(VAR N XS X Y YS ZS V1 V2 X1 X2 X3 X4)
(RULES 
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)
)