(V1),V2)
   active#(isLNat(afterNth(V1,V2))) -> mark#(U41(isNatural(V1),V2))
   active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
   active#(isLNat(cons(V1,V2))) -> U51#(isNatural(V1),V2)
   active#(isLNat(cons(V1,V2))) -> mark#(U51(isNatural(V1),V2))
   active#(isLNat(fst(V1))) -> isPLNat#(V1)
   active#(isLNat(fst(V1))) -> U61#(isPLNat(V1))
   active#(isLNat(fst(V1))) -> mark#(U61(isPLNat(V1)))
   active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
   active#(isLNat(natsFrom(V1))) -> U71#(isNatural(V1))
   active#(isLNat(natsFrom(V1))) -> mark#(U71(isNatural(V1)))
   active#(isLNat(snd(V1))) -> isPLNat#(V1)
   active#(isLNat(snd(V1))) -> U81#(isPLNat(V1))
   active#(isLNat(snd(V1))) -> mark#(U81(isPLNat(V1)))
   active#(isLNat(tail(V1))) -> isLNat#(V1)
   active#(isLNat(tail(V1))) -> U91#(isLNat(V1))
   active#(isLNat(tail(V1))) -> mark#(U91(isLNat(V1)))
   active#(isLNat(take(V1,V2))) -> isNatural#(V1)
   active#(isLNat(take(V1,V2))) -> U101#(isNatural(V1),V2)
   active#(isLNat(take(V1,V2))) -> mark#(U101(isNatural(V1),V2))
   active#(isNatural(0())) -> mark#(tt())
   active#(isNatural(head(V1))) -> isLNat#(V1)
   active#(isNatural(head(V1))) -> U111#(isLNat(V1))
   active#(isNatural(head(V1))) -> mark#(U111(isLNat(V1)))
   active#(isNatural(s(V1))) -> isNatural#(V1)
   active#(isNatural(s(V1))) -> U121#(isNatural(V1))
   active#(isNatural(s(V1))) -> mark#(U121(isNatural(V1)))
   active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
   active#(isNatural(sel(V1,V2))) -> U131#(isNatural(V1),V2)
   active#(isNatural(sel(V1,V2))) -> mark#(U131(isNatural(V1),V2))
   active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
   active#(isPLNat(pair(V1,V2))) -> U141#(isLNat(V1),V2)
   active#(isPLNat(pair(V1,V2))) -> mark#(U141(isLNat(V1),V2))
   active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
   active#(isPLNat(splitAt(V1,V2))) -> U151#(isNatural(V1),V2)
   active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(isNatural(V1),V2))
   active#(natsFrom(N)) -> isNatural#(N)
   active#(natsFrom(N)) -> U161#(isNatural(N),N)
   active#(natsFrom(N)) -> mark#(U161(isNatural(N),N))
   active#(sel(N,XS)) -> isNatural#(N)
   active#(sel(N,XS)) -> U171#(isNatural(N),N,XS)
   active#(sel(N,XS)) -> mark#(U171(isNatural(N),N,XS))
   active#(snd(pair(X,Y))) -> isLNat#(X)
   active#(snd(pair(X,Y))) -> U181#(isLNat(X),Y)
   active#(snd(pair(X,Y))) -> mark#(U181(isLNat(X),Y))
   active#(splitAt(0(),XS)) -> isLNat#(XS)
   active#(splitAt(0(),XS)) -> U191#(isLNat(XS),XS)
   active#(splitAt(0(),XS)) -> mark#(U191(isLNat(XS),XS))
   active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
   active#(splitAt(s(N),cons(X,XS))) -> U201#(isNatural(N),N,X,XS)
   active#(splitAt(s(N),cons(X,XS))) -> mark#(U201(isNatural(N),N,X,XS))
   active#(tail(cons(N,XS))) -> isNatural#(N)
   active#(tail(cons(N,XS))) -> U211#(isNatural(N),XS)
   active#(tail(cons(N,XS))) -> mark#(U211(isNatural(N),XS))
   active#(take(N,XS)) -> isNatural#(N)
   active#(take(N,XS)) -> U221#(isNatural(N),N,XS)
   active#(take(N,XS)) -> mark#(U221(isNatural(N),N,XS))
   mark#(U101(X1,X2)) -> mark#(X1)
   mark#(U101(X1,X2)) -> U101#(mark(X1),X2)
   mark#(U101(X1,X2)) -> active#(U101(mark(X1),X2))
   mark#(tt()) -> active#(tt())
   mark#(U102(X)) -> mark#(X)
   mark#(U102(X)) -> U102#(mark(X))
   mark#(U102(X)) -> active#(U102(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#(U12(X1,X2,X3)) -> mark#(X1)
   mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3)
   mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3))
   mark#(U111(X)) -> mark#(X)
   mark#(U111(X)) -> U111#(mark(X))
   mark#(U111(X)) -> active#(U111(mark(X)))
   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#(U121(X)) -> mark#(X)
   mark#(U121(X)) -> U121#(mark(X))
   mark#(U121(X)) -> active#(U121(mark(X)))
   mark#(U131(X1,X2)) -> mark#(X1)
   mark#(U131(X1,X2)) -> U131#(mark(X1),X2)
   mark#(U131(X1,X2)) -> active#(U131(mark(X1),X2))
   mark#(U132(X)) -> mark#(X)
   mark#(U132(X)) -> U132#(mark(X))
   mark#(U132(X)) -> active#(U132(mark(X)))
   mark#(U141(X1,X2)) -> mark#(X1)
   mark#(U141(X1,X2)) -> U141#(mark(X1),X2)
   mark#(U141(X1,X2)) -> active#(U141(mark(X1),X2))
   mark#(U142(X)) -> mark#(X)
   mark#(U142(X)) -> U142#(mark(X))
   mark#(U142(X)) -> active#(U142(mark(X)))
   mark#(U151(X1,X2)) -> mark#(X1)
   mark#(U151(X1,X2)) -> U151#(mark(X1),X2)
   mark#(U151(X1,X2)) -> active#(U151(mark(X1),X2))
   mark#(U152(X)) -> mark#(X)
   mark#(U152(X)) -> U152#(mark(X))
   mark#(U152(X)) -> active#(U152(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#(U172(X1,X2,X3)) -> mark#(X1)
   mark#(U172(X1,X2,X3)) -> U172#(mark(X1),X2,X3)
   mark#(U172(X1,X2,X3)) -> active#(U172(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#(U182(X1,X2)) -> mark#(X1)
   mark#(U182(X1,X2)) -> U182#(mark(X1),X2)
   mark#(U182(X1,X2)) -> active#(U182(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,X3,X4)) -> mark#(X1)
   mark#(U202(X1,X2,X3,X4)) -> U202#(mark(X1),X2,X3,X4)
   mark#(U202(X1,X2,X3,X4)) -> active#(U202(mark(X1),X2,X3,X4))
   mark#(isNatural(X)) -> active#(isNatural(X))
   mark#(U203(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U203(X1,X2,X3,X4)) -> U203#(mark(X1),X2,X3,X4)
   mark#(U203(X1,X2,X3,X4)) -> active#(U203(mark(X1),X2,X3,X4))
   mark#(U204(X1,X2)) -> mark#(X1)
   mark#(U204(X1,X2)) -> U204#(mark(X1),X2)
   mark#(U204(X1,X2)) -> active#(U204(mark(X1),X2))
   mark#(U21(X1,X2,X3)) -> mark#(X1)
   mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
   mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
   mark#(U22(X1,X2)) -> mark#(X1)
   mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
   mark#(U22(X1,X2)) -> active#(U22(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#(U212(X1,X2)) -> mark#(X1)
   mark#(U212(X1,X2)) -> U212#(mark(X1),X2)
   mark#(U212(X1,X2)) -> active#(U212(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#(U222(X1,X2,X3)) -> mark#(X1)
   mark#(U222(X1,X2,X3)) -> U222#(mark(X1),X2,X3)
   mark#(U222(X1,X2,X3)) -> active#(U222(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,X3)) -> mark#(X1)
   mark#(U31(X1,X2,X3)) -> U31#(mark(X1),X2,X3)
   mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3))
   mark#(U32(X1,X2)) -> mark#(X1)
   mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
   mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
   mark#(U41(X1,X2)) -> mark#(X1)
   mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
   mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2))
   mark#(U42(X)) -> mark#(X)
   mark#(U42(X)) -> U42#(mark(X))
   mark#(U42(X)) -> active#(U42(mark(X)))
   mark#(U51(X1,X2)) -> mark#(X1)
   mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
   mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
   mark#(U52(X)) -> mark#(X)
   mark#(U52(X)) -> U52#(mark(X))
   mark#(U52(X)) -> active#(U52(mark(X)))
   mark#(U61(X)) -> mark#(X)
   mark#(U61(X)) -> U61#(mark(X))
   mark#(U61(X)) -> active#(U61(mark(X)))
   mark#(U71(X)) -> mark#(X)
   mark#(U71(X)) -> U71#(mark(X))
   mark#(U71(X)) -> active#(U71(mark(X)))
   mark#(U81(X)) -> mark#(X)
   mark#(U81(X)) -> U81#(mark(X))
   mark#(U81(X)) -> active#(U81(mark(X)))
   mark#(U91(X)) -> mark#(X)
   mark#(U91(X)) -> U91#(mark(X))
   mark#(U91(X)) -> active#(U91(mark(X)))
   mark#(isPLNat(X)) -> active#(isPLNat(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) -> U101#(X1,X2)
   U101#(X1,mark(X2)) -> U101#(X1,X2)
   U101#(active(X1),X2) -> U101#(X1,X2)
   U101#(X1,active(X2)) -> U101#(X1,X2)
   U102#(mark(X)) -> U102#(X)
   U102#(active(X)) -> U102#(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)
   U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
   U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3)
   U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3)
   U12#(active(X1),X2,X3) -> U12#(X1,X2,X3)
   U12#(X1,active(X2),X3) -> U12#(X1,X2,X3)
   U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3)
   U111#(mark(X)) -> U111#(X)
   U111#(active(X)) -> U111#(X)
   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)
   U121#(mark(X)) -> U121#(X)
   U121#(active(X)) -> U121#(X)
   U131#(mark(X1),X2) -> U131#(X1,X2)
   U131#(X1,mark(X2)) -> U131#(X1,X2)
   U131#(active(X1),X2) -> U131#(X1,X2)
   U131#(X1,active(X2)) -> U131#(X1,X2)
   U132#(mark(X)) -> U132#(X)
   U132#(active(X)) -> U132#(X)
   U141#(mark(X1),X2) -> U141#(X1,X2)
   U141#(X1,mark(X2)) -> U141#(X1,X2)
   U141#(active(X1),X2) -> U141#(X1,X2)
   U141#(X1,active(X2)) -> U141#(X1,X2)
   U142#(mark(X)) -> U142#(X)
   U142#(active(X)) -> U142#(X)
   U151#(mark(X1),X2) -> U151#(X1,X2)
   U151#(X1,mark(X2)) -> U151#(X1,X2)
   U151#(active(X1),X2) -> U151#(X1,X2)
   U151#(X1,active(X2)) -> U151#(X1,X2)
   U152#(mark(X)) -> U152#(X)
   U152#(active(X)) -> U152#(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)
   U172#(mark(X1),X2,X3) -> U172#(X1,X2,X3)
   U172#(X1,mark(X2),X3) -> U172#(X1,X2,X3)
   U172#(X1,X2,mark(X3)) -> U172#(X1,X2,X3)
   U172#(active(X1),X2,X3) -> U172#(X1,X2,X3)
   U172#(X1,active(X2),X3) -> U172#(X1,X2,X3)
   U172#(X1,X2,active(X3)) -> U172#(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)
   U182#(mark(X1),X2) -> U182#(X1,X2)
   U182#(X1,mark(X2)) -> U182#(X1,X2)
   U182#(active(X1),X2) -> U182#(X1,X2)
   U182#(X1,active(X2)) -> U182#(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,X3,X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,mark(X2),X3,X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,X2,mark(X3),X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,X2,X3,mark(X4)) -> U202#(X1,X2,X3,X4)
   U202#(active(X1),X2,X3,X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,active(X2),X3,X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,X2,active(X3),X4) -> U202#(X1,X2,X3,X4)
   U202#(X1,X2,X3,active(X4)) -> U202#(X1,X2,X3,X4)
   isNatural#(mark(X)) -> isNatural#(X)
   isNatural#(active(X)) -> isNatural#(X)
   U203#(mark(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,mark(X2),X3,X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,X2,mark(X3),X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,X2,X3,mark(X4)) -> U203#(X1,X2,X3,X4)
   U203#(active(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,active(X2),X3,X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,X2,active(X3),X4) -> U203#(X1,X2,X3,X4)
   U203#(X1,X2,X3,active(X4)) -> U203#(X1,X2,X3,X4)
   U204#(mark(X1),X2) -> U204#(X1,X2)
   U204#(X1,mark(X2)) -> U204#(X1,X2)
   U204#(active(X1),X2) -> U204#(X1,X2)
   U204#(X1,active(X2)) -> U204#(X1,X2)
   U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
   U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
   U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
   U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
   U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
   U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
   U22#(mark(X1),X2) -> U22#(X1,X2)
   U22#(X1,mark(X2)) -> U22#(X1,X2)
   U22#(active(X1),X2) -> U22#(X1,X2)
   U22#(X1,active(X2)) -> U22#(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)
   U212#(mark(X1),X2) -> U212#(X1,X2)
   U212#(X1,mark(X2)) -> U212#(X1,X2)
   U212#(active(X1),X2) -> U212#(X1,X2)
   U212#(X1,active(X2)) -> U212#(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)
   U222#(mark(X1),X2,X3) -> U222#(X1,X2,X3)
   U222#(X1,mark(X2),X3) -> U222#(X1,X2,X3)
   U222#(X1,X2,mark(X3)) -> U222#(X1,X2,X3)
   U222#(active(X1),X2,X3) -> U222#(X1,X2,X3)
   U222#(X1,active(X2),X3) -> U222#(X1,X2,X3)
   U222#(X1,X2,active(X3)) -> U222#(X1,X2,X3)
   fst#(mark(X)) -> fst#(X)
   fst#(active(X)) -> fst#(X)
   U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3)
   U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3)
   U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3)
   U31#(active(X1),X2,X3) -> U31#(X1,X2,X3)
   U31#(X1,active(X2),X3) -> U31#(X1,X2,X3)
   U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3)
   U32#(mark(X1),X2) -> U32#(X1,X2)
   U32#(X1,mark(X2)) -> U32#(X1,X2)
   U32#(active(X1),X2) -> U32#(X1,X2)
   U32#(X1,active(X2)) -> U32#(X1,X2)
   U41#(mark(X1),X2) -> U41#(X1,X2)
   U41#(X1,mark(X2)) -> U41#(X1,X2)
   U41#(active(X1),X2) -> U41#(X1,X2)
   U41#(X1,active(X2)) -> U41#(X1,X2)
   U42#(mark(X)) -> U42#(X)
   U42#(active(X)) -> U42#(X)
   U51#(mark(X1),X2) -> U51#(X1,X2)
   U51#(X1,mark(X2)) -> U51#(X1,X2)
   U51#(active(X1),X2) -> U51#(X1,X2)
   U51#(X1,active(X2)) -> U51#(X1,X2)
   U52#(mark(X)) -> U52#(X)
   U52#(active(X)) -> U52#(X)
   U61#(mark(X)) -> U61#(X)
   U61#(active(X)) -> U61#(X)
   U71#(mark(X)) -> U71#(X)
   U71#(active(X)) -> U71#(X)
   U81#(mark(X)) -> U81#(X)
   U81#(active(X)) -> U81#(X)
   U91#(mark(X)) -> U91#(X)
   U91#(active(X)) -> U91#(X)
   isPLNat#(mark(X)) -> isPLNat#(X)
   isPLNat#(active(X)) -> isPLNat#(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(),V2)) -> mark(U102(isLNat(V2)))
   active(U102(tt())) -> mark(tt())
   active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
   active(U111(tt())) -> mark(tt())
   active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
   active(U121(tt())) -> mark(tt())
   active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
   active(U132(tt())) -> mark(tt())
   active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
   active(U142(tt())) -> mark(tt())
   active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
   active(U152(tt())) -> mark(tt())
   active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
   active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
   active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
   active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
   active(U182(tt(),Y)) -> mark(Y)
   active(U191(tt(),XS)) -> mark(pair(nil(),XS))
   active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
   active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
   active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
   active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
   active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
   active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
   active(U212(tt(),XS)) -> mark(XS)
   active(U22(tt(),X)) -> mark(X)
   active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
   active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
   active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
   active(U32(tt(),N)) -> mark(N)
   active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
   active(U42(tt())) -> mark(tt())
   active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
   active(U52(tt())) -> mark(tt())
   active(U61(tt())) -> mark(tt())
   active(U71(tt())) -> mark(tt())
   active(U81(tt())) -> mark(tt())
   active(U91(tt())) -> mark(tt())
   active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
   active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
   active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
   active(isLNat(nil())) -> mark(tt())
   active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
   active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
   active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
   active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
   active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
   active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
   active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
   active(isNatural(0())) -> mark(tt())
   active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
   active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
   active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
   active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
   active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
   active(natsFrom(N)) -> mark(U161(isNatural(N),N))
   active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
   active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
   active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
   active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
   active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
   active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
   mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(U102(X)) -> active(U102(mark(X)))
   mark(isLNat(X)) -> active(isLNat(X))
   mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
   mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
   mark(U111(X)) -> active(U111(mark(X)))
   mark(snd(X)) -> active(snd(mark(X)))
   mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
   mark(U121(X)) -> active(U121(mark(X)))
   mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
   mark(U132(X)) -> active(U132(mark(X)))
   mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
   mark(U142(X)) -> active(U142(mark(X)))
   mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
   mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
   mark(isNatural(X)) -> active(isNatural(X))
   mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
   mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
   mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
   mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
   mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
   mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
   mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
   mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
   mark(fst(X)) -> active(fst(mark(X)))
   mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
   mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
   mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
   mark(U42(X)) -> active(U42(mark(X)))
   mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
   mark(U52(X)) -> active(U52(mark(X)))
   mark(U61(X)) -> active(U61(mark(X)))
   mark(U71(X)) -> active(U71(mark(X)))
   mark(U81(X)) -> active(U81(mark(X)))
   mark(U91(X)) -> active(U91(mark(X)))
   mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
   U101(X1,mark(X2)) -> U101(X1,X2)
   U101(active(X1),X2) -> U101(X1,X2)
   U101(X1,active(X2)) -> U101(X1,X2)
   U102(mark(X)) -> U102(X)
   U102(active(X)) -> U102(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)
   U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
   U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
   U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
   U12(active(X1),X2,X3) -> U12(X1,X2,X3)
   U12(X1,active(X2),X3) -> U12(X1,X2,X3)
   U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
   U111(mark(X)) -> U111(X)
   U111(active(X)) -> U111(X)
   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)
   U121(mark(X)) -> U121(X)
   U121(active(X)) -> U121(X)
   U131(mark(X1),X2) -> U131(X1,X2)
   U131(X1,mark(X2)) -> U131(X1,X2)
   U131(active(X1),X2) -> U131(X1,X2)
   U131(X1,active(X2)) -> U131(X1,X2)
   U132(mark(X)) -> U132(X)
   U132(active(X)) -> U132(X)
   U141(mark(X1),X2) -> U141(X1,X2)
   U141(X1,mark(X2)) -> U141(X1,X2)
   U141(active(X1),X2) -> U141(X1,X2)
   U141(X1,active(X2)) -> U141(X1,X2)
   U142(mark(X)) -> U142(X)
   U142(active(X)) -> U142(X)
   U151(mark(X1),X2) -> U151(X1,X2)
   U151(X1,mark(X2)) -> U151(X1,X2)
   U151(active(X1),X2) -> U151(X1,X2)
   U151(X1,active(X2)) -> U151(X1,X2)
   U152(mark(X)) -> U152(X)
   U152(active(X)) -> U152(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)
   U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
   U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
   U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
   U172(active(X1),X2,X3) -> U172(X1,X2,X3)
   U172(X1,active(X2),X3) -> U172(X1,X2,X3)
   U172(X1,X2,active(X3)) -> U172(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)
   U182(mark(X1),X2) -> U182(X1,X2)
   U182(X1,mark(X2)) -> U182(X1,X2)
   U182(active(X1),X2) -> U182(X1,X2)
   U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
   U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
   U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
   U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
   U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
   U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
   U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
   U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
   isNatural(mark(X)) -> isNatural(X)
   isNatural(active(X)) -> isNatural(X)
   U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
   U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
   U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
   U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
   U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
   U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
   U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
   U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
   U204(mark(X1),X2) -> U204(X1,X2)
   U204(X1,mark(X2)) -> U204(X1,X2)
   U204(active(X1),X2) -> U204(X1,X2)
   U204(X1,active(X2)) -> U204(X1,X2)
   U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
   U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
   U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
   U21(active(X1),X2,X3) -> U21(X1,X2,X3)
   U21(X1,active(X2),X3) -> U21(X1,X2,X3)
   U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
   U22(mark(X1),X2) -> U22(X1,X2)
   U22(X1,mark(X2)) -> U22(X1,X2)
   U22(active(X1),X2) -> U22(X1,X2)
   U22(X1,active(X2)) -> U22(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)
   U212(mark(X1),X2) -> U212(X1,X2)
   U212(X1,mark(X2)) -> U212(X1,X2)
   U212(active(X1),X2) -> U212(X1,X2)
   U212(X1,active(X2)) -> U212(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)
   U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
   U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
   U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
   U222(active(X1),X2,X3) -> U222(X1,X2,X3)
   U222(X1,active(X2),X3) -> U222(X1,X2,X3)
   U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
   fst(mark(X)) -> fst(X)
   fst(active(X)) -> fst(X)
   U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
   U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
   U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
   U31(active(X1),X2,X3) -> U31(X1,X2,X3)
   U31(X1,active(X2),X3) -> U31(X1,X2,X3)
   U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
   U32(mark(X1),X2) -> U32(X1,X2)
   U32(X1,mark(X2)) -> U32(X1,X2)
   U32(active(X1),X2) -> U32(X1,X2)
   U32(X1,active(X2)) -> U32(X1,X2)
   U41(mark(X1),X2) -> U41(X1,X2)
   U41(X1,mark(X2)) -> U41(X1,X2)
   U41(active(X1),X2) -> U41(X1,X2)
   U41(X1,active(X2)) -> U41(X1,X2)
   U42(mark(X)) -> U42(X)
   U42(active(X)) -> U42(X)
   U51(mark(X1),X2) -> U51(X1,X2)
   U51(X1,mark(X2)) -> U51(X1,X2)
   U51(active(X1),X2) -> U51(X1,X2)
   U51(X1,active(X2)) -> U51(X1,X2)
   U52(mark(X)) -> U52(X)
   U52(active(X)) -> U52(X)
   U61(mark(X)) -> U61(X)
   U61(active(X)) -> U61(X)
   U71(mark(X)) -> U71(X)
   U71(active(X)) -> U71(X)
   U81(mark(X)) -> U81(X)
   U81(active(X)) -> U81(X)
   U91(mark(X)) -> U91(X)
   U91(active(X)) -> U91(X)
   isPLNat(mark(X)) -> isPLNat(X)
   isPLNat(active(X)) -> isPLNat(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)
  CDG Processor:
   DPs:
    active#(U101(tt(),V2)) -> isLNat#(V2)
    active#(U101(tt(),V2)) -> U102#(isLNat(V2))
    active#(U101(tt(),V2)) -> mark#(U102(isLNat(V2)))
    active#(U102(tt())) -> mark#(tt())
    active#(U11(tt(),N,XS)) -> isLNat#(XS)
    active#(U11(tt(),N,XS)) -> U12#(isLNat(XS),N,XS)
    active#(U11(tt(),N,XS)) -> mark#(U12(isLNat(XS),N,XS))
    active#(U111(tt())) -> mark#(tt())
    active#(U12(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U12(tt(),N,XS)) -> snd#(splitAt(N,XS))
    active#(U12(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
    active#(U121(tt())) -> mark#(tt())
    active#(U131(tt(),V2)) -> isLNat#(V2)
    active#(U131(tt(),V2)) -> U132#(isLNat(V2))
    active#(U131(tt(),V2)) -> mark#(U132(isLNat(V2)))
    active#(U132(tt())) -> mark#(tt())
    active#(U141(tt(),V2)) -> isLNat#(V2)
    active#(U141(tt(),V2)) -> U142#(isLNat(V2))
    active#(U141(tt(),V2)) -> mark#(U142(isLNat(V2)))
    active#(U142(tt())) -> mark#(tt())
    active#(U151(tt(),V2)) -> isLNat#(V2)
    active#(U151(tt(),V2)) -> U152#(isLNat(V2))
    active#(U151(tt(),V2)) -> mark#(U152(isLNat(V2)))
    active#(U152(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)) -> isLNat#(XS)
    active#(U171(tt(),N,XS)) -> U172#(isLNat(XS),N,XS)
    active#(U171(tt(),N,XS)) -> mark#(U172(isLNat(XS),N,XS))
    active#(U172(tt(),N,XS)) -> afterNth#(N,XS)
    active#(U172(tt(),N,XS)) -> head#(afterNth(N,XS))
    active#(U172(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
    active#(U181(tt(),Y)) -> isLNat#(Y)
    active#(U181(tt(),Y)) -> U182#(isLNat(Y),Y)
    active#(U181(tt(),Y)) -> mark#(U182(isLNat(Y),Y))
    active#(U182(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)) -> isNatural#(X)
    active#(U201(tt(),N,X,XS)) -> U202#(isNatural(X),N,X,XS)
    active#(U201(tt(),N,X,XS)) -> mark#(U202(isNatural(X),N,X,XS))
    active#(U202(tt(),N,X,XS)) -> isLNat#(XS)
    active#(U202(tt(),N,X,XS)) -> U203#(isLNat(XS),N,X,XS)
    active#(U202(tt(),N,X,XS)) -> mark#(U203(isLNat(XS),N,X,XS))
    active#(U203(tt(),N,X,XS)) -> splitAt#(N,XS)
    active#(U203(tt(),N,X,XS)) -> U204#(splitAt(N,XS),X)
    active#(U203(tt(),N,X,XS)) -> mark#(U204(splitAt(N,XS),X))
    active#(U204(pair(YS,ZS),X)) -> cons#(X,YS)
    active#(U204(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
    active#(U204(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
    active#(U21(tt(),X,Y)) -> isLNat#(Y)
    active#(U21(tt(),X,Y)) -> U22#(isLNat(Y),X)
    active#(U21(tt(),X,Y)) -> mark#(U22(isLNat(Y),X))
    active#(U211(tt(),XS)) -> isLNat#(XS)
    active#(U211(tt(),XS)) -> U212#(isLNat(XS),XS)
    active#(U211(tt(),XS)) -> mark#(U212(isLNat(XS),XS))
    active#(U212(tt(),XS)) -> mark#(XS)
    active#(U22(tt(),X)) -> mark#(X)
    active#(U221(tt(),N,XS)) -> isLNat#(XS)
    active#(U221(tt(),N,XS)) -> U222#(isLNat(XS),N,XS)
    active#(U221(tt(),N,XS)) -> mark#(U222(isLNat(XS),N,XS))
    active#(U222(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U222(tt(),N,XS)) -> fst#(splitAt(N,XS))
    active#(U222(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
    active#(U31(tt(),N,XS)) -> isLNat#(XS)
    active#(U31(tt(),N,XS)) -> U32#(isLNat(XS),N)
    active#(U31(tt(),N,XS)) -> mark#(U32(isLNat(XS),N))
    active#(U32(tt(),N)) -> mark#(N)
    active#(U41(tt(),V2)) -> isLNat#(V2)
    active#(U41(tt(),V2)) -> U42#(isLNat(V2))
    active#(U41(tt(),V2)) -> mark#(U42(isLNat(V2)))
    active#(U42(tt())) -> mark#(tt())
    active#(U51(tt(),V2)) -> isLNat#(V2)
    active#(U51(tt(),V2)) -> U52#(isLNat(V2))
    active#(U51(tt(),V2)) -> mark#(U52(isLNat(V2)))
    active#(U52(tt())) -> mark#(tt())
    active#(U61(tt())) -> mark#(tt())
    active#(U71(tt())) -> mark#(tt())
    active#(U81(tt())) -> mark#(tt())
    active#(U91(tt())) -> mark#(tt())
    active#(afterNth(N,XS)) -> isNatural#(N)
    active#(afterNth(N,XS)) -> U11#(isNatural(N),N,XS)
    active#(afterNth(N,XS)) -> mark#(U11(isNatural(N),N,XS))
    active#(fst(pair(X,Y))) -> isLNat#(X)
    active#(fst(pair(X,Y))) -> U21#(isLNat(X),X,Y)
    active#(fst(pair(X,Y))) -> mark#(U21(isLNat(X),X,Y))
    active#(head(cons(N,XS))) -> isNatural#(N)
    active#(head(cons(N,XS))) -> U31#(isNatural(N),N,XS)
    active#(head(cons(N,XS))) -> mark#(U31(isNatural(N),N,XS))
    active#(isLNat(nil())) -> mark#(tt())
    active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
    active#(isLNat(afterNth(V1,V2))) -> U41#(isNatural(V1),V2)
    active#(isLNat(afterNth(V1,V2))) -> mark#(U41(isNatural(V1),V2))
    active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
    active#(isLNat(cons(V1,V2))) -> U51#(isNatural(V1),V2)
    active#(isLNat(cons(V1,V2))) -> mark#(U51(isNatural(V1),V2))
    active#(isLNat(fst(V1))) -> isPLNat#(V1)
    active#(isLNat(fst(V1))) -> U61#(isPLNat(V1))
    active#(isLNat(fst(V1))) -> mark#(U61(isPLNat(V1)))
    active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
    active#(isLNat(natsFrom(V1))) -> U71#(isNatural(V1))
    active#(isLNat(natsFrom(V1))) -> mark#(U71(isNatural(V1)))
    active#(isLNat(snd(V1))) -> isPLNat#(V1)
    active#(isLNat(snd(V1))) -> U81#(isPLNat(V1))
    active#(isLNat(snd(V1))) -> mark#(U81(isPLNat(V1)))
    active#(isLNat(tail(V1))) -> isLNat#(V1)
    active#(isLNat(tail(V1))) -> U91#(isLNat(V1))
    active#(isLNat(tail(V1))) -> mark#(U91(isLNat(V1)))
    active#(isLNat(take(V1,V2))) -> isNatural#(V1)
    active#(isLNat(take(V1,V2))) -> U101#(isNatural(V1),V2)
    active#(isLNat(take(V1,V2))) -> mark#(U101(isNatural(V1),V2))
    active#(isNatural(0())) -> mark#(tt())
    active#(isNatural(head(V1))) -> isLNat#(V1)
    active#(isNatural(head(V1))) -> U111#(isLNat(V1))
    active#(isNatural(head(V1))) -> mark#(U111(isLNat(V1)))
    active#(isNatural(s(V1))) -> isNatural#(V1)
    active#(isNatural(s(V1))) -> U121#(isNatural(V1))
    active#(isNatural(s(V1))) -> mark#(U121(isNatural(V1)))
    active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
    active#(isNatural(sel(V1,V2))) -> U131#(isNatural(V1),V2)
    active#(isNatural(sel(V1,V2))) -> mark#(U131(isNatural(V1),V2))
    active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
    active#(isPLNat(pair(V1,V2))) -> U141#(isLNat(V1),V2)
    active#(isPLNat(pair(V1,V2))) -> mark#(U141(isLNat(V1),V2))
    active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
    active#(isPLNat(splitAt(V1,V2))) -> U151#(isNatural(V1),V2)
    active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(isNatural(V1),V2))
    active#(natsFrom(N)) -> isNatural#(N)
    active#(natsFrom(N)) -> U161#(isNatural(N),N)
    active#(natsFrom(N)) -> mark#(U161(isNatural(N),N))
    active#(sel(N,XS)) -> isNatural#(N)
    active#(sel(N,XS)) -> U171#(isNatural(N),N,XS)
    active#(sel(N,XS)) -> mark#(U171(isNatural(N),N,XS))
    active#(snd(pair(X,Y))) -> isLNat#(X)
    active#(snd(pair(X,Y))) -> U181#(isLNat(X),Y)
    active#(snd(pair(X,Y))) -> mark#(U181(isLNat(X),Y))
    active#(splitAt(0(),XS)) -> isLNat#(XS)
    active#(splitAt(0(),XS)) -> U191#(isLNat(XS),XS)
    active#(splitAt(0(),XS)) -> mark#(U191(isLNat(XS),XS))
    active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
    active#(splitAt(s(N),cons(X,XS))) -> U201#(isNatural(N),N,X,XS)
    active#(splitAt(s(N),cons(X,XS))) -> mark#(U201(isNatural(N),N,X,XS))
    active#(tail(cons(N,XS))) -> isNatural#(N)
    active#(tail(cons(N,XS))) -> U211#(isNatural(N),XS)
    active#(tail(cons(N,XS))) -> mark#(U211(isNatural(N),XS))
    active#(take(N,XS)) -> isNatural#(N)
    active#(take(N,XS)) -> U221#(isNatural(N),N,XS)
    active#(take(N,XS)) -> mark#(U221(isNatural(N),N,XS))
    mark#(U101(X1,X2)) -> mark#(X1)
    mark#(U101(X1,X2)) -> U101#(mark(X1),X2)
    mark#(U101(X1,X2)) -> active#(U101(mark(X1),X2))
    mark#(tt()) -> active#(tt())
    mark#(U102(X)) -> mark#(X)
    mark#(U102(X)) -> U102#(mark(X))
    mark#(U102(X)) -> active#(U102(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#(U12(X1,X2,X3)) -> mark#(X1)
    mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3)
    mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3))
    mark#(U111(X)) -> mark#(X)
    mark#(U111(X)) -> U111#(mark(X))
    mark#(U111(X)) -> active#(U111(mark(X)))
    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#(U121(X)) -> mark#(X)
    mark#(U121(X)) -> U121#(mark(X))
    mark#(U121(X)) -> active#(U121(mark(X)))
    mark#(U131(X1,X2)) -> mark#(X1)
    mark#(U131(X1,X2)) -> U131#(mark(X1),X2)
    mark#(U131(X1,X2)) -> active#(U131(mark(X1),X2))
    mark#(U132(X)) -> mark#(X)
    mark#(U132(X)) -> U132#(mark(X))
    mark#(U132(X)) -> active#(U132(mark(X)))
    mark#(U141(X1,X2)) -> mark#(X1)
    mark#(U141(X1,X2)) -> U141#(mark(X1),X2)
    mark#(U141(X1,X2)) -> active#(U141(mark(X1),X2))
    mark#(U142(X)) -> mark#(X)
    mark#(U142(X)) -> U142#(mark(X))
    mark#(U142(X)) -> active#(U142(mark(X)))
    mark#(U151(X1,X2)) -> mark#(X1)
    mark#(U151(X1,X2)) -> U151#(mark(X1),X2)
    mark#(U151(X1,X2)) -> active#(U151(mark(X1),X2))
    mark#(U152(X)) -> mark#(X)
    mark#(U152(X)) -> U152#(mark(X))
    mark#(U152(X)) -> active#(U152(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#(U172(X1,X2,X3)) -> mark#(X1)
    mark#(U172(X1,X2,X3)) -> U172#(mark(X1),X2,X3)
    mark#(U172(X1,X2,X3)) -> active#(U172(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#(U182(X1,X2)) -> mark#(X1)
    mark#(U182(X1,X2)) -> U182#(mark(X1),X2)
    mark#(U182(X1,X2)) -> active#(U182(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,X3,X4)) -> mark#(X1)
    mark#(U202(X1,X2,X3,X4)) -> U202#(mark(X1),X2,X3,X4)
    mark#(U202(X1,X2,X3,X4)) -> active#(U202(mark(X1),X2,X3,X4))
    mark#(isNatural(X)) -> active#(isNatural(X))
    mark#(U203(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U203(X1,X2,X3,X4)) -> U203#(mark(X1),X2,X3,X4)
    mark#(U203(X1,X2,X3,X4)) -> active#(U203(mark(X1),X2,X3,X4))
    mark#(U204(X1,X2)) -> mark#(X1)
    mark#(U204(X1,X2)) -> U204#(mark(X1),X2)
    mark#(U204(X1,X2)) -> active#(U204(mark(X1),X2))
    mark#(U21(X1,X2,X3)) -> mark#(X1)
    mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
    mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
    mark#(U22(X1,X2)) -> mark#(X1)
    mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
    mark#(U22(X1,X2)) -> active#(U22(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#(U212(X1,X2)) -> mark#(X1)
    mark#(U212(X1,X2)) -> U212#(mark(X1),X2)
    mark#(U212(X1,X2)) -> active#(U212(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#(U222(X1,X2,X3)) -> mark#(X1)
    mark#(U222(X1,X2,X3)) -> U222#(mark(X1),X2,X3)
    mark#(U222(X1,X2,X3)) -> active#(U222(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,X3)) -> mark#(X1)
    mark#(U31(X1,X2,X3)) -> U31#(mark(X1),X2,X3)
    mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3))
    mark#(U32(X1,X2)) -> mark#(X1)
    mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
    mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
    mark#(U41(X1,X2)) -> mark#(X1)
    mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
    mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2))
    mark#(U42(X)) -> mark#(X)
    mark#(U42(X)) -> U42#(mark(X))
    mark#(U42(X)) -> active#(U42(mark(X)))
    mark#(U51(X1,X2)) -> mark#(X1)
    mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
    mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
    mark#(U52(X)) -> mark#(X)
    mark#(U52(X)) -> U52#(mark(X))
    mark#(U52(X)) -> active#(U52(mark(X)))
    mark#(U61(X)) -> mark#(X)
    mark#(U61(X)) -> U61#(mark(X))
    mark#(U61(X)) -> active#(U61(mark(X)))
    mark#(U71(X)) -> mark#(X)
    mark#(U71(X)) -> U71#(mark(X))
    mark#(U71(X)) -> active#(U71(mark(X)))
    mark#(U81(X)) -> mark#(X)
    mark#(U81(X)) -> U81#(mark(X))
    mark#(U81(X)) -> active#(U81(mark(X)))
    mark#(U91(X)) -> mark#(X)
    mark#(U91(X)) -> U91#(mark(X))
    mark#(U91(X)) -> active#(U91(mark(X)))
    mark#(isPLNat(X)) -> active#(isPLNat(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) -> U101#(X1,X2)
    U101#(X1,mark(X2)) -> U101#(X1,X2)
    U101#(active(X1),X2) -> U101#(X1,X2)
    U101#(X1,active(X2)) -> U101#(X1,X2)
    U102#(mark(X)) -> U102#(X)
    U102#(active(X)) -> U102#(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)
    U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
    U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3)
    U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3)
    U12#(active(X1),X2,X3) -> U12#(X1,X2,X3)
    U12#(X1,active(X2),X3) -> U12#(X1,X2,X3)
    U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3)
    U111#(mark(X)) -> U111#(X)
    U111#(active(X)) -> U111#(X)
    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)
    U121#(mark(X)) -> U121#(X)
    U121#(active(X)) -> U121#(X)
    U131#(mark(X1),X2) -> U131#(X1,X2)
    U131#(X1,mark(X2)) -> U131#(X1,X2)
    U131#(active(X1),X2) -> U131#(X1,X2)
    U131#(X1,active(X2)) -> U131#(X1,X2)
    U132#(mark(X)) -> U132#(X)
    U132#(active(X)) -> U132#(X)
    U141#(mark(X1),X2) -> U141#(X1,X2)
    U141#(X1,mark(X2)) -> U141#(X1,X2)
    U141#(active(X1),X2) -> U141#(X1,X2)
    U141#(X1,active(X2)) -> U141#(X1,X2)
    U142#(mark(X)) -> U142#(X)
    U142#(active(X)) -> U142#(X)
    U151#(mark(X1),X2) -> U151#(X1,X2)
    U151#(X1,mark(X2)) -> U151#(X1,X2)
    U151#(active(X1),X2) -> U151#(X1,X2)
    U151#(X1,active(X2)) -> U151#(X1,X2)
    U152#(mark(X)) -> U152#(X)
    U152#(active(X)) -> U152#(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)
    U172#(mark(X1),X2,X3) -> U172#(X1,X2,X3)
    U172#(X1,mark(X2),X3) -> U172#(X1,X2,X3)
    U172#(X1,X2,mark(X3)) -> U172#(X1,X2,X3)
    U172#(active(X1),X2,X3) -> U172#(X1,X2,X3)
    U172#(X1,active(X2),X3) -> U172#(X1,X2,X3)
    U172#(X1,X2,active(X3)) -> U172#(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)
    U182#(mark(X1),X2) -> U182#(X1,X2)
    U182#(X1,mark(X2)) -> U182#(X1,X2)
    U182#(active(X1),X2) -> U182#(X1,X2)
    U182#(X1,active(X2)) -> U182#(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,X3,X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,mark(X2),X3,X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,X2,mark(X3),X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,X2,X3,mark(X4)) -> U202#(X1,X2,X3,X4)
    U202#(active(X1),X2,X3,X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,active(X2),X3,X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,X2,active(X3),X4) -> U202#(X1,X2,X3,X4)
    U202#(X1,X2,X3,active(X4)) -> U202#(X1,X2,X3,X4)
    isNatural#(mark(X)) -> isNatural#(X)
    isNatural#(active(X)) -> isNatural#(X)
    U203#(mark(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,mark(X2),X3,X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,X2,mark(X3),X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,X2,X3,mark(X4)) -> U203#(X1,X2,X3,X4)
    U203#(active(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,active(X2),X3,X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,X2,active(X3),X4) -> U203#(X1,X2,X3,X4)
    U203#(X1,X2,X3,active(X4)) -> U203#(X1,X2,X3,X4)
    U204#(mark(X1),X2) -> U204#(X1,X2)
    U204#(X1,mark(X2)) -> U204#(X1,X2)
    U204#(active(X1),X2) -> U204#(X1,X2)
    U204#(X1,active(X2)) -> U204#(X1,X2)
    U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
    U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
    U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
    U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
    U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
    U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
    U22#(mark(X1),X2) -> U22#(X1,X2)
    U22#(X1,mark(X2)) -> U22#(X1,X2)
    U22#(active(X1),X2) -> U22#(X1,X2)
    U22#(X1,active(X2)) -> U22#(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)
    U212#(mark(X1),X2) -> U212#(X1,X2)
    U212#(X1,mark(X2)) -> U212#(X1,X2)
    U212#(active(X1),X2) -> U212#(X1,X2)
    U212#(X1,active(X2)) -> U212#(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)
    U222#(mark(X1),X2,X3) -> U222#(X1,X2,X3)
    U222#(X1,mark(X2),X3) -> U222#(X1,X2,X3)
    U222#(X1,X2,mark(X3)) -> U222#(X1,X2,X3)
    U222#(active(X1),X2,X3) -> U222#(X1,X2,X3)
    U222#(X1,active(X2),X3) -> U222#(X1,X2,X3)
    U222#(X1,X2,active(X3)) -> U222#(X1,X2,X3)
    fst#(mark(X)) -> fst#(X)
    fst#(active(X)) -> fst#(X)
    U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3)
    U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3)
    U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3)
    U31#(active(X1),X2,X3) -> U31#(X1,X2,X3)
    U31#(X1,active(X2),X3) -> U31#(X1,X2,X3)
    U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3)
    U32#(mark(X1),X2) -> U32#(X1,X2)
    U32#(X1,mark(X2)) -> U32#(X1,X2)
    U32#(active(X1),X2) -> U32#(X1,X2)
    U32#(X1,active(X2)) -> U32#(X1,X2)
    U41#(mark(X1),X2) -> U41#(X1,X2)
    U41#(X1,mark(X2)) -> U41#(X1,X2)
    U41#(active(X1),X2) -> U41#(X1,X2)
    U41#(X1,active(X2)) -> U41#(X1,X2)
    U42#(mark(X)) -> U42#(X)
    U42#(active(X)) -> U42#(X)
    U51#(mark(X1),X2) -> U51#(X1,X2)
    U51#(X1,mark(X2)) -> U51#(X1,X2)
    U51#(active(X1),X2) -> U51#(X1,X2)
    U51#(X1,active(X2)) -> U51#(X1,X2)
    U52#(mark(X)) -> U52#(X)
    U52#(active(X)) -> U52#(X)
    U61#(mark(X)) -> U61#(X)
    U61#(active(X)) -> U61#(X)
    U71#(mark(X)) -> U71#(X)
    U71#(active(X)) -> U71#(X)
    U81#(mark(X)) -> U81#(X)
    U81#(active(X)) -> U81#(X)
    U91#(mark(X)) -> U91#(X)
    U91#(active(X)) -> U91#(X)
    isPLNat#(mark(X)) -> isPLNat#(X)
    isPLNat#(active(X)) -> isPLNat#(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(),V2)) -> mark(U102(isLNat(V2)))
    active(U102(tt())) -> mark(tt())
    active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
    active(U111(tt())) -> mark(tt())
    active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
    active(U121(tt())) -> mark(tt())
    active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
    active(U132(tt())) -> mark(tt())
    active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
    active(U142(tt())) -> mark(tt())
    active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
    active(U152(tt())) -> mark(tt())
    active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
    active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
    active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
    active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
    active(U182(tt(),Y)) -> mark(Y)
    active(U191(tt(),XS)) -> mark(pair(nil(),XS))
    active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
    active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
    active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
    active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
    active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
    active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
    active(U212(tt(),XS)) -> mark(XS)
    active(U22(tt(),X)) -> mark(X)
    active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
    active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
    active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
    active(U32(tt(),N)) -> mark(N)
    active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
    active(U42(tt())) -> mark(tt())
    active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
    active(U52(tt())) -> mark(tt())
    active(U61(tt())) -> mark(tt())
    active(U71(tt())) -> mark(tt())
    active(U81(tt())) -> mark(tt())
    active(U91(tt())) -> mark(tt())
    active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
    active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
    active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
    active(isLNat(nil())) -> mark(tt())
    active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
    active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
    active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
    active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
    active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
    active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
    active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
    active(isNatural(0())) -> mark(tt())
    active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
    active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
    active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
    active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
    active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
    active(natsFrom(N)) -> mark(U161(isNatural(N),N))
    active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
    active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
    active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
    active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
    active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
    active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
    mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
    mark(tt()) -> active(tt())
    mark(U102(X)) -> active(U102(mark(X)))
    mark(isLNat(X)) -> active(isLNat(X))
    mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
    mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
    mark(U111(X)) -> active(U111(mark(X)))
    mark(snd(X)) -> active(snd(mark(X)))
    mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
    mark(U121(X)) -> active(U121(mark(X)))
    mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
    mark(U132(X)) -> active(U132(mark(X)))
    mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
    mark(U142(X)) -> active(U142(mark(X)))
    mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
    mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
    mark(isNatural(X)) -> active(isNatural(X))
    mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
    mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
    mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
    mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
    mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
    mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
    mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
    mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
    mark(fst(X)) -> active(fst(mark(X)))
    mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
    mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
    mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
    mark(U42(X)) -> active(U42(mark(X)))
    mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
    mark(U52(X)) -> active(U52(mark(X)))
    mark(U61(X)) -> active(U61(mark(X)))
    mark(U71(X)) -> active(U71(mark(X)))
    mark(U81(X)) -> active(U81(mark(X)))
    mark(U91(X)) -> active(U91(mark(X)))
    mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
    U101(X1,mark(X2)) -> U101(X1,X2)
    U101(active(X1),X2) -> U101(X1,X2)
    U101(X1,active(X2)) -> U101(X1,X2)
    U102(mark(X)) -> U102(X)
    U102(active(X)) -> U102(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)
    U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
    U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
    U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
    U12(active(X1),X2,X3) -> U12(X1,X2,X3)
    U12(X1,active(X2),X3) -> U12(X1,X2,X3)
    U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
    U111(mark(X)) -> U111(X)
    U111(active(X)) -> U111(X)
    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)
    U121(mark(X)) -> U121(X)
    U121(active(X)) -> U121(X)
    U131(mark(X1),X2) -> U131(X1,X2)
    U131(X1,mark(X2)) -> U131(X1,X2)
    U131(active(X1),X2) -> U131(X1,X2)
    U131(X1,active(X2)) -> U131(X1,X2)
    U132(mark(X)) -> U132(X)
    U132(active(X)) -> U132(X)
    U141(mark(X1),X2) -> U141(X1,X2)
    U141(X1,mark(X2)) -> U141(X1,X2)
    U141(active(X1),X2) -> U141(X1,X2)
    U141(X1,active(X2)) -> U141(X1,X2)
    U142(mark(X)) -> U142(X)
    U142(active(X)) -> U142(X)
    U151(mark(X1),X2) -> U151(X1,X2)
    U151(X1,mark(X2)) -> U151(X1,X2)
    U151(active(X1),X2) -> U151(X1,X2)
    U151(X1,active(X2)) -> U151(X1,X2)
    U152(mark(X)) -> U152(X)
    U152(active(X)) -> U152(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)
    U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
    U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
    U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
    U172(active(X1),X2,X3) -> U172(X1,X2,X3)
    U172(X1,active(X2),X3) -> U172(X1,X2,X3)
    U172(X1,X2,active(X3)) -> U172(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)
    U182(mark(X1),X2) -> U182(X1,X2)
    U182(X1,mark(X2)) -> U182(X1,X2)
    U182(active(X1),X2) -> U182(X1,X2)
    U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
    U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
    U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
    U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
    U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
    U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
    U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
    U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
    isNatural(mark(X)) -> isNatural(X)
    isNatural(active(X)) -> isNatural(X)
    U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
    U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
    U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
    U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
    U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
    U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
    U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
    U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
    U204(mark(X1),X2) -> U204(X1,X2)
    U204(X1,mark(X2)) -> U204(X1,X2)
    U204(active(X1),X2) -> U204(X1,X2)
    U204(X1,active(X2)) -> U204(X1,X2)
    U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
    U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
    U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
    U21(active(X1),X2,X3) -> U21(X1,X2,X3)
    U21(X1,active(X2),X3) -> U21(X1,X2,X3)
    U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
    U22(mark(X1),X2) -> U22(X1,X2)
    U22(X1,mark(X2)) -> U22(X1,X2)
    U22(active(X1),X2) -> U22(X1,X2)
    U22(X1,active(X2)) -> U22(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)
    U212(mark(X1),X2) -> U212(X1,X2)
    U212(X1,mark(X2)) -> U212(X1,X2)
    U212(active(X1),X2) -> U212(X1,X2)
    U212(X1,active(X2)) -> U212(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)
    U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
    U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
    U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
    U222(active(X1),X2,X3) -> U222(X1,X2,X3)
    U222(X1,active(X2),X3) -> U222(X1,X2,X3)
    U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
    fst(mark(X)) -> fst(X)
    fst(active(X)) -> fst(X)
    U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
    U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
    U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
    U31(active(X1),X2,X3) -> U31(X1,X2,X3)
    U31(X1,active(X2),X3) -> U31(X1,X2,X3)
    U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
    U32(mark(X1),X2) -> U32(X1,X2)
    U32(X1,mark(X2)) -> U32(X1,X2)
    U32(active(X1),X2) -> U32(X1,X2)
    U32(X1,active(X2)) -> U32(X1,X2)
    U41(mark(X1),X2) -> U41(X1,X2)
    U41(X1,mark(X2)) -> U41(X1,X2)
    U41(active(X1),X2) -> U41(X1,X2)
    U41(X1,active(X2)) -> U41(X1,X2)
    U42(mark(X)) -> U42(X)
    U42(active(X)) -> U42(X)
    U51(mark(X1),X2) -> U51(X1,X2)
    U51(X1,mark(X2)) -> U51(X1,X2)
    U51(active(X1),X2) -> U51(X1,X2)
    U51(X1,active(X2)) -> U51(X1,X2)
    U52(mark(X)) -> U52(X)
    U52(active(X)) -> U52(X)
    U61(mark(X)) -> U61(X)
    U61(active(X)) -> U61(X)
    U71(mark(X)) -> U71(X)
    U71(active(X)) -> U71(X)
    U81(mark(X)) -> U81(X)
    U81(active(X)) -> U81(X)
    U91(mark(X)) -> U91(X)
    U91(active(X)) -> U91(X)
    isPLNat(mark(X)) -> isPLNat(X)
    isPLNat(active(X)) -> isPLNat(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:
    ...
   Restore Modifier:
    DPs:
     active#(U101(tt(),V2)) -> isLNat#(V2)
     active#(U101(tt(),V2)) -> U102#(isLNat(V2))
     active#(U101(tt(),V2)) -> mark#(U102(isLNat(V2)))
     active#(U102(tt())) -> mark#(tt())
     active#(U11(tt(),N,XS)) -> isLNat#(XS)
     active#(U11(tt(),N,XS)) -> U12#(isLNat(XS),N,XS)
     active#(U11(tt(),N,XS)) -> mark#(U12(isLNat(XS),N,XS))
     active#(U111(tt())) -> mark#(tt())
     active#(U12(tt(),N,XS)) -> splitAt#(N,XS)
     active#(U12(tt(),N,XS)) -> snd#(splitAt(N,XS))
     active#(U12(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
     active#(U121(tt())) -> mark#(tt())
     active#(U131(tt(),V2)) -> isLNat#(V2)
     active#(U131(tt(),V2)) -> U132#(isLNat(V2))
     active#(U131(tt(),V2)) -> mark#(U132(isLNat(V2)))
     active#(U132(tt())) -> mark#(tt())
     active#(U141(tt(),V2)) -> isLNat#(V2)
     active#(U141(tt(),V2)) -> U142#(isLNat(V2))
     active#(U141(tt(),V2)) -> mark#(U142(isLNat(V2)))
     active#(U142(tt())) -> mark#(tt())
     active#(U151(tt(),V2)) -> isLNat#(V2)
     active#(U151(tt(),V2)) -> U152#(isLNat(V2))
     active#(U151(tt(),V2)) -> mark#(U152(isLNat(V2)))
     active#(U152(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)) -> isLNat#(XS)
     active#(U171(tt(),N,XS)) -> U172#(isLNat(XS),N,XS)
     active#(U171(tt(),N,XS)) -> mark#(U172(isLNat(XS),N,XS))
     active#(U172(tt(),N,XS)) -> afterNth#(N,XS)
     active#(U172(tt(),N,XS)) -> head#(afterNth(N,XS))
     active#(U172(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
     active#(U181(tt(),Y)) -> isLNat#(Y)
     active#(U181(tt(),Y)) -> U182#(isLNat(Y),Y)
     active#(U181(tt(),Y)) -> mark#(U182(isLNat(Y),Y))
     active#(U182(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)) -> isNatural#(X)
     active#(U201(tt(),N,X,XS)) -> U202#(isNatural(X),N,X,XS)
     active#(U201(tt(),N,X,XS)) -> mark#(U202(isNatural(X),N,X,XS))
     active#(U202(tt(),N,X,XS)) -> isLNat#(XS)
     active#(U202(tt(),N,X,XS)) -> U203#(isLNat(XS),N,X,XS)
     active#(U202(tt(),N,X,XS)) -> mark#(U203(isLNat(XS),N,X,XS))
     active#(U203(tt(),N,X,XS)) -> splitAt#(N,XS)
     active#(U203(tt(),N,X,XS)) -> U204#(splitAt(N,XS),X)
     active#(U203(tt(),N,X,XS)) -> mark#(U204(splitAt(N,XS),X))
     active#(U204(pair(YS,ZS),X)) -> cons#(X,YS)
     active#(U204(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
     active#(U204(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
     active#(U21(tt(),X,Y)) -> isLNat#(Y)
     active#(U21(tt(),X,Y)) -> U22#(isLNat(Y),X)
     active#(U21(tt(),X,Y)) -> mark#(U22(isLNat(Y),X))
     active#(U211(tt(),XS)) -> isLNat#(XS)
     active#(U211(tt(),XS)) -> U212#(isLNat(XS),XS)
     active#(U211(tt(),XS)) -> mark#(U212(isLNat(XS),XS))
     active#(U212(tt(),XS)) -> mark#(XS)
     active#(U22(tt(),X)) -> mark#(X)
     active#(U221(tt(),N,XS)) -> isLNat#(XS)
     active#(U221(tt(),N,XS)) -> U222#(isLNat(XS),N,XS)
     active#(U221(tt(),N,XS)) -> mark#(U222(isLNat(XS),N,XS))
     active#(U222(tt(),N,XS)) -> splitAt#(N,XS)
     active#(U222(tt(),N,XS)) -> fst#(splitAt(N,XS))
     active#(U222(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
     active#(U31(tt(),N,XS)) -> isLNat#(XS)
     active#(U31(tt(),N,XS)) -> U32#(isLNat(XS),N)
     active#(U31(tt(),N,XS)) -> mark#(U32(isLNat(XS),N))
     active#(U32(tt(),N)) -> mark#(N)
     active#(U41(tt(),V2)) -> isLNat#(V2)
     active#(U41(tt(),V2)) -> U42#(isLNat(V2))
     active#(U41(tt(),V2)) -> mark#(U42(isLNat(V2)))
     active#(U42(tt())) -> mark#(tt())
     active#(U51(tt(),V2)) -> isLNat#(V2)
     active#(U51(tt(),V2)) -> U52#(isLNat(V2))
     active#(U51(tt(),V2)) -> mark#(U52(isLNat(V2)))
     active#(U52(tt())) -> mark#(tt())
     active#(U61(tt())) -> mark#(tt())
     active#(U71(tt())) -> mark#(tt())
     active#(U81(tt())) -> mark#(tt())
     active#(U91(tt())) -> mark#(tt())
     active#(afterNth(N,XS)) -> isNatural#(N)
     active#(afterNth(N,XS)) -> U11#(isNatural(N),N,XS)
     active#(afterNth(N,XS)) -> mark#(U11(isNatural(N),N,XS))
     active#(fst(pair(X,Y))) -> isLNat#(X)
     active#(fst(pair(X,Y))) -> U21#(isLNat(X),X,Y)
     active#(fst(pair(X,Y))) -> mark#(U21(isLNat(X),X,Y))
     active#(head(cons(N,XS))) -> isNatural#(N)
     active#(head(cons(N,XS))) -> U31#(isNatural(N),N,XS)
     active#(head(cons(N,XS))) -> mark#(U31(isNatural(N),N,XS))
     active#(isLNat(nil())) -> mark#(tt())
     active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
     active#(isLNat(afterNth(V1,V2))) -> U41#(isNatural(V1),V2)
     active#(isLNat(afterNth(V1,V2))) -> mark#(U41(isNatural(V1),V2))
     active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
     active#(isLNat(cons(V1,V2))) -> U51#(isNatural(V1),V2)
     active#(isLNat(cons(V1,V2))) -> mark#(U51(isNatural(V1),V2))
     active#(isLNat(fst(V1))) -> isPLNat#(V1)
     active#(isLNat(fst(V1))) -> U61#(isPLNat(V1))
     active#(isLNat(fst(V1))) -> mark#(U61(isPLNat(V1)))
     active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
     active#(isLNat(natsFrom(V1))) -> U71#(isNatural(V1))
     active#(isLNat(natsFrom(V1))) -> mark#(U71(isNatural(V1)))
     active#(isLNat(snd(V1))) -> isPLNat#(V1)
     active#(isLNat(snd(V1))) -> U81#(isPLNat(V1))
     active#(isLNat(snd(V1))) -> mark#(U81(isPLNat(V1)))
     active#(isLNat(tail(V1))) -> isLNat#(V1)
     active#(isLNat(tail(V1))) -> U91#(isLNat(V1))
     active#(isLNat(tail(V1))) -> mark#(U91(isLNat(V1)))
     active#(isLNat(take(V1,V2))) -> isNatural#(V1)
     active#(isLNat(take(V1,V2))) -> U101#(isNatural(V1),V2)
     active#(isLNat(take(V1,V2))) -> mark#(U101(isNatural(V1),V2))
     active#(isNatural(0())) -> mark#(tt())
     active#(isNatural(head(V1))) -> isLNat#(V1)
     active#(isNatural(head(V1))) -> U111#(isLNat(V1))
     active#(isNatural(head(V1))) -> mark#(U111(isLNat(V1)))
     active#(isNatural(s(V1))) -> isNatural#(V1)
     active#(isNatural(s(V1))) -> U121#(isNatural(V1))
     active#(isNatural(s(V1))) -> mark#(U121(isNatural(V1)))
     active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
     active#(isNatural(sel(V1,V2))) -> U131#(isNatural(V1),V2)
     active#(isNatural(sel(V1,V2))) -> mark#(U131(isNatural(V1),V2))
     active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
     active#(isPLNat(pair(V1,V2))) -> U141#(isLNat(V1),V2)
     active#(isPLNat(pair(V1,V2))) -> mark#(U141(isLNat(V1),V2))
     active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
     active#(isPLNat(splitAt(V1,V2))) -> U151#(isNatural(V1),V2)
     active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(isNatural(V1),V2))
     active#(natsFrom(N)) -> isNatural#(N)
     active#(natsFrom(N)) -> U161#(isNatural(N),N)
     active#(natsFrom(N)) -> mark#(U161(isNatural(N),N))
     active#(sel(N,XS)) -> isNatural#(N)
     active#(sel(N,XS)) -> U171#(isNatural(N),N,XS)
     active#(sel(N,XS)) -> mark#(U171(isNatural(N),N,XS))
     active#(snd(pair(X,Y))) -> isLNat#(X)
     active#(snd(pair(X,Y))) -> U181#(isLNat(X),Y)
     active#(snd(pair(X,Y))) -> mark#(U181(isLNat(X),Y))
     active#(splitAt(0(),XS)) -> isLNat#(XS)
     active#(splitAt(0(),XS)) -> U191#(isLNat(XS),XS)
     active#(splitAt(0(),XS)) -> mark#(U191(isLNat(XS),XS))
     active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
     active#(splitAt(s(N),cons(X,XS))) -> U201#(isNatural(N),N,X,XS)
     active#(splitAt(s(N),cons(X,XS))) -> mark#(U201(isNatural(N),N,X,XS))
     active#(tail(cons(N,XS))) -> isNatural#(N)
     active#(tail(cons(N,XS))) -> U211#(isNatural(N),XS)
     active#(tail(cons(N,XS))) -> mark#(U211(isNatural(N),XS))
     active#(take(N,XS)) -> isNatural#(N)
     active#(take(N,XS)) -> U221#(isNatural(N),N,XS)
     active#(take(N,XS)) -> mark#(U221(isNatural(N),N,XS))
     mark#(U101(X1,X2)) -> mark#(X1)
     mark#(U101(X1,X2)) -> U101#(mark(X1),X2)
     mark#(U101(X1,X2)) -> active#(U101(mark(X1),X2))
     mark#(tt()) -> active#(tt())
     mark#(U102(X)) -> mark#(X)
     mark#(U102(X)) -> U102#(mark(X))
     mark#(U102(X)) -> active#(U102(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#(U12(X1,X2,X3)) -> mark#(X1)
     mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3)
     mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3))
     mark#(U111(X)) -> mark#(X)
     mark#(U111(X)) -> U111#(mark(X))
     mark#(U111(X)) -> active#(U111(mark(X)))
     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#(U121(X)) -> mark#(X)
     mark#(U121(X)) -> U121#(mark(X))
     mark#(U121(X)) -> active#(U121(mark(X)))
     mark#(U131(X1,X2)) -> mark#(X1)
     mark#(U131(X1,X2)) -> U131#(mark(X1),X2)
     mark#(U131(X1,X2)) -> active#(U131(mark(X1),X2))
     mark#(U132(X)) -> mark#(X)
     mark#(U132(X)) -> U132#(mark(X))
     mark#(U132(X)) -> active#(U132(mark(X)))
     mark#(U141(X1,X2)) -> mark#(X1)
     mark#(U141(X1,X2)) -> U141#(mark(X1),X2)
     mark#(U141(X1,X2)) -> active#(U141(mark(X1),X2))
     mark#(U142(X)) -> mark#(X)
     mark#(U142(X)) -> U142#(mark(X))
     mark#(U142(X)) -> active#(U142(mark(X)))
     mark#(U151(X1,X2)) -> mark#(X1)
     mark#(U151(X1,X2)) -> U151#(mark(X1),X2)
     mark#(U151(X1,X2)) -> active#(U151(mark(X1),X2))
     mark#(U152(X)) -> mark#(X)
     mark#(U152(X)) -> U152#(mark(X))
     mark#(U152(X)) -> active#(U152(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#(U172(X1,X2,X3)) -> mark#(X1)
     mark#(U172(X1,X2,X3)) -> U172#(mark(X1),X2,X3)
     mark#(U172(X1,X2,X3)) -> active#(U172(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#(U182(X1,X2)) -> mark#(X1)
     mark#(U182(X1,X2)) -> U182#(mark(X1),X2)
     mark#(U182(X1,X2)) -> active#(U182(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,X3,X4)) -> mark#(X1)
     mark#(U202(X1,X2,X3,X4)) -> U202#(mark(X1),X2,X3,X4)
     mark#(U202(X1,X2,X3,X4)) -> active#(U202(mark(X1),X2,X3,X4))
     mark#(isNatural(X)) -> active#(isNatural(X))
     mark#(U203(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U203(X1,X2,X3,X4)) -> U203#(mark(X1),X2,X3,X4)
     mark#(U203(X1,X2,X3,X4)) -> active#(U203(mark(X1),X2,X3,X4))
     mark#(U204(X1,X2)) -> mark#(X1)
     mark#(U204(X1,X2)) -> U204#(mark(X1),X2)
     mark#(U204(X1,X2)) -> active#(U204(mark(X1),X2))
     mark#(U21(X1,X2,X3)) -> mark#(X1)
     mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
     mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
     mark#(U22(X1,X2)) -> mark#(X1)
     mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
     mark#(U22(X1,X2)) -> active#(U22(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#(U212(X1,X2)) -> mark#(X1)
     mark#(U212(X1,X2)) -> U212#(mark(X1),X2)
     mark#(U212(X1,X2)) -> active#(U212(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#(U222(X1,X2,X3)) -> mark#(X1)
     mark#(U222(X1,X2,X3)) -> U222#(mark(X1),X2,X3)
     mark#(U222(X1,X2,X3)) -> active#(U222(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,X3)) -> mark#(X1)
     mark#(U31(X1,X2,X3)) -> U31#(mark(X1),X2,X3)
     mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3))
     mark#(U32(X1,X2)) -> mark#(X1)
     mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
     mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
     mark#(U41(X1,X2)) -> mark#(X1)
     mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
     mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2))
     mark#(U42(X)) -> mark#(X)
     mark#(U42(X)) -> U42#(mark(X))
     mark#(U42(X)) -> active#(U42(mark(X)))
     mark#(U51(X1,X2)) -> mark#(X1)
     mark#(U51(X1,X2)) -> U51#(mark(X1),X2)
     mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
     mark#(U52(X)) -> mark#(X)
     mark#(U52(X)) -> U52#(mark(X))
     mark#(U52(X)) -> active#(U52(mark(X)))
     mark#(U61(X)) -> mark#(X)
     mark#(U61(X)) -> U61#(mark(X))
     mark#(U61(X)) -> active#(U61(mark(X)))
     mark#(U71(X)) -> mark#(X)
     mark#(U71(X)) -> U71#(mark(X))
     mark#(U71(X)) -> active#(U71(mark(X)))
     mark#(U81(X)) -> mark#(X)
     mark#(U81(X)) -> U81#(mark(X))
     mark#(U81(X)) -> active#(U81(mark(X)))
     mark#(U91(X)) -> mark#(X)
     mark#(U91(X)) -> U91#(mark(X))
     mark#(U91(X)) -> active#(U91(mark(X)))
     mark#(isPLNat(X)) -> active#(isPLNat(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) -> U101#(X1,X2)
     U101#(X1,mark(X2)) -> U101#(X1,X2)
     U101#(active(X1),X2) -> U101#(X1,X2)
     U101#(X1,active(X2)) -> U101#(X1,X2)
     U102#(mark(X)) -> U102#(X)
     U102#(active(X)) -> U102#(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)
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3)
     U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3)
     U12#(active(X1),X2,X3) -> U12#(X1,X2,X3)
     U12#(X1,active(X2),X3) -> U12#(X1,X2,X3)
     U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3)
     U111#(mark(X)) -> U111#(X)
     U111#(active(X)) -> U111#(X)
     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)
     U121#(mark(X)) -> U121#(X)
     U121#(active(X)) -> U121#(X)
     U131#(mark(X1),X2) -> U131#(X1,X2)
     U131#(X1,mark(X2)) -> U131#(X1,X2)
     U131#(active(X1),X2) -> U131#(X1,X2)
     U131#(X1,active(X2)) -> U131#(X1,X2)
     U132#(mark(X)) -> U132#(X)
     U132#(active(X)) -> U132#(X)
     U141#(mark(X1),X2) -> U141#(X1,X2)
     U141#(X1,mark(X2)) -> U141#(X1,X2)
     U141#(active(X1),X2) -> U141#(X1,X2)
     U141#(X1,active(X2)) -> U141#(X1,X2)
     U142#(mark(X)) -> U142#(X)
     U142#(active(X)) -> U142#(X)
     U151#(mark(X1),X2) -> U151#(X1,X2)
     U151#(X1,mark(X2)) -> U151#(X1,X2)
     U151#(active(X1),X2) -> U151#(X1,X2)
     U151#(X1,active(X2)) -> U151#(X1,X2)
     U152#(mark(X)) -> U152#(X)
     U152#(active(X)) -> U152#(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)
     U172#(mark(X1),X2,X3) -> U172#(X1,X2,X3)
     U172#(X1,mark(X2),X3) -> U172#(X1,X2,X3)
     U172#(X1,X2,mark(X3)) -> U172#(X1,X2,X3)
     U172#(active(X1),X2,X3) -> U172#(X1,X2,X3)
     U172#(X1,active(X2),X3) -> U172#(X1,X2,X3)
     U172#(X1,X2,active(X3)) -> U172#(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)
     U182#(mark(X1),X2) -> U182#(X1,X2)
     U182#(X1,mark(X2)) -> U182#(X1,X2)
     U182#(active(X1),X2) -> U182#(X1,X2)
     U182#(X1,active(X2)) -> U182#(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,X3,X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,mark(X2),X3,X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,X2,mark(X3),X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,X2,X3,mark(X4)) -> U202#(X1,X2,X3,X4)
     U202#(active(X1),X2,X3,X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,active(X2),X3,X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,X2,active(X3),X4) -> U202#(X1,X2,X3,X4)
     U202#(X1,X2,X3,active(X4)) -> U202#(X1,X2,X3,X4)
     isNatural#(mark(X)) -> isNatural#(X)
     isNatural#(active(X)) -> isNatural#(X)
     U203#(mark(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,mark(X2),X3,X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,X2,mark(X3),X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,X2,X3,mark(X4)) -> U203#(X1,X2,X3,X4)
     U203#(active(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,active(X2),X3,X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,X2,active(X3),X4) -> U203#(X1,X2,X3,X4)
     U203#(X1,X2,X3,active(X4)) -> U203#(X1,X2,X3,X4)
     U204#(mark(X1),X2) -> U204#(X1,X2)
     U204#(X1,mark(X2)) -> U204#(X1,X2)
     U204#(active(X1),X2) -> U204#(X1,X2)
     U204#(X1,active(X2)) -> U204#(X1,X2)
     U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
     U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
     U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
     U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
     U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
     U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
     U22#(mark(X1),X2) -> U22#(X1,X2)
     U22#(X1,mark(X2)) -> U22#(X1,X2)
     U22#(active(X1),X2) -> U22#(X1,X2)
     U22#(X1,active(X2)) -> U22#(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)
     U212#(mark(X1),X2) -> U212#(X1,X2)
     U212#(X1,mark(X2)) -> U212#(X1,X2)
     U212#(active(X1),X2) -> U212#(X1,X2)
     U212#(X1,active(X2)) -> U212#(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)
     U222#(mark(X1),X2,X3) -> U222#(X1,X2,X3)
     U222#(X1,mark(X2),X3) -> U222#(X1,X2,X3)
     U222#(X1,X2,mark(X3)) -> U222#(X1,X2,X3)
     U222#(active(X1),X2,X3) -> U222#(X1,X2,X3)
     U222#(X1,active(X2),X3) -> U222#(X1,X2,X3)
     U222#(X1,X2,active(X3)) -> U222#(X1,X2,X3)
     fst#(mark(X)) -> fst#(X)
     fst#(active(X)) -> fst#(X)
     U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3)
     U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3)
     U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3)
     U31#(active(X1),X2,X3) -> U31#(X1,X2,X3)
     U31#(X1,active(X2),X3) -> U31#(X1,X2,X3)
     U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3)
     U32#(mark(X1),X2) -> U32#(X1,X2)
     U32#(X1,mark(X2)) -> U32#(X1,X2)
     U32#(active(X1),X2) -> U32#(X1,X2)
     U32#(X1,active(X2)) -> U32#(X1,X2)
     U41#(mark(X1),X2) -> U41#(X1,X2)
     U41#(X1,mark(X2)) -> U41#(X1,X2)
     U41#(active(X1),X2) -> U41#(X1,X2)
     U41#(X1,active(X2)) -> U41#(X1,X2)
     U42#(mark(X)) -> U42#(X)
     U42#(active(X)) -> U42#(X)
     U51#(mark(X1),X2) -> U51#(X1,X2)
     U51#(X1,mark(X2)) -> U51#(X1,X2)
     U51#(active(X1),X2) -> U51#(X1,X2)
     U51#(X1,active(X2)) -> U51#(X1,X2)
     U52#(mark(X)) -> U52#(X)
     U52#(active(X)) -> U52#(X)
     U61#(mark(X)) -> U61#(X)
     U61#(active(X)) -> U61#(X)
     U71#(mark(X)) -> U71#(X)
     U71#(active(X)) -> U71#(X)
     U81#(mark(X)) -> U81#(X)
     U81#(active(X)) -> U81#(X)
     U91#(mark(X)) -> U91#(X)
     U91#(active(X)) -> U91#(X)
     isPLNat#(mark(X)) -> isPLNat#(X)
     isPLNat#(active(X)) -> isPLNat#(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(),V2)) -> mark(U102(isLNat(V2)))
     active(U102(tt())) -> mark(tt())
     active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
     active(U111(tt())) -> mark(tt())
     active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U121(tt())) -> mark(tt())
     active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
     active(U132(tt())) -> mark(tt())
     active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
     active(U142(tt())) -> mark(tt())
     active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
     active(U152(tt())) -> mark(tt())
     active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
     active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
     active(U182(tt(),Y)) -> mark(Y)
     active(U191(tt(),XS)) -> mark(pair(nil(),XS))
     active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
     active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
     active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
     active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
     active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
     active(U212(tt(),XS)) -> mark(XS)
     active(U22(tt(),X)) -> mark(X)
     active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
     active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
     active(U32(tt(),N)) -> mark(N)
     active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
     active(U42(tt())) -> mark(tt())
     active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
     active(U52(tt())) -> mark(tt())
     active(U61(tt())) -> mark(tt())
     active(U71(tt())) -> mark(tt())
     active(U81(tt())) -> mark(tt())
     active(U91(tt())) -> mark(tt())
     active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
     active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
     active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
     active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
     active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
     active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
     active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
     active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
     active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
     active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
     active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
     active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
     active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
     active(natsFrom(N)) -> mark(U161(isNatural(N),N))
     active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
     active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
     active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
     active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
     active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
     active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
     mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
     mark(tt()) -> active(tt())
     mark(U102(X)) -> active(U102(mark(X)))
     mark(isLNat(X)) -> active(isLNat(X))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
     mark(U111(X)) -> active(U111(mark(X)))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U121(X)) -> active(U121(mark(X)))
     mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
     mark(U132(X)) -> active(U132(mark(X)))
     mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
     mark(U142(X)) -> active(U142(mark(X)))
     mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
     mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
     mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
     mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
     mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
     mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
     mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
     mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
     mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
     mark(fst(X)) -> active(fst(mark(X)))
     mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
     mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
     mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
     mark(U42(X)) -> active(U42(mark(X)))
     mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
     mark(U52(X)) -> active(U52(mark(X)))
     mark(U61(X)) -> active(U61(mark(X)))
     mark(U71(X)) -> active(U71(mark(X)))
     mark(U81(X)) -> active(U81(mark(X)))
     mark(U91(X)) -> active(U91(mark(X)))
     mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
     U101(X1,mark(X2)) -> U101(X1,X2)
     U101(active(X1),X2) -> U101(X1,X2)
     U101(X1,active(X2)) -> U101(X1,X2)
     U102(mark(X)) -> U102(X)
     U102(active(X)) -> U102(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)
     U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
     U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
     U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
     U12(active(X1),X2,X3) -> U12(X1,X2,X3)
     U12(X1,active(X2),X3) -> U12(X1,X2,X3)
     U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
     U111(mark(X)) -> U111(X)
     U111(active(X)) -> U111(X)
     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)
     U121(mark(X)) -> U121(X)
     U121(active(X)) -> U121(X)
     U131(mark(X1),X2) -> U131(X1,X2)
     U131(X1,mark(X2)) -> U131(X1,X2)
     U131(active(X1),X2) -> U131(X1,X2)
     U131(X1,active(X2)) -> U131(X1,X2)
     U132(mark(X)) -> U132(X)
     U132(active(X)) -> U132(X)
     U141(mark(X1),X2) -> U141(X1,X2)
     U141(X1,mark(X2)) -> U141(X1,X2)
     U141(active(X1),X2) -> U141(X1,X2)
     U141(X1,active(X2)) -> U141(X1,X2)
     U142(mark(X)) -> U142(X)
     U142(active(X)) -> U142(X)
     U151(mark(X1),X2) -> U151(X1,X2)
     U151(X1,mark(X2)) -> U151(X1,X2)
     U151(active(X1),X2) -> U151(X1,X2)
     U151(X1,active(X2)) -> U151(X1,X2)
     U152(mark(X)) -> U152(X)
     U152(active(X)) -> U152(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)
     U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
     U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
     U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
     U172(active(X1),X2,X3) -> U172(X1,X2,X3)
     U172(X1,active(X2),X3) -> U172(X1,X2,X3)
     U172(X1,X2,active(X3)) -> U172(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)
     U182(mark(X1),X2) -> U182(X1,X2)
     U182(X1,mark(X2)) -> U182(X1,X2)
     U182(active(X1),X2) -> U182(X1,X2)
     U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
     U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
     U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
     U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
     U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
     U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
     U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
     U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
     U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
     U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
     U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
     U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
     U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
     U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
     U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
     U204(mark(X1),X2) -> U204(X1,X2)
     U204(X1,mark(X2)) -> U204(X1,X2)
     U204(active(X1),X2) -> U204(X1,X2)
     U204(X1,active(X2)) -> U204(X1,X2)
     U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
     U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
     U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
     U21(active(X1),X2,X3) -> U21(X1,X2,X3)
     U21(X1,active(X2),X3) -> U21(X1,X2,X3)
     U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
     U22(mark(X1),X2) -> U22(X1,X2)
     U22(X1,mark(X2)) -> U22(X1,X2)
     U22(active(X1),X2) -> U22(X1,X2)
     U22(X1,active(X2)) -> U22(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)
     U212(mark(X1),X2) -> U212(X1,X2)
     U212(X1,mark(X2)) -> U212(X1,X2)
     U212(active(X1),X2) -> U212(X1,X2)
     U212(X1,active(X2)) -> U212(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)
     U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
     U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
     U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
     U222(active(X1),X2,X3) -> U222(X1,X2,X3)
     U222(X1,active(X2),X3) -> U222(X1,X2,X3)
     U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(X)
     U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
     U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
     U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
     U31(active(X1),X2,X3) -> U31(X1,X2,X3)
     U31(X1,active(X2),X3) -> U31(X1,X2,X3)
     U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
     U32(mark(X1),X2) -> U32(X1,X2)
     U32(X1,mark(X2)) -> U32(X1,X2)
     U32(active(X1),X2) -> U32(X1,X2)
     U32(X1,active(X2)) -> U32(X1,X2)
     U41(mark(X1),X2) -> U41(X1,X2)
     U41(X1,mark(X2)) -> U41(X1,X2)
     U41(active(X1),X2) -> U41(X1,X2)
     U41(X1,active(X2)) -> U41(X1,X2)
     U42(mark(X)) -> U42(X)
     U42(active(X)) -> U42(X)
     U51(mark(X1),X2) -> U51(X1,X2)
     U51(X1,mark(X2)) -> U51(X1,X2)
     U51(active(X1),X2) -> U51(X1,X2)
     U51(X1,active(X2)) -> U51(X1,X2)
     U52(mark(X)) -> U52(X)
     U52(active(X)) -> U52(X)
     U61(mark(X)) -> U61(X)
     U61(active(X)) -> U61(X)
     U71(mark(X)) -> U71(X)
     U71(active(X)) -> U71(X)
     U81(mark(X)) -> U81(X)
     U81(active(X)) -> U81(X)
     U91(mark(X)) -> U91(X)
     U91(active(X)) -> U91(X)
     isPLNat(mark(X)) -> isPLNat(X)
     isPLNat(active(X)) -> isPLNat(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)
    SCC Processor:
     #sccs: 54
     #rules: 339
     #arcs: 11071/259081
     DPs:
      mark#(sel(X1,X2)) -> mark#(X2)
      mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2)))
      active#(sel(N,XS)) -> mark#(U171(isNatural(N),N,XS))
      mark#(U171(X1,X2,X3)) -> active#(U171(mark(X1),X2,X3))
      active#(U171(tt(),N,XS)) -> mark#(U172(isLNat(XS),N,XS))
      mark#(U172(X1,X2,X3)) -> active#(U172(mark(X1),X2,X3))
      active#(U172(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
      mark#(head(X)) -> active#(head(mark(X)))
      active#(head(cons(N,XS))) -> mark#(U31(isNatural(N),N,XS))
      mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3))
      active#(U31(tt(),N,XS)) -> mark#(U32(isLNat(XS),N))
      mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
      active#(U32(tt(),N)) -> mark#(N)
      mark#(sel(X1,X2)) -> mark#(X1)
      mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2)))
      active#(take(N,XS)) -> mark#(U221(isNatural(N),N,XS))
      mark#(U221(X1,X2,X3)) -> active#(U221(mark(X1),X2,X3))
      active#(U221(tt(),N,XS)) -> mark#(U222(isLNat(XS),N,XS))
      mark#(U222(X1,X2,X3)) -> active#(U222(mark(X1),X2,X3))
      active#(U222(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
      mark#(fst(X)) -> active#(fst(mark(X)))
      active#(fst(pair(X,Y))) -> mark#(U21(isLNat(X),X,Y))
      mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
      active#(U21(tt(),X,Y)) -> mark#(U22(isLNat(Y),X))
      mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
      active#(U22(tt(),X)) -> mark#(X)
      mark#(take(X1,X2)) -> mark#(X1)
      mark#(take(X1,X2)) -> mark#(X2)
      mark#(tail(X)) -> active#(tail(mark(X)))
      active#(tail(cons(N,XS))) -> mark#(U211(isNatural(N),XS))
      mark#(U211(X1,X2)) -> active#(U211(mark(X1),X2))
      active#(U211(tt(),XS)) -> mark#(U212(isLNat(XS),XS))
      mark#(U212(X1,X2)) -> active#(U212(mark(X1),X2))
      active#(U212(tt(),XS)) -> mark#(XS)
      mark#(tail(X)) -> mark#(X)
      mark#(isPLNat(X)) -> active#(isPLNat(X))
      active#(isPLNat(splitAt(V1,V2))) -> mark#(U151(isNatural(V1),V2))
      mark#(U151(X1,X2)) -> active#(U151(mark(X1),X2))
      active#(U151(tt(),V2)) -> mark#(U152(isLNat(V2)))
      mark#(U152(X)) -> mark#(X)
      mark#(U91(X)) -> mark#(X)
      mark#(U81(X)) -> mark#(X)
      mark#(U71(X)) -> mark#(X)
      mark#(U61(X)) -> mark#(X)
      mark#(U52(X)) -> mark#(X)
      mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2))
      active#(U51(tt(),V2)) -> mark#(U52(isLNat(V2)))
      mark#(U51(X1,X2)) -> mark#(X1)
      mark#(U42(X)) -> mark#(X)
      mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2))
      active#(U41(tt(),V2)) -> mark#(U42(isLNat(V2)))
      mark#(U41(X1,X2)) -> mark#(X1)
      mark#(U32(X1,X2)) -> mark#(X1)
      mark#(U31(X1,X2,X3)) -> mark#(X1)
      mark#(fst(X)) -> mark#(X)
      mark#(U222(X1,X2,X3)) -> mark#(X1)
      mark#(U221(X1,X2,X3)) -> mark#(X1)
      mark#(U212(X1,X2)) -> mark#(X1)
      mark#(U211(X1,X2)) -> mark#(X1)
      mark#(U22(X1,X2)) -> mark#(X1)
      mark#(U21(X1,X2,X3)) -> mark#(X1)
      mark#(U204(X1,X2)) -> active#(U204(mark(X1),X2))
      active#(U204(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
      mark#(pair(X1,X2)) -> mark#(X1)
      mark#(U204(X1,X2)) -> mark#(X1)
      mark#(U203(X1,X2,X3,X4)) -> active#(U203(mark(X1),X2,X3,X4))
      active#(U203(tt(),N,X,XS)) -> mark#(U204(splitAt(N,XS),X))
      mark#(U203(X1,X2,X3,X4)) -> mark#(X1)
      mark#(isNatural(X)) -> active#(isNatural(X))
      active#(isNatural(sel(V1,V2))) -> mark#(U131(isNatural(V1),V2))
      mark#(U131(X1,X2)) -> active#(U131(mark(X1),X2))
      active#(U131(tt(),V2)) -> mark#(U132(isLNat(V2)))
      mark#(U132(X)) -> mark#(X)
      mark#(U202(X1,X2,X3,X4)) -> active#(U202(mark(X1),X2,X3,X4))
      active#(U202(tt(),N,X,XS)) -> mark#(U203(isLNat(XS),N,X,XS))
      mark#(U202(X1,X2,X3,X4)) -> mark#(X1)
      mark#(U201(X1,X2,X3,X4)) -> active#(U201(mark(X1),X2,X3,X4))
      active#(U201(tt(),N,X,XS)) -> mark#(U202(isNatural(X),N,X,XS))
      mark#(U201(X1,X2,X3,X4)) -> mark#(X1)
      mark#(pair(X1,X2)) -> mark#(X2)
      mark#(U191(X1,X2)) -> active#(U191(mark(X1),X2))
      active#(U191(tt(),XS)) -> mark#(pair(nil(),XS))
      mark#(U191(X1,X2)) -> mark#(X1)
      mark#(U182(X1,X2)) -> active#(U182(mark(X1),X2))
      active#(U182(tt(),Y)) -> mark#(Y)
      mark#(U182(X1,X2)) -> mark#(X1)
      mark#(U181(X1,X2)) -> active#(U181(mark(X1),X2))
      active#(U181(tt(),Y)) -> mark#(U182(isLNat(Y),Y))
      mark#(U181(X1,X2)) -> mark#(X1)
      mark#(afterNth(X1,X2)) -> active#(afterNth(mark(X1),mark(X2)))
      active#(afterNth(N,XS)) -> mark#(U11(isNatural(N),N,XS))
      mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
      active#(U11(tt(),N,XS)) -> mark#(U12(isLNat(XS),N,XS))
      mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3))
      active#(U12(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
      mark#(snd(X)) -> active#(snd(mark(X)))
      active#(snd(pair(X,Y))) -> mark#(U181(isLNat(X),Y))
      mark#(snd(X)) -> mark#(X)
      mark#(afterNth(X1,X2)) -> mark#(X1)
      mark#(afterNth(X1,X2)) -> mark#(X2)
      mark#(head(X)) -> mark#(X)
      mark#(U172(X1,X2,X3)) -> mark#(X1)
      mark#(U171(X1,X2,X3)) -> mark#(X1)
      mark#(s(X)) -> mark#(X)
      mark#(natsFrom(X)) -> active#(natsFrom(mark(X)))
      active#(natsFrom(N)) -> mark#(U161(isNatural(N),N))
      mark#(U161(X1,X2)) -> active#(U161(mark(X1),X2))
      active#(U161(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(natsFrom(X)) -> mark#(X)
      mark#(U161(X1,X2)) -> mark#(X1)
      mark#(U151(X1,X2)) -> mark#(X1)
      mark#(U142(X)) -> mark#(X)
      mark#(U141(X1,X2)) -> active#(U141(mark(X1),X2))
      active#(U141(tt(),V2)) -> mark#(U142(isLNat(V2)))
      mark#(U141(X1,X2)) -> mark#(X1)
      mark#(U131(X1,X2)) -> mark#(X1)
      mark#(U121(X)) -> mark#(X)
      mark#(splitAt(X1,X2)) -> active#(splitAt(mark(X1),mark(X2)))
      active#(splitAt(s(N),cons(X,XS))) -> mark#(U201(isNatural(N),N,X,XS))
      active#(splitAt(0(),XS)) -> mark#(U191(isLNat(XS),XS))
      mark#(splitAt(X1,X2)) -> mark#(X1)
      mark#(splitAt(X1,X2)) -> mark#(X2)
      mark#(U111(X)) -> mark#(X)
      mark#(U12(X1,X2,X3)) -> mark#(X1)
      mark#(U11(X1,X2,X3)) -> mark#(X1)
      mark#(isLNat(X)) -> active#(isLNat(X))
      active#(isLNat(take(V1,V2))) -> mark#(U101(isNatural(V1),V2))
      mark#(U101(X1,X2)) -> active#(U101(mark(X1),X2))
      active#(U101(tt(),V2)) -> mark#(U102(isLNat(V2)))
      mark#(U102(X)) -> mark#(X)
      mark#(U101(X1,X2)) -> mark#(X1)
      active#(isLNat(tail(V1))) -> mark#(U91(isLNat(V1)))
      active#(isLNat(snd(V1))) -> mark#(U81(isPLNat(V1)))
      active#(isLNat(natsFrom(V1))) -> mark#(U71(isNatural(V1)))
      active#(isLNat(fst(V1))) -> mark#(U61(isPLNat(V1)))
      active#(isLNat(cons(V1,V2))) -> mark#(U51(isNatural(V1),V2))
      active#(isLNat(afterNth(V1,V2))) -> mark#(U41(isNatural(V1),V2))
      active#(isNatural(s(V1))) -> mark#(U121(isNatural(V1)))
      active#(isNatural(head(V1))) -> mark#(U111(isLNat(V1)))
      active#(isPLNat(pair(V1,V2))) -> mark#(U141(isLNat(V1),V2))
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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#(active(X)) -> U102#(X)
      U102#(mark(X)) -> U102#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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#(active(X)) -> isLNat#(X)
      isLNat#(mark(X)) -> isLNat#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
      U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3)
      U12#(X1,active(X2),X3) -> U12#(X1,X2,X3)
      U12#(active(X1),X2,X3) -> U12#(X1,X2,X3)
      U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3)
      U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U132#(X)
      U132#(active(X)) -> U132#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U142#(X)
      U142#(active(X)) -> U142#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U152#(X)
      U152#(active(X)) -> U152#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U172#(mark(X1),X2,X3) -> U172#(X1,X2,X3)
      U172#(X1,X2,active(X3)) -> U172#(X1,X2,X3)
      U172#(X1,active(X2),X3) -> U172#(X1,X2,X3)
      U172#(active(X1),X2,X3) -> U172#(X1,X2,X3)
      U172#(X1,X2,mark(X3)) -> U172#(X1,X2,X3)
      U172#(X1,mark(X2),X3) -> U172#(X1,X2,X3)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U182#(mark(X1),X2) -> U182#(X1,X2)
      U182#(X1,active(X2)) -> U182#(X1,X2)
      U182#(active(X1),X2) -> U182#(X1,X2)
      U182#(X1,mark(X2)) -> U182#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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#(mark(X)) -> isNatural#(X)
      isNatural#(active(X)) -> isNatural#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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,X3,X4) -> U202#(X1,X2,X3,X4)
      U202#(X1,X2,X3,active(X4)) -> U202#(X1,X2,X3,X4)
      U202#(X1,X2,active(X3),X4) -> U202#(X1,X2,X3,X4)
      U202#(X1,active(X2),X3,X4) -> U202#(X1,X2,X3,X4)
      U202#(active(X1),X2,X3,X4) -> U202#(X1,X2,X3,X4)
      U202#(X1,X2,X3,mark(X4)) -> U202#(X1,X2,X3,X4)
      U202#(X1,X2,mark(X3),X4) -> U202#(X1,X2,X3,X4)
      U202#(X1,mark(X2),X3,X4) -> U202#(X1,X2,X3,X4)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U203#(mark(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
      U203#(X1,X2,X3,active(X4)) -> U203#(X1,X2,X3,X4)
      U203#(X1,X2,active(X3),X4) -> U203#(X1,X2,X3,X4)
      U203#(X1,active(X2),X3,X4) -> U203#(X1,X2,X3,X4)
      U203#(active(X1),X2,X3,X4) -> U203#(X1,X2,X3,X4)
      U203#(X1,X2,X3,mark(X4)) -> U203#(X1,X2,X3,X4)
      U203#(X1,X2,mark(X3),X4) -> U203#(X1,X2,X3,X4)
      U203#(X1,mark(X2),X3,X4) -> U203#(X1,X2,X3,X4)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U204#(mark(X1),X2) -> U204#(X1,X2)
      U204#(X1,active(X2)) -> U204#(X1,X2)
      U204#(active(X1),X2) -> U204#(X1,X2)
      U204#(X1,mark(X2)) -> U204#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U22#(mark(X1),X2) -> U22#(X1,X2)
      U22#(X1,active(X2)) -> U22#(X1,X2)
      U22#(active(X1),X2) -> U22#(X1,X2)
      U22#(X1,mark(X2)) -> U22#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U212#(mark(X1),X2) -> U212#(X1,X2)
      U212#(X1,active(X2)) -> U212#(X1,X2)
      U212#(active(X1),X2) -> U212#(X1,X2)
      U212#(X1,mark(X2)) -> U212#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U222#(mark(X1),X2,X3) -> U222#(X1,X2,X3)
      U222#(X1,X2,active(X3)) -> U222#(X1,X2,X3)
      U222#(X1,active(X2),X3) -> U222#(X1,X2,X3)
      U222#(active(X1),X2,X3) -> U222#(X1,X2,X3)
      U222#(X1,X2,mark(X3)) -> U222#(X1,X2,X3)
      U222#(X1,mark(X2),X3) -> U222#(X1,X2,X3)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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:
      U32#(mark(X1),X2) -> U32#(X1,X2)
      U32#(X1,active(X2)) -> U32#(X1,X2)
      U32#(active(X1),X2) -> U32#(X1,X2)
      U32#(X1,mark(X2)) -> U32#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U42#(X)
      U42#(active(X)) -> U42#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U52#(X)
      U52#(active(X)) -> U52#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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,X3) -> U21#(X1,X2,X3)
      U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
      U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
      U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
      U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
      U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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,X3) -> U31#(X1,X2,X3)
      U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3)
      U31#(X1,active(X2),X3) -> U31#(X1,X2,X3)
      U31#(active(X1),X2,X3) -> U31#(X1,X2,X3)
      U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3)
      U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U41#(X1,X2)
      U41#(X1,active(X2)) -> U41#(X1,X2)
      U41#(active(X1),X2) -> U41#(X1,X2)
      U41#(X1,mark(X2)) -> U41#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U51#(X1,X2)
      U51#(X1,active(X2)) -> U51#(X1,X2)
      U51#(active(X1),X2) -> U51#(X1,X2)
      U51#(X1,mark(X2)) -> U51#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U61#(X)
      U61#(active(X)) -> U61#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U71#(X)
      U71#(active(X)) -> U71#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U81#(X)
      U81#(active(X)) -> U81#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U91#(X)
      U91#(active(X)) -> U91#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U101#(X1,X2)
      U101#(X1,active(X2)) -> U101#(X1,X2)
      U101#(active(X1),X2) -> U101#(X1,X2)
      U101#(X1,mark(X2)) -> U101#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U111#(X)
      U111#(active(X)) -> U111#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(X)) -> U121#(X)
      U121#(active(X)) -> U121#(X)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U131#(X1,X2)
      U131#(X1,active(X2)) -> U131#(X1,X2)
      U131#(active(X1),X2) -> U131#(X1,X2)
      U131#(X1,mark(X2)) -> U131#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U141#(X1,X2)
      U141#(X1,active(X2)) -> U141#(X1,X2)
      U141#(active(X1),X2) -> U141#(X1,X2)
      U141#(X1,mark(X2)) -> U141#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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) -> U151#(X1,X2)
      U151#(X1,active(X2)) -> U151#(X1,X2)
      U151#(active(X1),X2) -> U151#(X1,X2)
      U151#(X1,mark(X2)) -> U151#(X1,X2)
     TRS:
      active(U101(tt(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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(),V2)) -> mark(U102(isLNat(V2)))
      active(U102(tt())) -> mark(tt())
      active(U11(tt(),N,XS)) -> mark(U12(isLNat(XS),N,XS))
      active(U111(tt())) -> mark(tt())
      active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U121(tt())) -> mark(tt())
      active(U131(tt(),V2)) -> mark(U132(isLNat(V2)))
      active(U132(tt())) -> mark(tt())
      active(U141(tt(),V2)) -> mark(U142(isLNat(V2)))
      active(U142(tt())) -> mark(tt())
      active(U151(tt(),V2)) -> mark(U152(isLNat(V2)))
      active(U152(tt())) -> mark(tt())
      active(U161(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U171(tt(),N,XS)) -> mark(U172(isLNat(XS),N,XS))
      active(U172(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U181(tt(),Y)) -> mark(U182(isLNat(Y),Y))
      active(U182(tt(),Y)) -> mark(Y)
      active(U191(tt(),XS)) -> mark(pair(nil(),XS))
      active(U201(tt(),N,X,XS)) -> mark(U202(isNatural(X),N,X,XS))
      active(U202(tt(),N,X,XS)) -> mark(U203(isLNat(XS),N,X,XS))
      active(U203(tt(),N,X,XS)) -> mark(U204(splitAt(N,XS),X))
      active(U204(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U21(tt(),X,Y)) -> mark(U22(isLNat(Y),X))
      active(U211(tt(),XS)) -> mark(U212(isLNat(XS),XS))
      active(U212(tt(),XS)) -> mark(XS)
      active(U22(tt(),X)) -> mark(X)
      active(U221(tt(),N,XS)) -> mark(U222(isLNat(XS),N,XS))
      active(U222(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U31(tt(),N,XS)) -> mark(U32(isLNat(XS),N))
      active(U32(tt(),N)) -> mark(N)
      active(U41(tt(),V2)) -> mark(U42(isLNat(V2)))
      active(U42(tt())) -> mark(tt())
      active(U51(tt(),V2)) -> mark(U52(isLNat(V2)))
      active(U52(tt())) -> mark(tt())
      active(U61(tt())) -> mark(tt())
      active(U71(tt())) -> mark(tt())
      active(U81(tt())) -> mark(tt())
      active(U91(tt())) -> mark(tt())
      active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
      active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
      active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(U41(isNatural(V1),V2))
      active(isLNat(cons(V1,V2))) -> mark(U51(isNatural(V1),V2))
      active(isLNat(fst(V1))) -> mark(U61(isPLNat(V1)))
      active(isLNat(natsFrom(V1))) -> mark(U71(isNatural(V1)))
      active(isLNat(snd(V1))) -> mark(U81(isPLNat(V1)))
      active(isLNat(tail(V1))) -> mark(U91(isLNat(V1)))
      active(isLNat(take(V1,V2))) -> mark(U101(isNatural(V1),V2))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(U111(isLNat(V1)))
      active(isNatural(s(V1))) -> mark(U121(isNatural(V1)))
      active(isNatural(sel(V1,V2))) -> mark(U131(isNatural(V1),V2))
      active(isPLNat(pair(V1,V2))) -> mark(U141(isLNat(V1),V2))
      active(isPLNat(splitAt(V1,V2))) -> mark(U151(isNatural(V1),V2))
      active(natsFrom(N)) -> mark(U161(isNatural(N),N))
      active(sel(N,XS)) -> mark(U171(isNatural(N),N,XS))
      active(snd(pair(X,Y))) -> mark(U181(isLNat(X),Y))
      active(splitAt(0(),XS)) -> mark(U191(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) -> mark(U201(isNatural(N),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U211(isNatural(N),XS))
      active(take(N,XS)) -> mark(U221(isNatural(N),N,XS))
      mark(U101(X1,X2)) -> active(U101(mark(X1),X2))
      mark(tt()) -> active(tt())
      mark(U102(X)) -> active(U102(mark(X)))
      mark(isLNat(X)) -> active(isLNat(X))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
      mark(U111(X)) -> active(U111(mark(X)))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U121(X)) -> active(U121(mark(X)))
      mark(U131(X1,X2)) -> active(U131(mark(X1),X2))
      mark(U132(X)) -> active(U132(mark(X)))
      mark(U141(X1,X2)) -> active(U141(mark(X1),X2))
      mark(U142(X)) -> active(U142(mark(X)))
      mark(U151(X1,X2)) -> active(U151(mark(X1),X2))
      mark(U152(X)) -> active(U152(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(U172(X1,X2,X3)) -> active(U172(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(U182(X1,X2)) -> active(U182(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,X3,X4)) -> active(U202(mark(X1),X2,X3,X4))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(U203(X1,X2,X3,X4)) -> active(U203(mark(X1),X2,X3,X4))
      mark(U204(X1,X2)) -> active(U204(mark(X1),X2))
      mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
      mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
      mark(U211(X1,X2)) -> active(U211(mark(X1),X2))
      mark(U212(X1,X2)) -> active(U212(mark(X1),X2))
      mark(U221(X1,X2,X3)) -> active(U221(mark(X1),X2,X3))
      mark(U222(X1,X2,X3)) -> active(U222(mark(X1),X2,X3))
      mark(fst(X)) -> active(fst(mark(X)))
      mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
      mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
      mark(U42(X)) -> active(U42(mark(X)))
      mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
      mark(U52(X)) -> active(U52(mark(X)))
      mark(U61(X)) -> active(U61(mark(X)))
      mark(U71(X)) -> active(U71(mark(X)))
      mark(U81(X)) -> active(U81(mark(X)))
      mark(U91(X)) -> active(U91(mark(X)))
      mark(isPLNat(X)) -> active(isPLNat(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) -> U101(X1,X2)
      U101(X1,mark(X2)) -> U101(X1,X2)
      U101(active(X1),X2) -> U101(X1,X2)
      U101(X1,active(X2)) -> U101(X1,X2)
      U102(mark(X)) -> U102(X)
      U102(active(X)) -> U102(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)
      U12(mark(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,mark(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,mark(X3)) -> U12(X1,X2,X3)
      U12(active(X1),X2,X3) -> U12(X1,X2,X3)
      U12(X1,active(X2),X3) -> U12(X1,X2,X3)
      U12(X1,X2,active(X3)) -> U12(X1,X2,X3)
      U111(mark(X)) -> U111(X)
      U111(active(X)) -> U111(X)
      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)
      U121(mark(X)) -> U121(X)
      U121(active(X)) -> U121(X)
      U131(mark(X1),X2) -> U131(X1,X2)
      U131(X1,mark(X2)) -> U131(X1,X2)
      U131(active(X1),X2) -> U131(X1,X2)
      U131(X1,active(X2)) -> U131(X1,X2)
      U132(mark(X)) -> U132(X)
      U132(active(X)) -> U132(X)
      U141(mark(X1),X2) -> U141(X1,X2)
      U141(X1,mark(X2)) -> U141(X1,X2)
      U141(active(X1),X2) -> U141(X1,X2)
      U141(X1,active(X2)) -> U141(X1,X2)
      U142(mark(X)) -> U142(X)
      U142(active(X)) -> U142(X)
      U151(mark(X1),X2) -> U151(X1,X2)
      U151(X1,mark(X2)) -> U151(X1,X2)
      U151(active(X1),X2) -> U151(X1,X2)
      U151(X1,active(X2)) -> U151(X1,X2)
      U152(mark(X)) -> U152(X)
      U152(active(X)) -> U152(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)
      U172(mark(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,mark(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,mark(X3)) -> U172(X1,X2,X3)
      U172(active(X1),X2,X3) -> U172(X1,X2,X3)
      U172(X1,active(X2),X3) -> U172(X1,X2,X3)
      U172(X1,X2,active(X3)) -> U172(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)
      U182(mark(X1),X2) -> U182(X1,X2)
      U182(X1,mark(X2)) -> U182(X1,X2)
      U182(active(X1),X2) -> U182(X1,X2)
      U182(X1,active(X2)) -> U182(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,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,mark(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,mark(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,mark(X4)) -> U202(X1,X2,X3,X4)
      U202(active(X1),X2,X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,active(X2),X3,X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,active(X3),X4) -> U202(X1,X2,X3,X4)
      U202(X1,X2,X3,active(X4)) -> U202(X1,X2,X3,X4)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      U203(mark(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,mark(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,mark(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,mark(X4)) -> U203(X1,X2,X3,X4)
      U203(active(X1),X2,X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,active(X2),X3,X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,active(X3),X4) -> U203(X1,X2,X3,X4)
      U203(X1,X2,X3,active(X4)) -> U203(X1,X2,X3,X4)
      U204(mark(X1),X2) -> U204(X1,X2)
      U204(X1,mark(X2)) -> U204(X1,X2)
      U204(active(X1),X2) -> U204(X1,X2)
      U204(X1,active(X2)) -> U204(X1,X2)
      U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
      U21(active(X1),X2,X3) -> U21(X1,X2,X3)
      U21(X1,active(X2),X3) -> U21(X1,X2,X3)
      U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
      U22(mark(X1),X2) -> U22(X1,X2)
      U22(X1,mark(X2)) -> U22(X1,X2)
      U22(active(X1),X2) -> U22(X1,X2)
      U22(X1,active(X2)) -> U22(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)
      U212(mark(X1),X2) -> U212(X1,X2)
      U212(X1,mark(X2)) -> U212(X1,X2)
      U212(active(X1),X2) -> U212(X1,X2)
      U212(X1,active(X2)) -> U212(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)
      U222(mark(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,mark(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,mark(X3)) -> U222(X1,X2,X3)
      U222(active(X1),X2,X3) -> U222(X1,X2,X3)
      U222(X1,active(X2),X3) -> U222(X1,X2,X3)
      U222(X1,X2,active(X3)) -> U222(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(X)
      U31(mark(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,mark(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,mark(X3)) -> U31(X1,X2,X3)
      U31(active(X1),X2,X3) -> U31(X1,X2,X3)
      U31(X1,active(X2),X3) -> U31(X1,X2,X3)
      U31(X1,X2,active(X3)) -> U31(X1,X2,X3)
      U32(mark(X1),X2) -> U32(X1,X2)
      U32(X1,mark(X2)) -> U32(X1,X2)
      U32(active(X1),X2) -> U32(X1,X2)
      U32(X1,active(X2)) -> U32(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(X1,X2)
      U42(mark(X)) -> U42(X)
      U42(active(X)) -> U42(X)
      U51(mark(X1),X2) -> U51(X1,X2)
      U51(X1,mark(X2)) -> U51(X1,X2)
      U51(active(X1),X2) -> U51(X1,X2)
      U51(X1,active(X2)) -> U51(X1,X2)
      U52(mark(X)) -> U52(X)
      U52(active(X)) -> U52(X)
      U61(mark(X)) -> U61(X)
      U61(active(X)) -> U61(X)
      U71(mark(X)) -> U71(X)
      U71(active(X)) -> U71(X)
      U81(mark(X)) -> U81(X)
      U81(active(X)) -> U81(X)
      U91(mark(X)) -> U91(X)
      U91(active(X)) -> U91(X)
      isPLNat(mark(X)) -> isPLNat(X)
      isPLNat(active(X)) -> isPLNat(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