(VAR V2 L N IL M V1 V X1 X2 X3 X4 X)
(RULES 
active(zeros) -> mark(cons(0,zeros))
active(U11(tt)) -> mark(tt)
active(U21(tt)) -> mark(tt)
active(U31(tt)) -> mark(tt)
active(U41(tt,V2)) -> mark(U42(isNatIList(V2)))
active(U42(tt)) -> mark(tt)
active(U51(tt,V2)) -> mark(U52(isNatList(V2)))
active(U52(tt)) -> mark(tt)
active(U61(tt,V2)) -> mark(U62(isNatIList(V2)))
active(U62(tt)) -> mark(tt)
active(U71(tt,L,N)) -> mark(U72(isNat(N),L))
active(U72(tt,L)) -> mark(s(length(L)))
active(U81(tt)) -> mark(nil)
active(U91(tt,IL,M,N)) -> mark(U92(isNat(M),IL,M,N))
active(U92(tt,IL,M,N)) -> mark(U93(isNat(N),IL,M,N))
active(U93(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
active(isNat(0)) -> mark(tt)
active(isNat(length(V1))) -> mark(U11(isNatList(V1)))
active(isNat(s(V1))) -> mark(U21(isNat(V1)))
active(isNatIList(V)) -> mark(U31(isNatList(V)))
active(isNatIList(zeros)) -> mark(tt)
active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2))
active(isNatList(nil)) -> mark(tt)
active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2))
active(isNatList(take(V1,V2))) -> mark(U61(isNat(V1),V2))
active(length(nil)) -> mark(0)
active(length(cons(N,L))) -> mark(U71(isNatList(L),L,N))
active(take(0,IL)) -> mark(U81(isNatIList(IL)))
active(take(s(M),cons(N,IL))) -> mark(U91(isNatIList(IL),IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X)) -> U11(active(X))
active(U21(X)) -> U21(active(X))
active(U31(X)) -> U31(active(X))
active(U41(X1,X2)) -> U41(active(X1),X2)
active(U42(X)) -> U42(active(X))
active(U51(X1,X2)) -> U51(active(X1),X2)
active(U52(X)) -> U52(active(X))
active(U61(X1,X2)) -> U61(active(X1),X2)
active(U62(X)) -> U62(active(X))
active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
active(U72(X1,X2)) -> U72(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
active(U81(X)) -> U81(active(X))
active(U91(X1,X2,X3,X4)) -> U91(active(X1),X2,X3,X4)
active(U92(X1,X2,X3,X4)) -> U92(active(X1),X2,X3,X4)
active(U93(X1,X2,X3,X4)) -> U93(active(X1),X2,X3,X4)
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X)) -> mark(U11(X))
U21(mark(X)) -> mark(U21(X))
U31(mark(X)) -> mark(U31(X))
U41(mark(X1),X2) -> mark(U41(X1,X2))
U42(mark(X)) -> mark(U42(X))
U51(mark(X1),X2) -> mark(U51(X1,X2))
U52(mark(X)) -> mark(U52(X))
U61(mark(X1),X2) -> mark(U61(X1,X2))
U62(mark(X)) -> mark(U62(X))
U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
U72(mark(X1),X2) -> mark(U72(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
U81(mark(X)) -> mark(U81(X))
U91(mark(X1),X2,X3,X4) -> mark(U91(X1,X2,X3,X4))
U92(mark(X1),X2,X3,X4) -> mark(U92(X1,X2,X3,X4))
U93(mark(X1),X2,X3,X4) -> mark(U93(X1,X2,X3,X4))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
proper(zeros) -> ok(zeros)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(U11(X)) -> U11(proper(X))
proper(tt) -> ok(tt)
proper(U21(X)) -> U21(proper(X))
proper(U31(X)) -> U31(proper(X))
proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
proper(U42(X)) -> U42(proper(X))
proper(isNatIList(X)) -> isNatIList(proper(X))
proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
proper(U52(X)) -> U52(proper(X))
proper(isNatList(X)) -> isNatList(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X)) -> U62(proper(X))
proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(isNat(X)) -> isNat(proper(X))
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(U81(X)) -> U81(proper(X))
proper(nil) -> ok(nil)
proper(U91(X1,X2,X3,X4)) -> U91(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U92(X1,X2,X3,X4)) -> U92(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U93(X1,X2,X3,X4)) -> U93(proper(X1),proper(X2),proper(X3),proper(X4))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X)) -> ok(U11(X))
U21(ok(X)) -> ok(U21(X))
U31(ok(X)) -> ok(U31(X))
U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
U42(ok(X)) -> ok(U42(X))
isNatIList(ok(X)) -> ok(isNatIList(X))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(ok(X)) -> ok(U52(X))
isNatList(ok(X)) -> ok(isNatList(X))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(ok(X)) -> ok(U62(X))
U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
U81(ok(X)) -> ok(U81(X))
U91(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U91(X1,X2,X3,X4))
U92(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U92(X1,X2,X3,X4))
U93(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U93(X1,X2,X3,X4))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)