MAYBE

Problem:
 active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
 active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
 active(U21(tt(),X)) -> mark(X)
 active(U31(tt(),N)) -> mark(N)
 active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
 active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
 active(U61(tt(),Y)) -> mark(Y)
 active(U71(tt(),XS)) -> mark(pair(nil(),XS))
 active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
 active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
 active(U91(tt(),XS)) -> mark(XS)
 active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
 active(and(tt(),X)) -> mark(X)
 active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
 active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
 active(isLNat(nil())) -> mark(tt())
 active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
 active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
 active(isLNat(fst(V1))) -> mark(isPLNat(V1))
 active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
 active(isLNat(snd(V1))) -> mark(isPLNat(V1))
 active(isLNat(tail(V1))) -> mark(isLNat(V1))
 active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
 active(isNatural(0())) -> mark(tt())
 active(isNatural(head(V1))) -> mark(isLNat(V1))
 active(isNatural(s(V1))) -> mark(isNatural(V1))
 active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
 active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
 active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
 active(natsFrom(N)) -> mark(U41(isNatural(N),N))
 active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
 active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
 active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
 active(splitAt(s(N),cons(X,XS))) ->
 mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
 active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
 active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
 mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
 mark(tt()) -> active(tt())
 mark(fst(X)) -> active(fst(mark(X)))
 mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
 mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
 mark(snd(X)) -> active(snd(mark(X)))
 mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
 mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
 mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
 mark(head(X)) -> active(head(mark(X)))
 mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
 mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
 mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
 mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
 mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
 mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNatural(X)) -> active(isNatural(X))
 mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
 U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
 U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
 U101(active(X1),X2,X3) -> U101(X1,X2,X3)
 U101(X1,active(X2),X3) -> U101(X1,X2,X3)
 U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
 fst(mark(X)) -> fst(X)
 fst(active(X)) -> fst(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)
 U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
 U11(active(X1),X2,X3) -> U11(X1,X2,X3)
 U11(X1,active(X2),X3) -> U11(X1,X2,X3)
 U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
 snd(mark(X)) -> snd(X)
 snd(active(X)) -> snd(X)
 U21(mark(X1),X2) -> U21(X1,X2)
 U21(X1,mark(X2)) -> U21(X1,X2)
 U21(active(X1),X2) -> U21(X1,X2)
 U21(X1,active(X2)) -> U21(X1,X2)
 U31(mark(X1),X2) -> U31(X1,X2)
 U31(X1,mark(X2)) -> U31(X1,X2)
 U31(active(X1),X2) -> U31(X1,X2)
 U31(X1,active(X2)) -> U31(X1,X2)
 U41(mark(X1),X2) -> U41(X1,X2)
 U41(X1,mark(X2)) -> U41(X1,X2)
 U41(active(X1),X2) -> U41(X1,X2)
 U41(X1,active(X2)) -> U41(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)
 U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
 U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
 U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
 U51(active(X1),X2,X3) -> U51(X1,X2,X3)
 U51(X1,active(X2),X3) -> U51(X1,X2,X3)
 U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
 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)
 U61(mark(X1),X2) -> U61(X1,X2)
 U61(X1,mark(X2)) -> U61(X1,X2)
 U61(active(X1),X2) -> U61(X1,X2)
 U61(X1,active(X2)) -> U61(X1,X2)
 U71(mark(X1),X2) -> U71(X1,X2)
 U71(X1,mark(X2)) -> U71(X1,X2)
 U71(active(X1),X2) -> U71(X1,X2)
 U71(X1,active(X2)) -> U71(X1,X2)
 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)
 U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
 U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
 U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
 U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
 U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
 U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
 U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
 U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
 U82(mark(X1),X2) -> U82(X1,X2)
 U82(X1,mark(X2)) -> U82(X1,X2)
 U82(active(X1),X2) -> U82(X1,X2)
 U82(X1,active(X2)) -> U82(X1,X2)
 U91(mark(X1),X2) -> U91(X1,X2)
 U91(X1,mark(X2)) -> U91(X1,X2)
 U91(active(X1),X2) -> U91(X1,X2)
 U91(X1,active(X2)) -> U91(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isNatural(mark(X)) -> isNatural(X)
 isNatural(active(X)) -> isNatural(X)
 isLNat(mark(X)) -> isLNat(X)
 isLNat(active(X)) -> isLNat(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(),N,XS)) -> splitAt#(N,XS)
   active#(U101(tt(),N,XS)) -> fst#(splitAt(N,XS))
   active#(U101(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
   active#(U11(tt(),N,XS)) -> splitAt#(N,XS)
   active#(U11(tt(),N,XS)) -> snd#(splitAt(N,XS))
   active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
   active#(U21(tt(),X)) -> mark#(X)
   active#(U31(tt(),N)) -> mark#(N)
   active#(U41(tt(),N)) -> s#(N)
   active#(U41(tt(),N)) -> natsFrom#(s(N))
   active#(U41(tt(),N)) -> cons#(N,natsFrom(s(N)))
   active#(U41(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
   active#(U51(tt(),N,XS)) -> afterNth#(N,XS)
   active#(U51(tt(),N,XS)) -> head#(afterNth(N,XS))
   active#(U51(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
   active#(U61(tt(),Y)) -> mark#(Y)
   active#(U71(tt(),XS)) -> pair#(nil(),XS)
   active#(U71(tt(),XS)) -> mark#(pair(nil(),XS))
   active#(U81(tt(),N,X,XS)) -> splitAt#(N,XS)
   active#(U81(tt(),N,X,XS)) -> U82#(splitAt(N,XS),X)
   active#(U81(tt(),N,X,XS)) -> mark#(U82(splitAt(N,XS),X))
   active#(U82(pair(YS,ZS),X)) -> cons#(X,YS)
   active#(U82(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
   active#(U82(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
   active#(U91(tt(),XS)) -> mark#(XS)
   active#(afterNth(N,XS)) -> isLNat#(XS)
   active#(afterNth(N,XS)) -> isNatural#(N)
   active#(afterNth(N,XS)) -> and#(isNatural(N),isLNat(XS))
   active#(afterNth(N,XS)) -> U11#(and(isNatural(N),isLNat(XS)),N,XS)
   active#(afterNth(N,XS)) -> mark#(U11(and(isNatural(N),isLNat(XS)),N,XS))
   active#(and(tt(),X)) -> mark#(X)
   active#(fst(pair(X,Y))) -> isLNat#(Y)
   active#(fst(pair(X,Y))) -> isLNat#(X)
   active#(fst(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
   active#(fst(pair(X,Y))) -> U21#(and(isLNat(X),isLNat(Y)),X)
   active#(fst(pair(X,Y))) -> mark#(U21(and(isLNat(X),isLNat(Y)),X))
   active#(head(cons(N,XS))) -> isLNat#(XS)
   active#(head(cons(N,XS))) -> isNatural#(N)
   active#(head(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
   active#(head(cons(N,XS))) -> U31#(and(isNatural(N),isLNat(XS)),N)
   active#(head(cons(N,XS))) -> mark#(U31(and(isNatural(N),isLNat(XS)),N))
   active#(isLNat(nil())) -> mark#(tt())
   active#(isLNat(afterNth(V1,V2))) -> isLNat#(V2)
   active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
   active#(isLNat(afterNth(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
   active#(isLNat(afterNth(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
   active#(isLNat(cons(V1,V2))) -> isLNat#(V2)
   active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
   active#(isLNat(cons(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
   active#(isLNat(cons(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
   active#(isLNat(fst(V1))) -> isPLNat#(V1)
   active#(isLNat(fst(V1))) -> mark#(isPLNat(V1))
   active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
   active#(isLNat(natsFrom(V1))) -> mark#(isNatural(V1))
   active#(isLNat(snd(V1))) -> isPLNat#(V1)
   active#(isLNat(snd(V1))) -> mark#(isPLNat(V1))
   active#(isLNat(tail(V1))) -> isLNat#(V1)
   active#(isLNat(tail(V1))) -> mark#(isLNat(V1))
   active#(isLNat(take(V1,V2))) -> isLNat#(V2)
   active#(isLNat(take(V1,V2))) -> isNatural#(V1)
   active#(isLNat(take(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
   active#(isLNat(take(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
   active#(isNatural(0())) -> mark#(tt())
   active#(isNatural(head(V1))) -> isLNat#(V1)
   active#(isNatural(head(V1))) -> mark#(isLNat(V1))
   active#(isNatural(s(V1))) -> isNatural#(V1)
   active#(isNatural(s(V1))) -> mark#(isNatural(V1))
   active#(isNatural(sel(V1,V2))) -> isLNat#(V2)
   active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
   active#(isNatural(sel(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
   active#(isNatural(sel(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
   active#(isPLNat(pair(V1,V2))) -> isLNat#(V2)
   active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
   active#(isPLNat(pair(V1,V2))) -> and#(isLNat(V1),isLNat(V2))
   active#(isPLNat(pair(V1,V2))) -> mark#(and(isLNat(V1),isLNat(V2)))
   active#(isPLNat(splitAt(V1,V2))) -> isLNat#(V2)
   active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
   active#(isPLNat(splitAt(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
   active#(isPLNat(splitAt(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
   active#(natsFrom(N)) -> isNatural#(N)
   active#(natsFrom(N)) -> U41#(isNatural(N),N)
   active#(natsFrom(N)) -> mark#(U41(isNatural(N),N))
   active#(sel(N,XS)) -> isLNat#(XS)
   active#(sel(N,XS)) -> isNatural#(N)
   active#(sel(N,XS)) -> and#(isNatural(N),isLNat(XS))
   active#(sel(N,XS)) -> U51#(and(isNatural(N),isLNat(XS)),N,XS)
   active#(sel(N,XS)) -> mark#(U51(and(isNatural(N),isLNat(XS)),N,XS))
   active#(snd(pair(X,Y))) -> isLNat#(Y)
   active#(snd(pair(X,Y))) -> isLNat#(X)
   active#(snd(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
   active#(snd(pair(X,Y))) -> U61#(and(isLNat(X),isLNat(Y)),Y)
   active#(snd(pair(X,Y))) -> mark#(U61(and(isLNat(X),isLNat(Y)),Y))
   active#(splitAt(0(),XS)) -> isLNat#(XS)
   active#(splitAt(0(),XS)) -> U71#(isLNat(XS),XS)
   active#(splitAt(0(),XS)) -> mark#(U71(isLNat(XS),XS))
   active#(splitAt(s(N),cons(X,XS))) -> isLNat#(XS)
   active#(splitAt(s(N),cons(X,XS))) -> isNatural#(X)
   active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(X),isLNat(XS))
   active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
   active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(N),and(isNatural(X),isLNat(XS)))
   active#(splitAt(s(N),cons(X,XS))) -> U81#(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
   active#(splitAt(s(N),cons(X,XS))) ->
   mark#(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
   active#(tail(cons(N,XS))) -> isLNat#(XS)
   active#(tail(cons(N,XS))) -> isNatural#(N)
   active#(tail(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
   active#(tail(cons(N,XS))) -> U91#(and(isNatural(N),isLNat(XS)),XS)
   active#(tail(cons(N,XS))) -> mark#(U91(and(isNatural(N),isLNat(XS)),XS))
   active#(take(N,XS)) -> isLNat#(XS)
   active#(take(N,XS)) -> isNatural#(N)
   active#(take(N,XS)) -> and#(isNatural(N),isLNat(XS))
   active#(take(N,XS)) -> U101#(and(isNatural(N),isLNat(XS)),N,XS)
   active#(take(N,XS)) -> mark#(U101(and(isNatural(N),isLNat(XS)),N,XS))
   mark#(U101(X1,X2,X3)) -> mark#(X1)
   mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3)
   mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
   mark#(tt()) -> active#(tt())
   mark#(fst(X)) -> mark#(X)
   mark#(fst(X)) -> fst#(mark(X))
   mark#(fst(X)) -> active#(fst(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#(U11(X1,X2,X3)) -> mark#(X1)
   mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3)
   mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
   mark#(snd(X)) -> mark#(X)
   mark#(snd(X)) -> snd#(mark(X))
   mark#(snd(X)) -> active#(snd(mark(X)))
   mark#(U21(X1,X2)) -> mark#(X1)
   mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
   mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
   mark#(U31(X1,X2)) -> mark#(X1)
   mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
   mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
   mark#(U41(X1,X2)) -> mark#(X1)
   mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
   mark#(U41(X1,X2)) -> active#(U41(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#(U51(X1,X2,X3)) -> mark#(X1)
   mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
   mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
   mark#(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#(U61(X1,X2)) -> mark#(X1)
   mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
   mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
   mark#(U71(X1,X2)) -> mark#(X1)
   mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
   mark#(U71(X1,X2)) -> active#(U71(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#(U81(X1,X2,X3,X4)) -> mark#(X1)
   mark#(U81(X1,X2,X3,X4)) -> U81#(mark(X1),X2,X3,X4)
   mark#(U81(X1,X2,X3,X4)) -> active#(U81(mark(X1),X2,X3,X4))
   mark#(U82(X1,X2)) -> mark#(X1)
   mark#(U82(X1,X2)) -> U82#(mark(X1),X2)
   mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
   mark#(U91(X1,X2)) -> mark#(X1)
   mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
   mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> and#(mark(X1),X2)
   mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
   mark#(isNatural(X)) -> active#(isNatural(X))
   mark#(isLNat(X)) -> active#(isLNat(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,X3) -> U101#(X1,X2,X3)
   U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
   U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
   U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
   U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
   U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
   fst#(mark(X)) -> fst#(X)
   fst#(active(X)) -> fst#(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)
   U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
   U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
   U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
   U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
   U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
   U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
   snd#(mark(X)) -> snd#(X)
   snd#(active(X)) -> snd#(X)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U21#(X1,mark(X2)) -> U21#(X1,X2)
   U21#(active(X1),X2) -> U21#(X1,X2)
   U21#(X1,active(X2)) -> U21#(X1,X2)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U31#(X1,mark(X2)) -> U31#(X1,X2)
   U31#(active(X1),X2) -> U31#(X1,X2)
   U31#(X1,active(X2)) -> U31#(X1,X2)
   U41#(mark(X1),X2) -> U41#(X1,X2)
   U41#(X1,mark(X2)) -> U41#(X1,X2)
   U41#(active(X1),X2) -> U41#(X1,X2)
   U41#(X1,active(X2)) -> U41#(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)
   U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
   U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
   U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
   U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
   U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
   U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
   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)
   U61#(mark(X1),X2) -> U61#(X1,X2)
   U61#(X1,mark(X2)) -> U61#(X1,X2)
   U61#(active(X1),X2) -> U61#(X1,X2)
   U61#(X1,active(X2)) -> U61#(X1,X2)
   U71#(mark(X1),X2) -> U71#(X1,X2)
   U71#(X1,mark(X2)) -> U71#(X1,X2)
   U71#(active(X1),X2) -> U71#(X1,X2)
   U71#(X1,active(X2)) -> U71#(X1,X2)
   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)
   U81#(mark(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,mark(X2),X3,X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,X2,mark(X3),X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,X2,X3,mark(X4)) -> U81#(X1,X2,X3,X4)
   U81#(active(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,active(X2),X3,X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,X2,active(X3),X4) -> U81#(X1,X2,X3,X4)
   U81#(X1,X2,X3,active(X4)) -> U81#(X1,X2,X3,X4)
   U82#(mark(X1),X2) -> U82#(X1,X2)
   U82#(X1,mark(X2)) -> U82#(X1,X2)
   U82#(active(X1),X2) -> U82#(X1,X2)
   U82#(X1,active(X2)) -> U82#(X1,X2)
   U91#(mark(X1),X2) -> U91#(X1,X2)
   U91#(X1,mark(X2)) -> U91#(X1,X2)
   U91#(active(X1),X2) -> U91#(X1,X2)
   U91#(X1,active(X2)) -> U91#(X1,X2)
   and#(mark(X1),X2) -> and#(X1,X2)
   and#(X1,mark(X2)) -> and#(X1,X2)
   and#(active(X1),X2) -> and#(X1,X2)
   and#(X1,active(X2)) -> and#(X1,X2)
   isNatural#(mark(X)) -> isNatural#(X)
   isNatural#(active(X)) -> isNatural#(X)
   isLNat#(mark(X)) -> isLNat#(X)
   isLNat#(active(X)) -> isLNat#(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
   active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
   active(U21(tt(),X)) -> mark(X)
   active(U31(tt(),N)) -> mark(N)
   active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
   active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
   active(U61(tt(),Y)) -> mark(Y)
   active(U71(tt(),XS)) -> mark(pair(nil(),XS))
   active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
   active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
   active(U91(tt(),XS)) -> mark(XS)
   active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
   active(and(tt(),X)) -> mark(X)
   active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
   active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
   active(isLNat(nil())) -> mark(tt())
   active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
   active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
   active(isLNat(fst(V1))) -> mark(isPLNat(V1))
   active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
   active(isLNat(snd(V1))) -> mark(isPLNat(V1))
   active(isLNat(tail(V1))) -> mark(isLNat(V1))
   active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
   active(isNatural(0())) -> mark(tt())
   active(isNatural(head(V1))) -> mark(isLNat(V1))
   active(isNatural(s(V1))) -> mark(isNatural(V1))
   active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
   active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
   active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
   active(natsFrom(N)) -> mark(U41(isNatural(N),N))
   active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
   active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
   active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
   active(splitAt(s(N),cons(X,XS))) ->
   mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
   active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
   active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
   mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
   mark(tt()) -> active(tt())
   mark(fst(X)) -> active(fst(mark(X)))
   mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
   mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
   mark(snd(X)) -> active(snd(mark(X)))
   mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
   mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
   mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
   mark(head(X)) -> active(head(mark(X)))
   mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
   mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
   mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
   mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
   mark(nil()) -> active(nil())
   mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
   mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
   mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(isNatural(X)) -> active(isNatural(X))
   mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
   U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
   U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
   U101(active(X1),X2,X3) -> U101(X1,X2,X3)
   U101(X1,active(X2),X3) -> U101(X1,X2,X3)
   U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
   fst(mark(X)) -> fst(X)
   fst(active(X)) -> fst(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)
   U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
   U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
   U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
   U11(active(X1),X2,X3) -> U11(X1,X2,X3)
   U11(X1,active(X2),X3) -> U11(X1,X2,X3)
   U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
   snd(mark(X)) -> snd(X)
   snd(active(X)) -> snd(X)
   U21(mark(X1),X2) -> U21(X1,X2)
   U21(X1,mark(X2)) -> U21(X1,X2)
   U21(active(X1),X2) -> U21(X1,X2)
   U21(X1,active(X2)) -> U21(X1,X2)
   U31(mark(X1),X2) -> U31(X1,X2)
   U31(X1,mark(X2)) -> U31(X1,X2)
   U31(active(X1),X2) -> U31(X1,X2)
   U31(X1,active(X2)) -> U31(X1,X2)
   U41(mark(X1),X2) -> U41(X1,X2)
   U41(X1,mark(X2)) -> U41(X1,X2)
   U41(active(X1),X2) -> U41(X1,X2)
   U41(X1,active(X2)) -> U41(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)
   U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
   U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
   U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
   U51(active(X1),X2,X3) -> U51(X1,X2,X3)
   U51(X1,active(X2),X3) -> U51(X1,X2,X3)
   U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
   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)
   U61(mark(X1),X2) -> U61(X1,X2)
   U61(X1,mark(X2)) -> U61(X1,X2)
   U61(active(X1),X2) -> U61(X1,X2)
   U61(X1,active(X2)) -> U61(X1,X2)
   U71(mark(X1),X2) -> U71(X1,X2)
   U71(X1,mark(X2)) -> U71(X1,X2)
   U71(active(X1),X2) -> U71(X1,X2)
   U71(X1,active(X2)) -> U71(X1,X2)
   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)
   U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
   U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
   U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
   U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
   U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
   U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
   U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
   U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
   U82(mark(X1),X2) -> U82(X1,X2)
   U82(X1,mark(X2)) -> U82(X1,X2)
   U82(active(X1),X2) -> U82(X1,X2)
   U82(X1,active(X2)) -> U82(X1,X2)
   U91(mark(X1),X2) -> U91(X1,X2)
   U91(X1,mark(X2)) -> U91(X1,X2)
   U91(active(X1),X2) -> U91(X1,X2)
   U91(X1,active(X2)) -> U91(X1,X2)
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   isNatural(mark(X)) -> isNatural(X)
   isNatural(active(X)) -> isNatural(X)
   isLNat(mark(X)) -> isLNat(X)
   isLNat(active(X)) -> isLNat(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)
  EDG Processor:
   DPs:
    active#(U101(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U101(tt(),N,XS)) -> fst#(splitAt(N,XS))
    active#(U101(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
    active#(U11(tt(),N,XS)) -> splitAt#(N,XS)
    active#(U11(tt(),N,XS)) -> snd#(splitAt(N,XS))
    active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
    active#(U21(tt(),X)) -> mark#(X)
    active#(U31(tt(),N)) -> mark#(N)
    active#(U41(tt(),N)) -> s#(N)
    active#(U41(tt(),N)) -> natsFrom#(s(N))
    active#(U41(tt(),N)) -> cons#(N,natsFrom(s(N)))
    active#(U41(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
    active#(U51(tt(),N,XS)) -> afterNth#(N,XS)
    active#(U51(tt(),N,XS)) -> head#(afterNth(N,XS))
    active#(U51(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
    active#(U61(tt(),Y)) -> mark#(Y)
    active#(U71(tt(),XS)) -> pair#(nil(),XS)
    active#(U71(tt(),XS)) -> mark#(pair(nil(),XS))
    active#(U81(tt(),N,X,XS)) -> splitAt#(N,XS)
    active#(U81(tt(),N,X,XS)) -> U82#(splitAt(N,XS),X)
    active#(U81(tt(),N,X,XS)) -> mark#(U82(splitAt(N,XS),X))
    active#(U82(pair(YS,ZS),X)) -> cons#(X,YS)
    active#(U82(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
    active#(U82(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
    active#(U91(tt(),XS)) -> mark#(XS)
    active#(afterNth(N,XS)) -> isLNat#(XS)
    active#(afterNth(N,XS)) -> isNatural#(N)
    active#(afterNth(N,XS)) -> and#(isNatural(N),isLNat(XS))
    active#(afterNth(N,XS)) -> U11#(and(isNatural(N),isLNat(XS)),N,XS)
    active#(afterNth(N,XS)) -> mark#(U11(and(isNatural(N),isLNat(XS)),N,XS))
    active#(and(tt(),X)) -> mark#(X)
    active#(fst(pair(X,Y))) -> isLNat#(Y)
    active#(fst(pair(X,Y))) -> isLNat#(X)
    active#(fst(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
    active#(fst(pair(X,Y))) -> U21#(and(isLNat(X),isLNat(Y)),X)
    active#(fst(pair(X,Y))) -> mark#(U21(and(isLNat(X),isLNat(Y)),X))
    active#(head(cons(N,XS))) -> isLNat#(XS)
    active#(head(cons(N,XS))) -> isNatural#(N)
    active#(head(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
    active#(head(cons(N,XS))) -> U31#(and(isNatural(N),isLNat(XS)),N)
    active#(head(cons(N,XS))) -> mark#(U31(and(isNatural(N),isLNat(XS)),N))
    active#(isLNat(nil())) -> mark#(tt())
    active#(isLNat(afterNth(V1,V2))) -> isLNat#(V2)
    active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
    active#(isLNat(afterNth(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
    active#(isLNat(afterNth(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
    active#(isLNat(cons(V1,V2))) -> isLNat#(V2)
    active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
    active#(isLNat(cons(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
    active#(isLNat(cons(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
    active#(isLNat(fst(V1))) -> isPLNat#(V1)
    active#(isLNat(fst(V1))) -> mark#(isPLNat(V1))
    active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
    active#(isLNat(natsFrom(V1))) -> mark#(isNatural(V1))
    active#(isLNat(snd(V1))) -> isPLNat#(V1)
    active#(isLNat(snd(V1))) -> mark#(isPLNat(V1))
    active#(isLNat(tail(V1))) -> isLNat#(V1)
    active#(isLNat(tail(V1))) -> mark#(isLNat(V1))
    active#(isLNat(take(V1,V2))) -> isLNat#(V2)
    active#(isLNat(take(V1,V2))) -> isNatural#(V1)
    active#(isLNat(take(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
    active#(isLNat(take(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
    active#(isNatural(0())) -> mark#(tt())
    active#(isNatural(head(V1))) -> isLNat#(V1)
    active#(isNatural(head(V1))) -> mark#(isLNat(V1))
    active#(isNatural(s(V1))) -> isNatural#(V1)
    active#(isNatural(s(V1))) -> mark#(isNatural(V1))
    active#(isNatural(sel(V1,V2))) -> isLNat#(V2)
    active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
    active#(isNatural(sel(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
    active#(isNatural(sel(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
    active#(isPLNat(pair(V1,V2))) -> isLNat#(V2)
    active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
    active#(isPLNat(pair(V1,V2))) -> and#(isLNat(V1),isLNat(V2))
    active#(isPLNat(pair(V1,V2))) -> mark#(and(isLNat(V1),isLNat(V2)))
    active#(isPLNat(splitAt(V1,V2))) -> isLNat#(V2)
    active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
    active#(isPLNat(splitAt(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
    active#(isPLNat(splitAt(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
    active#(natsFrom(N)) -> isNatural#(N)
    active#(natsFrom(N)) -> U41#(isNatural(N),N)
    active#(natsFrom(N)) -> mark#(U41(isNatural(N),N))
    active#(sel(N,XS)) -> isLNat#(XS)
    active#(sel(N,XS)) -> isNatural#(N)
    active#(sel(N,XS)) -> and#(isNatural(N),isLNat(XS))
    active#(sel(N,XS)) -> U51#(and(isNatural(N),isLNat(XS)),N,XS)
    active#(sel(N,XS)) -> mark#(U51(and(isNatural(N),isLNat(XS)),N,XS))
    active#(snd(pair(X,Y))) -> isLNat#(Y)
    active#(snd(pair(X,Y))) -> isLNat#(X)
    active#(snd(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
    active#(snd(pair(X,Y))) -> U61#(and(isLNat(X),isLNat(Y)),Y)
    active#(snd(pair(X,Y))) -> mark#(U61(and(isLNat(X),isLNat(Y)),Y))
    active#(splitAt(0(),XS)) -> isLNat#(XS)
    active#(splitAt(0(),XS)) -> U71#(isLNat(XS),XS)
    active#(splitAt(0(),XS)) -> mark#(U71(isLNat(XS),XS))
    active#(splitAt(s(N),cons(X,XS))) -> isLNat#(XS)
    active#(splitAt(s(N),cons(X,XS))) -> isNatural#(X)
    active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(X),isLNat(XS))
    active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
    active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(N),and(isNatural(X),isLNat(XS)))
    active#(splitAt(s(N),cons(X,XS))) ->
    U81#(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
    active#(splitAt(s(N),cons(X,XS))) ->
    mark#(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
    active#(tail(cons(N,XS))) -> isLNat#(XS)
    active#(tail(cons(N,XS))) -> isNatural#(N)
    active#(tail(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
    active#(tail(cons(N,XS))) -> U91#(and(isNatural(N),isLNat(XS)),XS)
    active#(tail(cons(N,XS))) -> mark#(U91(and(isNatural(N),isLNat(XS)),XS))
    active#(take(N,XS)) -> isLNat#(XS)
    active#(take(N,XS)) -> isNatural#(N)
    active#(take(N,XS)) -> and#(isNatural(N),isLNat(XS))
    active#(take(N,XS)) -> U101#(and(isNatural(N),isLNat(XS)),N,XS)
    active#(take(N,XS)) -> mark#(U101(and(isNatural(N),isLNat(XS)),N,XS))
    mark#(U101(X1,X2,X3)) -> mark#(X1)
    mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3)
    mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
    mark#(tt()) -> active#(tt())
    mark#(fst(X)) -> mark#(X)
    mark#(fst(X)) -> fst#(mark(X))
    mark#(fst(X)) -> active#(fst(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#(U11(X1,X2,X3)) -> mark#(X1)
    mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3)
    mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
    mark#(snd(X)) -> mark#(X)
    mark#(snd(X)) -> snd#(mark(X))
    mark#(snd(X)) -> active#(snd(mark(X)))
    mark#(U21(X1,X2)) -> mark#(X1)
    mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
    mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
    mark#(U31(X1,X2)) -> mark#(X1)
    mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
    mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
    mark#(U41(X1,X2)) -> mark#(X1)
    mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
    mark#(U41(X1,X2)) -> active#(U41(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#(U51(X1,X2,X3)) -> mark#(X1)
    mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
    mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
    mark#(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#(U61(X1,X2)) -> mark#(X1)
    mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
    mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
    mark#(U71(X1,X2)) -> mark#(X1)
    mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
    mark#(U71(X1,X2)) -> active#(U71(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#(U81(X1,X2,X3,X4)) -> mark#(X1)
    mark#(U81(X1,X2,X3,X4)) -> U81#(mark(X1),X2,X3,X4)
    mark#(U81(X1,X2,X3,X4)) -> active#(U81(mark(X1),X2,X3,X4))
    mark#(U82(X1,X2)) -> mark#(X1)
    mark#(U82(X1,X2)) -> U82#(mark(X1),X2)
    mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
    mark#(U91(X1,X2)) -> mark#(X1)
    mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
    mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> and#(mark(X1),X2)
    mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
    mark#(isNatural(X)) -> active#(isNatural(X))
    mark#(isLNat(X)) -> active#(isLNat(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,X3) -> U101#(X1,X2,X3)
    U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
    U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
    U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
    U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
    U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
    fst#(mark(X)) -> fst#(X)
    fst#(active(X)) -> fst#(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)
    U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
    U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
    U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
    U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
    U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
    U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
    snd#(mark(X)) -> snd#(X)
    snd#(active(X)) -> snd#(X)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U21#(X1,mark(X2)) -> U21#(X1,X2)
    U21#(active(X1),X2) -> U21#(X1,X2)
    U21#(X1,active(X2)) -> U21#(X1,X2)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U31#(X1,mark(X2)) -> U31#(X1,X2)
    U31#(active(X1),X2) -> U31#(X1,X2)
    U31#(X1,active(X2)) -> U31#(X1,X2)
    U41#(mark(X1),X2) -> U41#(X1,X2)
    U41#(X1,mark(X2)) -> U41#(X1,X2)
    U41#(active(X1),X2) -> U41#(X1,X2)
    U41#(X1,active(X2)) -> U41#(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)
    U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
    U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
    U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
    U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
    U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
    U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
    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)
    U61#(mark(X1),X2) -> U61#(X1,X2)
    U61#(X1,mark(X2)) -> U61#(X1,X2)
    U61#(active(X1),X2) -> U61#(X1,X2)
    U61#(X1,active(X2)) -> U61#(X1,X2)
    U71#(mark(X1),X2) -> U71#(X1,X2)
    U71#(X1,mark(X2)) -> U71#(X1,X2)
    U71#(active(X1),X2) -> U71#(X1,X2)
    U71#(X1,active(X2)) -> U71#(X1,X2)
    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)
    U81#(mark(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,mark(X2),X3,X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,X2,mark(X3),X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,X2,X3,mark(X4)) -> U81#(X1,X2,X3,X4)
    U81#(active(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,active(X2),X3,X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,X2,active(X3),X4) -> U81#(X1,X2,X3,X4)
    U81#(X1,X2,X3,active(X4)) -> U81#(X1,X2,X3,X4)
    U82#(mark(X1),X2) -> U82#(X1,X2)
    U82#(X1,mark(X2)) -> U82#(X1,X2)
    U82#(active(X1),X2) -> U82#(X1,X2)
    U82#(X1,active(X2)) -> U82#(X1,X2)
    U91#(mark(X1),X2) -> U91#(X1,X2)
    U91#(X1,mark(X2)) -> U91#(X1,X2)
    U91#(active(X1),X2) -> U91#(X1,X2)
    U91#(X1,active(X2)) -> U91#(X1,X2)
    and#(mark(X1),X2) -> and#(X1,X2)
    and#(X1,mark(X2)) -> and#(X1,X2)
    and#(active(X1),X2) -> and#(X1,X2)
    and#(X1,active(X2)) -> and#(X1,X2)
    isNatural#(mark(X)) -> isNatural#(X)
    isNatural#(active(X)) -> isNatural#(X)
    isLNat#(mark(X)) -> isLNat#(X)
    isLNat#(active(X)) -> isLNat#(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
    active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
    active(U21(tt(),X)) -> mark(X)
    active(U31(tt(),N)) -> mark(N)
    active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
    active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
    active(U61(tt(),Y)) -> mark(Y)
    active(U71(tt(),XS)) -> mark(pair(nil(),XS))
    active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
    active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
    active(U91(tt(),XS)) -> mark(XS)
    active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
    active(and(tt(),X)) -> mark(X)
    active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
    active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
    active(isLNat(nil())) -> mark(tt())
    active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
    active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
    active(isLNat(fst(V1))) -> mark(isPLNat(V1))
    active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
    active(isLNat(snd(V1))) -> mark(isPLNat(V1))
    active(isLNat(tail(V1))) -> mark(isLNat(V1))
    active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
    active(isNatural(0())) -> mark(tt())
    active(isNatural(head(V1))) -> mark(isLNat(V1))
    active(isNatural(s(V1))) -> mark(isNatural(V1))
    active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
    active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
    active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
    active(natsFrom(N)) -> mark(U41(isNatural(N),N))
    active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
    active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
    active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
    active(splitAt(s(N),cons(X,XS))) ->
    mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
    active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
    active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
    mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
    mark(tt()) -> active(tt())
    mark(fst(X)) -> active(fst(mark(X)))
    mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
    mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
    mark(snd(X)) -> active(snd(mark(X)))
    mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
    mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
    mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
    mark(head(X)) -> active(head(mark(X)))
    mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
    mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
    mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
    mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
    mark(nil()) -> active(nil())
    mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
    mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
    mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
    mark(and(X1,X2)) -> active(and(mark(X1),X2))
    mark(isNatural(X)) -> active(isNatural(X))
    mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
    U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
    U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
    U101(active(X1),X2,X3) -> U101(X1,X2,X3)
    U101(X1,active(X2),X3) -> U101(X1,X2,X3)
    U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
    fst(mark(X)) -> fst(X)
    fst(active(X)) -> fst(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)
    U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
    U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
    U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
    U11(active(X1),X2,X3) -> U11(X1,X2,X3)
    U11(X1,active(X2),X3) -> U11(X1,X2,X3)
    U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
    snd(mark(X)) -> snd(X)
    snd(active(X)) -> snd(X)
    U21(mark(X1),X2) -> U21(X1,X2)
    U21(X1,mark(X2)) -> U21(X1,X2)
    U21(active(X1),X2) -> U21(X1,X2)
    U21(X1,active(X2)) -> U21(X1,X2)
    U31(mark(X1),X2) -> U31(X1,X2)
    U31(X1,mark(X2)) -> U31(X1,X2)
    U31(active(X1),X2) -> U31(X1,X2)
    U31(X1,active(X2)) -> U31(X1,X2)
    U41(mark(X1),X2) -> U41(X1,X2)
    U41(X1,mark(X2)) -> U41(X1,X2)
    U41(active(X1),X2) -> U41(X1,X2)
    U41(X1,active(X2)) -> U41(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)
    U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
    U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
    U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
    U51(active(X1),X2,X3) -> U51(X1,X2,X3)
    U51(X1,active(X2),X3) -> U51(X1,X2,X3)
    U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
    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)
    U61(mark(X1),X2) -> U61(X1,X2)
    U61(X1,mark(X2)) -> U61(X1,X2)
    U61(active(X1),X2) -> U61(X1,X2)
    U61(X1,active(X2)) -> U61(X1,X2)
    U71(mark(X1),X2) -> U71(X1,X2)
    U71(X1,mark(X2)) -> U71(X1,X2)
    U71(active(X1),X2) -> U71(X1,X2)
    U71(X1,active(X2)) -> U71(X1,X2)
    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)
    U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
    U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
    U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
    U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
    U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
    U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
    U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
    U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
    U82(mark(X1),X2) -> U82(X1,X2)
    U82(X1,mark(X2)) -> U82(X1,X2)
    U82(active(X1),X2) -> U82(X1,X2)
    U82(X1,active(X2)) -> U82(X1,X2)
    U91(mark(X1),X2) -> U91(X1,X2)
    U91(X1,mark(X2)) -> U91(X1,X2)
    U91(active(X1),X2) -> U91(X1,X2)
    U91(X1,active(X2)) -> U91(X1,X2)
    and(mark(X1),X2) -> and(X1,X2)
    and(X1,mark(X2)) -> and(X1,X2)
    and(active(X1),X2) -> and(X1,X2)
    and(X1,active(X2)) -> and(X1,X2)
    isNatural(mark(X)) -> isNatural(X)
    isNatural(active(X)) -> isNatural(X)
    isLNat(mark(X)) -> isLNat(X)
    isLNat(active(X)) -> isLNat(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(),N,XS)) -> splitAt#(N,XS)
     active#(U101(tt(),N,XS)) -> fst#(splitAt(N,XS))
     active#(U101(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
     active#(U11(tt(),N,XS)) -> splitAt#(N,XS)
     active#(U11(tt(),N,XS)) -> snd#(splitAt(N,XS))
     active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
     active#(U21(tt(),X)) -> mark#(X)
     active#(U31(tt(),N)) -> mark#(N)
     active#(U41(tt(),N)) -> s#(N)
     active#(U41(tt(),N)) -> natsFrom#(s(N))
     active#(U41(tt(),N)) -> cons#(N,natsFrom(s(N)))
     active#(U41(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
     active#(U51(tt(),N,XS)) -> afterNth#(N,XS)
     active#(U51(tt(),N,XS)) -> head#(afterNth(N,XS))
     active#(U51(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
     active#(U61(tt(),Y)) -> mark#(Y)
     active#(U71(tt(),XS)) -> pair#(nil(),XS)
     active#(U71(tt(),XS)) -> mark#(pair(nil(),XS))
     active#(U81(tt(),N,X,XS)) -> splitAt#(N,XS)
     active#(U81(tt(),N,X,XS)) -> U82#(splitAt(N,XS),X)
     active#(U81(tt(),N,X,XS)) -> mark#(U82(splitAt(N,XS),X))
     active#(U82(pair(YS,ZS),X)) -> cons#(X,YS)
     active#(U82(pair(YS,ZS),X)) -> pair#(cons(X,YS),ZS)
     active#(U82(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
     active#(U91(tt(),XS)) -> mark#(XS)
     active#(afterNth(N,XS)) -> isLNat#(XS)
     active#(afterNth(N,XS)) -> isNatural#(N)
     active#(afterNth(N,XS)) -> and#(isNatural(N),isLNat(XS))
     active#(afterNth(N,XS)) -> U11#(and(isNatural(N),isLNat(XS)),N,XS)
     active#(afterNth(N,XS)) -> mark#(U11(and(isNatural(N),isLNat(XS)),N,XS))
     active#(and(tt(),X)) -> mark#(X)
     active#(fst(pair(X,Y))) -> isLNat#(Y)
     active#(fst(pair(X,Y))) -> isLNat#(X)
     active#(fst(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
     active#(fst(pair(X,Y))) -> U21#(and(isLNat(X),isLNat(Y)),X)
     active#(fst(pair(X,Y))) -> mark#(U21(and(isLNat(X),isLNat(Y)),X))
     active#(head(cons(N,XS))) -> isLNat#(XS)
     active#(head(cons(N,XS))) -> isNatural#(N)
     active#(head(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
     active#(head(cons(N,XS))) -> U31#(and(isNatural(N),isLNat(XS)),N)
     active#(head(cons(N,XS))) -> mark#(U31(and(isNatural(N),isLNat(XS)),N))
     active#(isLNat(nil())) -> mark#(tt())
     active#(isLNat(afterNth(V1,V2))) -> isLNat#(V2)
     active#(isLNat(afterNth(V1,V2))) -> isNatural#(V1)
     active#(isLNat(afterNth(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
     active#(isLNat(afterNth(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
     active#(isLNat(cons(V1,V2))) -> isLNat#(V2)
     active#(isLNat(cons(V1,V2))) -> isNatural#(V1)
     active#(isLNat(cons(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
     active#(isLNat(cons(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
     active#(isLNat(fst(V1))) -> isPLNat#(V1)
     active#(isLNat(fst(V1))) -> mark#(isPLNat(V1))
     active#(isLNat(natsFrom(V1))) -> isNatural#(V1)
     active#(isLNat(natsFrom(V1))) -> mark#(isNatural(V1))
     active#(isLNat(snd(V1))) -> isPLNat#(V1)
     active#(isLNat(snd(V1))) -> mark#(isPLNat(V1))
     active#(isLNat(tail(V1))) -> isLNat#(V1)
     active#(isLNat(tail(V1))) -> mark#(isLNat(V1))
     active#(isLNat(take(V1,V2))) -> isLNat#(V2)
     active#(isLNat(take(V1,V2))) -> isNatural#(V1)
     active#(isLNat(take(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
     active#(isLNat(take(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
     active#(isNatural(0())) -> mark#(tt())
     active#(isNatural(head(V1))) -> isLNat#(V1)
     active#(isNatural(head(V1))) -> mark#(isLNat(V1))
     active#(isNatural(s(V1))) -> isNatural#(V1)
     active#(isNatural(s(V1))) -> mark#(isNatural(V1))
     active#(isNatural(sel(V1,V2))) -> isLNat#(V2)
     active#(isNatural(sel(V1,V2))) -> isNatural#(V1)
     active#(isNatural(sel(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
     active#(isNatural(sel(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
     active#(isPLNat(pair(V1,V2))) -> isLNat#(V2)
     active#(isPLNat(pair(V1,V2))) -> isLNat#(V1)
     active#(isPLNat(pair(V1,V2))) -> and#(isLNat(V1),isLNat(V2))
     active#(isPLNat(pair(V1,V2))) -> mark#(and(isLNat(V1),isLNat(V2)))
     active#(isPLNat(splitAt(V1,V2))) -> isLNat#(V2)
     active#(isPLNat(splitAt(V1,V2))) -> isNatural#(V1)
     active#(isPLNat(splitAt(V1,V2))) -> and#(isNatural(V1),isLNat(V2))
     active#(isPLNat(splitAt(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
     active#(natsFrom(N)) -> isNatural#(N)
     active#(natsFrom(N)) -> U41#(isNatural(N),N)
     active#(natsFrom(N)) -> mark#(U41(isNatural(N),N))
     active#(sel(N,XS)) -> isLNat#(XS)
     active#(sel(N,XS)) -> isNatural#(N)
     active#(sel(N,XS)) -> and#(isNatural(N),isLNat(XS))
     active#(sel(N,XS)) -> U51#(and(isNatural(N),isLNat(XS)),N,XS)
     active#(sel(N,XS)) -> mark#(U51(and(isNatural(N),isLNat(XS)),N,XS))
     active#(snd(pair(X,Y))) -> isLNat#(Y)
     active#(snd(pair(X,Y))) -> isLNat#(X)
     active#(snd(pair(X,Y))) -> and#(isLNat(X),isLNat(Y))
     active#(snd(pair(X,Y))) -> U61#(and(isLNat(X),isLNat(Y)),Y)
     active#(snd(pair(X,Y))) -> mark#(U61(and(isLNat(X),isLNat(Y)),Y))
     active#(splitAt(0(),XS)) -> isLNat#(XS)
     active#(splitAt(0(),XS)) -> U71#(isLNat(XS),XS)
     active#(splitAt(0(),XS)) -> mark#(U71(isLNat(XS),XS))
     active#(splitAt(s(N),cons(X,XS))) -> isLNat#(XS)
     active#(splitAt(s(N),cons(X,XS))) -> isNatural#(X)
     active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(X),isLNat(XS))
     active#(splitAt(s(N),cons(X,XS))) -> isNatural#(N)
     active#(splitAt(s(N),cons(X,XS))) -> and#(isNatural(N),and(isNatural(X),isLNat(XS)))
     active#(splitAt(s(N),cons(X,XS))) ->
     U81#(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
     active#(splitAt(s(N),cons(X,XS))) ->
     mark#(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
     active#(tail(cons(N,XS))) -> isLNat#(XS)
     active#(tail(cons(N,XS))) -> isNatural#(N)
     active#(tail(cons(N,XS))) -> and#(isNatural(N),isLNat(XS))
     active#(tail(cons(N,XS))) -> U91#(and(isNatural(N),isLNat(XS)),XS)
     active#(tail(cons(N,XS))) -> mark#(U91(and(isNatural(N),isLNat(XS)),XS))
     active#(take(N,XS)) -> isLNat#(XS)
     active#(take(N,XS)) -> isNatural#(N)
     active#(take(N,XS)) -> and#(isNatural(N),isLNat(XS))
     active#(take(N,XS)) -> U101#(and(isNatural(N),isLNat(XS)),N,XS)
     active#(take(N,XS)) -> mark#(U101(and(isNatural(N),isLNat(XS)),N,XS))
     mark#(U101(X1,X2,X3)) -> mark#(X1)
     mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3)
     mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
     mark#(tt()) -> active#(tt())
     mark#(fst(X)) -> mark#(X)
     mark#(fst(X)) -> fst#(mark(X))
     mark#(fst(X)) -> active#(fst(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#(U11(X1,X2,X3)) -> mark#(X1)
     mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3)
     mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
     mark#(snd(X)) -> mark#(X)
     mark#(snd(X)) -> snd#(mark(X))
     mark#(snd(X)) -> active#(snd(mark(X)))
     mark#(U21(X1,X2)) -> mark#(X1)
     mark#(U21(X1,X2)) -> U21#(mark(X1),X2)
     mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
     mark#(U31(X1,X2)) -> mark#(X1)
     mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
     mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
     mark#(U41(X1,X2)) -> mark#(X1)
     mark#(U41(X1,X2)) -> U41#(mark(X1),X2)
     mark#(U41(X1,X2)) -> active#(U41(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#(U51(X1,X2,X3)) -> mark#(X1)
     mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
     mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
     mark#(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#(U61(X1,X2)) -> mark#(X1)
     mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
     mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
     mark#(U71(X1,X2)) -> mark#(X1)
     mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
     mark#(U71(X1,X2)) -> active#(U71(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#(U81(X1,X2,X3,X4)) -> mark#(X1)
     mark#(U81(X1,X2,X3,X4)) -> U81#(mark(X1),X2,X3,X4)
     mark#(U81(X1,X2,X3,X4)) -> active#(U81(mark(X1),X2,X3,X4))
     mark#(U82(X1,X2)) -> mark#(X1)
     mark#(U82(X1,X2)) -> U82#(mark(X1),X2)
     mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
     mark#(U91(X1,X2)) -> mark#(X1)
     mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
     mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> and#(mark(X1),X2)
     mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
     mark#(isNatural(X)) -> active#(isNatural(X))
     mark#(isLNat(X)) -> active#(isLNat(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,X3) -> U101#(X1,X2,X3)
     U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
     U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
     U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
     U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
     U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
     fst#(mark(X)) -> fst#(X)
     fst#(active(X)) -> fst#(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)
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3)
     U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3)
     U11#(active(X1),X2,X3) -> U11#(X1,X2,X3)
     U11#(X1,active(X2),X3) -> U11#(X1,X2,X3)
     U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3)
     snd#(mark(X)) -> snd#(X)
     snd#(active(X)) -> snd#(X)
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U21#(X1,mark(X2)) -> U21#(X1,X2)
     U21#(active(X1),X2) -> U21#(X1,X2)
     U21#(X1,active(X2)) -> U21#(X1,X2)
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U31#(X1,mark(X2)) -> U31#(X1,X2)
     U31#(active(X1),X2) -> U31#(X1,X2)
     U31#(X1,active(X2)) -> U31#(X1,X2)
     U41#(mark(X1),X2) -> U41#(X1,X2)
     U41#(X1,mark(X2)) -> U41#(X1,X2)
     U41#(active(X1),X2) -> U41#(X1,X2)
     U41#(X1,active(X2)) -> U41#(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)
     U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
     U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
     U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
     U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
     U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
     U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
     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)
     U61#(mark(X1),X2) -> U61#(X1,X2)
     U61#(X1,mark(X2)) -> U61#(X1,X2)
     U61#(active(X1),X2) -> U61#(X1,X2)
     U61#(X1,active(X2)) -> U61#(X1,X2)
     U71#(mark(X1),X2) -> U71#(X1,X2)
     U71#(X1,mark(X2)) -> U71#(X1,X2)
     U71#(active(X1),X2) -> U71#(X1,X2)
     U71#(X1,active(X2)) -> U71#(X1,X2)
     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)
     U81#(mark(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,mark(X2),X3,X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,X2,mark(X3),X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,X2,X3,mark(X4)) -> U81#(X1,X2,X3,X4)
     U81#(active(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,active(X2),X3,X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,X2,active(X3),X4) -> U81#(X1,X2,X3,X4)
     U81#(X1,X2,X3,active(X4)) -> U81#(X1,X2,X3,X4)
     U82#(mark(X1),X2) -> U82#(X1,X2)
     U82#(X1,mark(X2)) -> U82#(X1,X2)
     U82#(active(X1),X2) -> U82#(X1,X2)
     U82#(X1,active(X2)) -> U82#(X1,X2)
     U91#(mark(X1),X2) -> U91#(X1,X2)
     U91#(X1,mark(X2)) -> U91#(X1,X2)
     U91#(active(X1),X2) -> U91#(X1,X2)
     U91#(X1,active(X2)) -> U91#(X1,X2)
     and#(mark(X1),X2) -> and#(X1,X2)
     and#(X1,mark(X2)) -> and#(X1,X2)
     and#(active(X1),X2) -> and#(X1,X2)
     and#(X1,active(X2)) -> and#(X1,X2)
     isNatural#(mark(X)) -> isNatural#(X)
     isNatural#(active(X)) -> isNatural#(X)
     isLNat#(mark(X)) -> isLNat#(X)
     isLNat#(active(X)) -> isLNat#(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
     active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
     active(U21(tt(),X)) -> mark(X)
     active(U31(tt(),N)) -> mark(N)
     active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
     active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
     active(U61(tt(),Y)) -> mark(Y)
     active(U71(tt(),XS)) -> mark(pair(nil(),XS))
     active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
     active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
     active(U91(tt(),XS)) -> mark(XS)
     active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
     active(and(tt(),X)) -> mark(X)
     active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
     active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
     active(isLNat(nil())) -> mark(tt())
     active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
     active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
     active(isLNat(fst(V1))) -> mark(isPLNat(V1))
     active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
     active(isLNat(snd(V1))) -> mark(isPLNat(V1))
     active(isLNat(tail(V1))) -> mark(isLNat(V1))
     active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
     active(isNatural(0())) -> mark(tt())
     active(isNatural(head(V1))) -> mark(isLNat(V1))
     active(isNatural(s(V1))) -> mark(isNatural(V1))
     active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
     active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
     active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
     active(natsFrom(N)) -> mark(U41(isNatural(N),N))
     active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
     active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
     active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
     active(splitAt(s(N),cons(X,XS))) ->
     mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
     active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
     active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
     mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
     mark(tt()) -> active(tt())
     mark(fst(X)) -> active(fst(mark(X)))
     mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
     mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
     mark(snd(X)) -> active(snd(mark(X)))
     mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
     mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
     mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
     mark(head(X)) -> active(head(mark(X)))
     mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
     mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
     mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
     mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
     mark(nil()) -> active(nil())
     mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
     mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
     mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
     mark(and(X1,X2)) -> active(and(mark(X1),X2))
     mark(isNatural(X)) -> active(isNatural(X))
     mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
     U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
     U101(active(X1),X2,X3) -> U101(X1,X2,X3)
     U101(X1,active(X2),X3) -> U101(X1,X2,X3)
     U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
     fst(mark(X)) -> fst(X)
     fst(active(X)) -> fst(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)
     U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
     U11(active(X1),X2,X3) -> U11(X1,X2,X3)
     U11(X1,active(X2),X3) -> U11(X1,X2,X3)
     U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
     snd(mark(X)) -> snd(X)
     snd(active(X)) -> snd(X)
     U21(mark(X1),X2) -> U21(X1,X2)
     U21(X1,mark(X2)) -> U21(X1,X2)
     U21(active(X1),X2) -> U21(X1,X2)
     U21(X1,active(X2)) -> U21(X1,X2)
     U31(mark(X1),X2) -> U31(X1,X2)
     U31(X1,mark(X2)) -> U31(X1,X2)
     U31(active(X1),X2) -> U31(X1,X2)
     U31(X1,active(X2)) -> U31(X1,X2)
     U41(mark(X1),X2) -> U41(X1,X2)
     U41(X1,mark(X2)) -> U41(X1,X2)
     U41(active(X1),X2) -> U41(X1,X2)
     U41(X1,active(X2)) -> U41(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)
     U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
     U51(active(X1),X2,X3) -> U51(X1,X2,X3)
     U51(X1,active(X2),X3) -> U51(X1,X2,X3)
     U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
     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)
     U61(mark(X1),X2) -> U61(X1,X2)
     U61(X1,mark(X2)) -> U61(X1,X2)
     U61(active(X1),X2) -> U61(X1,X2)
     U61(X1,active(X2)) -> U61(X1,X2)
     U71(mark(X1),X2) -> U71(X1,X2)
     U71(X1,mark(X2)) -> U71(X1,X2)
     U71(active(X1),X2) -> U71(X1,X2)
     U71(X1,active(X2)) -> U71(X1,X2)
     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)
     U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
     U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
     U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
     U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
     U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
     U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
     U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
     U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
     U82(mark(X1),X2) -> U82(X1,X2)
     U82(X1,mark(X2)) -> U82(X1,X2)
     U82(active(X1),X2) -> U82(X1,X2)
     U82(X1,active(X2)) -> U82(X1,X2)
     U91(mark(X1),X2) -> U91(X1,X2)
     U91(X1,mark(X2)) -> U91(X1,X2)
     U91(active(X1),X2) -> U91(X1,X2)
     U91(X1,active(X2)) -> U91(X1,X2)
     and(mark(X1),X2) -> and(X1,X2)
     and(X1,mark(X2)) -> and(X1,X2)
     and(active(X1),X2) -> and(X1,X2)
     and(X1,active(X2)) -> and(X1,X2)
     isNatural(mark(X)) -> isNatural(X)
     isNatural(active(X)) -> isNatural(X)
     isLNat(mark(X)) -> isLNat(X)
     isLNat(active(X)) -> isLNat(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: 28
     #rules: 190
     #arcs: 8922/87025
     DPs:
      mark#(sel(X1,X2)) -> mark#(X2)
      mark#(sel(X1,X2)) -> active#(sel(mark(X1),mark(X2)))
      active#(take(N,XS)) -> mark#(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark#(sel(X1,X2)) -> mark#(X1)
      mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2)))
      active#(tail(cons(N,XS))) -> mark#(U91(and(isNatural(N),isLNat(XS)),XS))
      mark#(take(X1,X2)) -> mark#(X1)
      mark#(take(X1,X2)) -> mark#(X2)
      mark#(tail(X)) -> active#(tail(mark(X)))
      active#(splitAt(s(N),cons(X,XS))) ->
      mark#(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      mark#(tail(X)) -> mark#(X)
      mark#(isPLNat(X)) -> active#(isPLNat(X))
      active#(splitAt(0(),XS)) -> mark#(U71(isLNat(XS),XS))
      mark#(isLNat(X)) -> active#(isLNat(X))
      active#(snd(pair(X,Y))) -> mark#(U61(and(isLNat(X),isLNat(Y)),Y))
      mark#(isNatural(X)) -> active#(isNatural(X))
      active#(sel(N,XS)) -> mark#(U51(and(isNatural(N),isLNat(XS)),N,XS))
      mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
      active#(natsFrom(N)) -> mark#(U41(isNatural(N),N))
      mark#(and(X1,X2)) -> mark#(X1)
      mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
      active#(isPLNat(splitAt(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
      mark#(U91(X1,X2)) -> mark#(X1)
      mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
      active#(isPLNat(pair(V1,V2))) -> mark#(and(isLNat(V1),isLNat(V2)))
      mark#(U82(X1,X2)) -> mark#(X1)
      mark#(U81(X1,X2,X3,X4)) -> active#(U81(mark(X1),X2,X3,X4))
      active#(isNatural(sel(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
      mark#(U81(X1,X2,X3,X4)) -> mark#(X1)
      mark#(pair(X1,X2)) -> active#(pair(mark(X1),mark(X2)))
      active#(isNatural(s(V1))) -> mark#(isNatural(V1))
      mark#(pair(X1,X2)) -> mark#(X1)
      mark#(pair(X1,X2)) -> mark#(X2)
      mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
      active#(isNatural(head(V1))) -> mark#(isLNat(V1))
      mark#(U71(X1,X2)) -> mark#(X1)
      mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
      active#(isLNat(take(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
      mark#(U61(X1,X2)) -> mark#(X1)
      mark#(afterNth(X1,X2)) -> active#(afterNth(mark(X1),mark(X2)))
      active#(isLNat(tail(V1))) -> mark#(isLNat(V1))
      mark#(afterNth(X1,X2)) -> mark#(X1)
      mark#(afterNth(X1,X2)) -> mark#(X2)
      mark#(head(X)) -> active#(head(mark(X)))
      active#(isLNat(snd(V1))) -> mark#(isPLNat(V1))
      mark#(head(X)) -> mark#(X)
      mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
      active#(isLNat(natsFrom(V1))) -> mark#(isNatural(V1))
      mark#(U51(X1,X2,X3)) -> mark#(X1)
      mark#(s(X)) -> active#(s(mark(X)))
      active#(isLNat(fst(V1))) -> mark#(isPLNat(V1))
      mark#(s(X)) -> mark#(X)
      mark#(natsFrom(X)) -> active#(natsFrom(mark(X)))
      active#(isLNat(cons(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
      mark#(natsFrom(X)) -> mark#(X)
      mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2))
      active#(isLNat(afterNth(V1,V2))) -> mark#(and(isNatural(V1),isLNat(V2)))
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2))
      active#(head(cons(N,XS))) -> mark#(U31(and(isNatural(N),isLNat(XS)),N))
      mark#(U41(X1,X2)) -> mark#(X1)
      mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
      active#(fst(pair(X,Y))) -> mark#(U21(and(isLNat(X),isLNat(Y)),X))
      mark#(U31(X1,X2)) -> mark#(X1)
      mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2))
      active#(and(tt(),X)) -> mark#(X)
      mark#(U21(X1,X2)) -> mark#(X1)
      mark#(snd(X)) -> active#(snd(mark(X)))
      active#(afterNth(N,XS)) -> mark#(U11(and(isNatural(N),isLNat(XS)),N,XS))
      mark#(snd(X)) -> mark#(X)
      mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3))
      active#(U91(tt(),XS)) -> mark#(XS)
      mark#(U11(X1,X2,X3)) -> mark#(X1)
      mark#(splitAt(X1,X2)) -> active#(splitAt(mark(X1),mark(X2)))
      active#(U82(pair(YS,ZS),X)) -> mark#(pair(cons(X,YS),ZS))
      mark#(splitAt(X1,X2)) -> mark#(X1)
      mark#(splitAt(X1,X2)) -> mark#(X2)
      mark#(fst(X)) -> active#(fst(mark(X)))
      active#(U81(tt(),N,X,XS)) -> mark#(U82(splitAt(N,XS),X))
      mark#(fst(X)) -> mark#(X)
      mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3))
      active#(U71(tt(),XS)) -> mark#(pair(nil(),XS))
      mark#(U101(X1,X2,X3)) -> mark#(X1)
      active#(U61(tt(),Y)) -> mark#(Y)
      active#(U51(tt(),N,XS)) -> mark#(head(afterNth(N,XS)))
      active#(U41(tt(),N)) -> mark#(cons(N,natsFrom(s(N))))
      active#(U31(tt(),N)) -> mark#(N)
      active#(U21(tt(),X)) -> mark#(X)
      active#(U11(tt(),N,XS)) -> mark#(snd(splitAt(N,XS)))
      active#(U101(tt(),N,XS)) -> mark#(fst(splitAt(N,XS)))
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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#(active(X)) -> fst#(X)
      fst#(mark(X)) -> fst#(X)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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#(X1,active(X2)) -> splitAt#(X1,X2)
      splitAt#(active(X1),X2) -> splitAt#(X1,X2)
      splitAt#(X1,mark(X2)) -> splitAt#(X1,X2)
      splitAt#(mark(X1),X2) -> splitAt#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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:
      U82#(mark(X1),X2) -> U82#(X1,X2)
      U82#(X1,active(X2)) -> U82#(X1,X2)
      U82#(active(X1),X2) -> U82#(X1,X2)
      U82#(X1,mark(X2)) -> U82#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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#(mark(X)) -> isLNat#(X)
      isLNat#(active(X)) -> isLNat#(X)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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:
      and#(mark(X1),X2) -> and#(X1,X2)
      and#(X1,active(X2)) -> and#(X1,X2)
      and#(active(X1),X2) -> and#(X1,X2)
      and#(X1,mark(X2)) -> and#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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) -> U21#(X1,X2)
      U21#(X1,active(X2)) -> U21#(X1,X2)
      U21#(active(X1),X2) -> U21#(X1,X2)
      U21#(X1,mark(X2)) -> U21#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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) -> U31#(X1,X2)
      U31#(X1,active(X2)) -> U31#(X1,X2)
      U31#(active(X1),X2) -> U31#(X1,X2)
      U31#(X1,mark(X2)) -> U31#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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,X3) -> U51#(X1,X2,X3)
      U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
      U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
      U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
      U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
      U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(X1),X2) -> U61#(X1,X2)
      U61#(X1,active(X2)) -> U61#(X1,X2)
      U61#(active(X1),X2) -> U61#(X1,X2)
      U61#(X1,mark(X2)) -> U61#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(X1),X2) -> U71#(X1,X2)
      U71#(X1,active(X2)) -> U71#(X1,X2)
      U71#(active(X1),X2) -> U71#(X1,X2)
      U71#(X1,mark(X2)) -> U71#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
      U81#(X1,X2,X3,active(X4)) -> U81#(X1,X2,X3,X4)
      U81#(X1,X2,active(X3),X4) -> U81#(X1,X2,X3,X4)
      U81#(X1,active(X2),X3,X4) -> U81#(X1,X2,X3,X4)
      U81#(active(X1),X2,X3,X4) -> U81#(X1,X2,X3,X4)
      U81#(X1,X2,X3,mark(X4)) -> U81#(X1,X2,X3,X4)
      U81#(X1,X2,mark(X3),X4) -> U81#(X1,X2,X3,X4)
      U81#(X1,mark(X2),X3,X4) -> U81#(X1,X2,X3,X4)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(X1),X2) -> U91#(X1,X2)
      U91#(X1,active(X2)) -> U91#(X1,X2)
      U91#(active(X1),X2) -> U91#(X1,X2)
      U91#(X1,mark(X2)) -> U91#(X1,X2)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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,X3) -> U101#(X1,X2,X3)
      U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3)
      U101#(X1,active(X2),X3) -> U101#(X1,X2,X3)
      U101#(active(X1),X2,X3) -> U101#(X1,X2,X3)
      U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3)
      U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3)
     TRS:
      active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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(),N,XS)) -> mark(fst(splitAt(N,XS)))
      active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
      active(U21(tt(),X)) -> mark(X)
      active(U31(tt(),N)) -> mark(N)
      active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
      active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
      active(U61(tt(),Y)) -> mark(Y)
      active(U71(tt(),XS)) -> mark(pair(nil(),XS))
      active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
      active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
      active(U91(tt(),XS)) -> mark(XS)
      active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
      active(and(tt(),X)) -> mark(X)
      active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
      active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
      active(isLNat(nil())) -> mark(tt())
      active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isLNat(fst(V1))) -> mark(isPLNat(V1))
      active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
      active(isLNat(snd(V1))) -> mark(isPLNat(V1))
      active(isLNat(tail(V1))) -> mark(isLNat(V1))
      active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isNatural(0())) -> mark(tt())
      active(isNatural(head(V1))) -> mark(isLNat(V1))
      active(isNatural(s(V1))) -> mark(isNatural(V1))
      active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
      active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
      active(natsFrom(N)) -> mark(U41(isNatural(N),N))
      active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
      active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
      active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
      active(splitAt(s(N),cons(X,XS))) ->
      mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
      active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
      active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
      mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3))
      mark(tt()) -> active(tt())
      mark(fst(X)) -> active(fst(mark(X)))
      mark(splitAt(X1,X2)) -> active(splitAt(mark(X1),mark(X2)))
      mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
      mark(snd(X)) -> active(snd(mark(X)))
      mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
      mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
      mark(U41(X1,X2)) -> active(U41(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(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
      mark(head(X)) -> active(head(mark(X)))
      mark(afterNth(X1,X2)) -> active(afterNth(mark(X1),mark(X2)))
      mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
      mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
      mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2)))
      mark(nil()) -> active(nil())
      mark(U81(X1,X2,X3,X4)) -> active(U81(mark(X1),X2,X3,X4))
      mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
      mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
      mark(and(X1,X2)) -> active(and(mark(X1),X2))
      mark(isNatural(X)) -> active(isNatural(X))
      mark(isLNat(X)) -> active(isLNat(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,X3) -> U101(X1,X2,X3)
      U101(X1,mark(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,mark(X3)) -> U101(X1,X2,X3)
      U101(active(X1),X2,X3) -> U101(X1,X2,X3)
      U101(X1,active(X2),X3) -> U101(X1,X2,X3)
      U101(X1,X2,active(X3)) -> U101(X1,X2,X3)
      fst(mark(X)) -> fst(X)
      fst(active(X)) -> fst(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)
      U11(mark(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,mark(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,mark(X3)) -> U11(X1,X2,X3)
      U11(active(X1),X2,X3) -> U11(X1,X2,X3)
      U11(X1,active(X2),X3) -> U11(X1,X2,X3)
      U11(X1,X2,active(X3)) -> U11(X1,X2,X3)
      snd(mark(X)) -> snd(X)
      snd(active(X)) -> snd(X)
      U21(mark(X1),X2) -> U21(X1,X2)
      U21(X1,mark(X2)) -> U21(X1,X2)
      U21(active(X1),X2) -> U21(X1,X2)
      U21(X1,active(X2)) -> U21(X1,X2)
      U31(mark(X1),X2) -> U31(X1,X2)
      U31(X1,mark(X2)) -> U31(X1,X2)
      U31(active(X1),X2) -> U31(X1,X2)
      U31(X1,active(X2)) -> U31(X1,X2)
      U41(mark(X1),X2) -> U41(X1,X2)
      U41(X1,mark(X2)) -> U41(X1,X2)
      U41(active(X1),X2) -> U41(X1,X2)
      U41(X1,active(X2)) -> U41(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)
      U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
      U51(active(X1),X2,X3) -> U51(X1,X2,X3)
      U51(X1,active(X2),X3) -> U51(X1,X2,X3)
      U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
      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)
      U61(mark(X1),X2) -> U61(X1,X2)
      U61(X1,mark(X2)) -> U61(X1,X2)
      U61(active(X1),X2) -> U61(X1,X2)
      U61(X1,active(X2)) -> U61(X1,X2)
      U71(mark(X1),X2) -> U71(X1,X2)
      U71(X1,mark(X2)) -> U71(X1,X2)
      U71(active(X1),X2) -> U71(X1,X2)
      U71(X1,active(X2)) -> U71(X1,X2)
      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)
      U81(mark(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,mark(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,mark(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,mark(X4)) -> U81(X1,X2,X3,X4)
      U81(active(X1),X2,X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,active(X2),X3,X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,active(X3),X4) -> U81(X1,X2,X3,X4)
      U81(X1,X2,X3,active(X4)) -> U81(X1,X2,X3,X4)
      U82(mark(X1),X2) -> U82(X1,X2)
      U82(X1,mark(X2)) -> U82(X1,X2)
      U82(active(X1),X2) -> U82(X1,X2)
      U82(X1,active(X2)) -> U82(X1,X2)
      U91(mark(X1),X2) -> U91(X1,X2)
      U91(X1,mark(X2)) -> U91(X1,X2)
      U91(active(X1),X2) -> U91(X1,X2)
      U91(X1,active(X2)) -> U91(X1,X2)
      and(mark(X1),X2) -> and(X1,X2)
      and(X1,mark(X2)) -> and(X1,X2)
      and(active(X1),X2) -> and(X1,X2)
      and(X1,active(X2)) -> and(X1,X2)
      isNatural(mark(X)) -> isNatural(X)
      isNatural(active(X)) -> isNatural(X)
      isLNat(mark(X)) -> isLNat(X)
      isLNat(active(X)) -> isLNat(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