(VAR V1 V V2 L IL M N X X1 X2 X3 X4)
(RULES 
active(zeros) -> mark(cons(0,zeros))
active(U11(tt,V1)) -> mark(U12(isNatList(V1)))
active(U12(tt)) -> mark(tt)
active(U21(tt,V1)) -> mark(U22(isNat(V1)))
active(U22(tt)) -> mark(tt)
active(U31(tt,V)) -> mark(U32(isNatList(V)))
active(U32(tt)) -> mark(tt)
active(U41(tt,V1,V2)) -> mark(U42(isNat(V1),V2))
active(U42(tt,V2)) -> mark(U43(isNatIList(V2)))
active(U43(tt)) -> mark(tt)
active(U51(tt,V1,V2)) -> mark(U52(isNat(V1),V2))
active(U52(tt,V2)) -> mark(U53(isNatList(V2)))
active(U53(tt)) -> mark(tt)
active(U61(tt,V1,V2)) -> mark(U62(isNat(V1),V2))
active(U62(tt,V2)) -> mark(U63(isNatIList(V2)))
active(U63(tt)) -> mark(tt)
active(U71(tt,L)) -> mark(s(length(L)))
active(U81(tt)) -> mark(nil)
active(U91(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
active(and(tt,X)) -> mark(X)
active(isNat(0)) -> mark(tt)
active(isNat(length(V1))) -> mark(U11(isNatIListKind(V1),V1))
active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
active(isNatIList(V)) -> mark(U31(isNatIListKind(V),V))
active(isNatIList(zeros)) -> mark(tt)
active(isNatIList(cons(V1,V2))) -> mark(U41(and(isNatKind(V1),isNatIListKind(V2)),V1,V2))
active(isNatIListKind(nil)) -> mark(tt)
active(isNatIListKind(zeros)) -> mark(tt)
active(isNatIListKind(cons(V1,V2))) -> mark(and(isNatKind(V1),isNatIListKind(V2)))
active(isNatIListKind(take(V1,V2))) -> mark(and(isNatKind(V1),isNatIListKind(V2)))
active(isNatKind(0)) -> mark(tt)
active(isNatKind(length(V1))) -> mark(isNatIListKind(V1))
active(isNatKind(s(V1))) -> mark(isNatKind(V1))
active(isNatList(nil)) -> mark(tt)
active(isNatList(cons(V1,V2))) -> mark(U51(and(isNatKind(V1),isNatIListKind(V2)),V1,V2))
active(isNatList(take(V1,V2))) -> mark(U61(and(isNatKind(V1),isNatIListKind(V2)),V1,V2))
active(length(nil)) -> mark(0)
active(length(cons(N,L))) -> mark(U71(and(and(isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L))
active(take(0,IL)) -> mark(U81(and(isNatIList(IL),isNatIListKind(IL))))
active(take(s(M),cons(N,IL))) -> mark(U91(and(and(isNatIList(IL),isNatIListKind(IL)),and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N)))),IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X)) -> U12(active(X))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U22(X)) -> U22(active(X))
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U32(X)) -> U32(active(X))
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U42(X1,X2)) -> U42(active(X1),X2)
active(U43(X)) -> U43(active(X))
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U52(X1,X2)) -> U52(active(X1),X2)
active(U53(X)) -> U53(active(X))
active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
active(U62(X1,X2)) -> U62(active(X1),X2)
active(U63(X)) -> U63(active(X))
active(U71(X1,X2)) -> U71(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(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(and(X1,X2)) -> and(active(X1),X2)
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X)) -> mark(U12(X))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U22(mark(X)) -> mark(U22(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U32(mark(X)) -> mark(U32(X))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U42(mark(X1),X2) -> mark(U42(X1,X2))
U43(mark(X)) -> mark(U43(X))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U52(mark(X1),X2) -> mark(U52(X1,X2))
U53(mark(X)) -> mark(U53(X))
U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
U62(mark(X1),X2) -> mark(U62(X1,X2))
U63(mark(X)) -> mark(U63(X))
U71(mark(X1),X2) -> mark(U71(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))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
and(mark(X1),X2) -> mark(and(X1,X2))
proper(zeros) -> ok(zeros)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(tt) -> ok(tt)
proper(U12(X)) -> U12(proper(X))
proper(isNatList(X)) -> isNatList(proper(X))
proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
proper(U22(X)) -> U22(proper(X))
proper(isNat(X)) -> isNat(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X)) -> U32(proper(X))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2)) -> U42(proper(X1),proper(X2))
proper(U43(X)) -> U43(proper(X))
proper(isNatIList(X)) -> isNatIList(proper(X))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
proper(U53(X)) -> U53(proper(X))
proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
proper(U63(X)) -> U63(proper(X))
proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
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(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
proper(isNatKind(X)) -> isNatKind(proper(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X)) -> ok(U12(X))
isNatList(ok(X)) -> ok(isNatList(X))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(ok(X)) -> ok(U22(X))
isNat(ok(X)) -> ok(isNat(X))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(ok(X)) -> ok(U32(X))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(ok(X1),ok(X2)) -> ok(U42(X1,X2))
U43(ok(X)) -> ok(U43(X))
isNatIList(ok(X)) -> ok(isNatIList(X))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
U53(ok(X)) -> ok(U53(X))
U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
U63(ok(X)) -> ok(U63(X))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
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))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
isNatKind(ok(X)) -> ok(isNatKind(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)