(VAR V1 V2 L N IL M V X1 X2 X3 X4 X)
(RULES 
active(zeros) -> mark(cons(0,zeros))
active(U101(tt,V1,V2)) -> mark(U102(isNatKind(V1),V1,V2))
active(U102(tt,V1,V2)) -> mark(U103(isNatIListKind(V2),V1,V2))
active(U103(tt,V1,V2)) -> mark(U104(isNatIListKind(V2),V1,V2))
active(U104(tt,V1,V2)) -> mark(U105(isNat(V1),V2))
active(U105(tt,V2)) -> mark(U106(isNatIList(V2)))
active(U106(tt)) -> mark(tt)
active(U11(tt,V1)) -> mark(U12(isNatIListKind(V1),V1))
active(U111(tt,L,N)) -> mark(U112(isNatIListKind(L),L,N))
active(U112(tt,L,N)) -> mark(U113(isNat(N),L,N))
active(U113(tt,L,N)) -> mark(U114(isNatKind(N),L))
active(U114(tt,L)) -> mark(s(length(L)))
active(U12(tt,V1)) -> mark(U13(isNatList(V1)))
active(U121(tt,IL)) -> mark(U122(isNatIListKind(IL)))
active(U122(tt)) -> mark(nil)
active(U13(tt)) -> mark(tt)
active(U131(tt,IL,M,N)) -> mark(U132(isNatIListKind(IL),IL,M,N))
active(U132(tt,IL,M,N)) -> mark(U133(isNat(M),IL,M,N))
active(U133(tt,IL,M,N)) -> mark(U134(isNatKind(M),IL,M,N))
active(U134(tt,IL,M,N)) -> mark(U135(isNat(N),IL,M,N))
active(U135(tt,IL,M,N)) -> mark(U136(isNatKind(N),IL,M,N))
active(U136(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
active(U21(tt,V1)) -> mark(U22(isNatKind(V1),V1))
active(U22(tt,V1)) -> mark(U23(isNat(V1)))
active(U23(tt)) -> mark(tt)
active(U31(tt,V)) -> mark(U32(isNatIListKind(V),V))
active(U32(tt,V)) -> mark(U33(isNatList(V)))
active(U33(tt)) -> mark(tt)
active(U41(tt,V1,V2)) -> mark(U42(isNatKind(V1),V1,V2))
active(U42(tt,V1,V2)) -> mark(U43(isNatIListKind(V2),V1,V2))
active(U43(tt,V1,V2)) -> mark(U44(isNatIListKind(V2),V1,V2))
active(U44(tt,V1,V2)) -> mark(U45(isNat(V1),V2))
active(U45(tt,V2)) -> mark(U46(isNatIList(V2)))
active(U46(tt)) -> mark(tt)
active(U51(tt,V2)) -> mark(U52(isNatIListKind(V2)))
active(U52(tt)) -> mark(tt)
active(U61(tt,V2)) -> mark(U62(isNatIListKind(V2)))
active(U62(tt)) -> mark(tt)
active(U71(tt)) -> mark(tt)
active(U81(tt)) -> mark(tt)
active(U91(tt,V1,V2)) -> mark(U92(isNatKind(V1),V1,V2))
active(U92(tt,V1,V2)) -> mark(U93(isNatIListKind(V2),V1,V2))
active(U93(tt,V1,V2)) -> mark(U94(isNatIListKind(V2),V1,V2))
active(U94(tt,V1,V2)) -> mark(U95(isNat(V1),V2))
active(U95(tt,V2)) -> mark(U96(isNatList(V2)))
active(U96(tt)) -> mark(tt)
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(isNatKind(V1),V1,V2))
active(isNatIListKind(nil)) -> mark(tt)
active(isNatIListKind(zeros)) -> mark(tt)
active(isNatIListKind(cons(V1,V2))) -> mark(U51(isNatKind(V1),V2))
active(isNatIListKind(take(V1,V2))) -> mark(U61(isNatKind(V1),V2))
active(isNatKind(0)) -> mark(tt)
active(isNatKind(length(V1))) -> mark(U71(isNatIListKind(V1)))
active(isNatKind(s(V1))) -> mark(U81(isNatKind(V1)))
active(isNatList(nil)) -> mark(tt)
active(isNatList(cons(V1,V2))) -> mark(U91(isNatKind(V1),V1,V2))
active(isNatList(take(V1,V2))) -> mark(U101(isNatKind(V1),V1,V2))
active(length(nil)) -> mark(0)
active(length(cons(N,L))) -> mark(U111(isNatList(L),L,N))
active(take(0,IL)) -> mark(U121(isNatIList(IL),IL))
active(take(s(M),cons(N,IL))) -> mark(U131(isNatIList(IL),IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
active(U105(X1,X2)) -> U105(active(X1),X2)
active(U106(X)) -> U106(active(X))
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(U111(X1,X2,X3)) -> U111(active(X1),X2,X3)
active(U112(X1,X2,X3)) -> U112(active(X1),X2,X3)
active(U113(X1,X2,X3)) -> U113(active(X1),X2,X3)
active(U114(X1,X2)) -> U114(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
active(U13(X)) -> U13(active(X))
active(U121(X1,X2)) -> U121(active(X1),X2)
active(U122(X)) -> U122(active(X))
active(U131(X1,X2,X3,X4)) -> U131(active(X1),X2,X3,X4)
active(U132(X1,X2,X3,X4)) -> U132(active(X1),X2,X3,X4)
active(U133(X1,X2,X3,X4)) -> U133(active(X1),X2,X3,X4)
active(U134(X1,X2,X3,X4)) -> U134(active(X1),X2,X3,X4)
active(U135(X1,X2,X3,X4)) -> U135(active(X1),X2,X3,X4)
active(U136(X1,X2,X3,X4)) -> U136(active(X1),X2,X3,X4)
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
active(U21(X1,X2)) -> U21(active(X1),X2)
active(U22(X1,X2)) -> U22(active(X1),X2)
active(U23(X)) -> U23(active(X))
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U32(X1,X2)) -> U32(active(X1),X2)
active(U33(X)) -> U33(active(X))
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
active(U45(X1,X2)) -> U45(active(X1),X2)
active(U46(X)) -> U46(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(X)) -> U71(active(X))
active(U81(X)) -> U81(active(X))
active(U91(X1,X2,X3)) -> U91(active(X1),X2,X3)
active(U92(X1,X2,X3)) -> U92(active(X1),X2,X3)
active(U93(X1,X2,X3)) -> U93(active(X1),X2,X3)
active(U94(X1,X2,X3)) -> U94(active(X1),X2,X3)
active(U95(X1,X2)) -> U95(active(X1),X2)
active(U96(X)) -> U96(active(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
U105(mark(X1),X2) -> mark(U105(X1,X2))
U106(mark(X)) -> mark(U106(X))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
U111(mark(X1),X2,X3) -> mark(U111(X1,X2,X3))
U112(mark(X1),X2,X3) -> mark(U112(X1,X2,X3))
U113(mark(X1),X2,X3) -> mark(U113(X1,X2,X3))
U114(mark(X1),X2) -> mark(U114(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
U13(mark(X)) -> mark(U13(X))
U121(mark(X1),X2) -> mark(U121(X1,X2))
U122(mark(X)) -> mark(U122(X))
U131(mark(X1),X2,X3,X4) -> mark(U131(X1,X2,X3,X4))
U132(mark(X1),X2,X3,X4) -> mark(U132(X1,X2,X3,X4))
U133(mark(X1),X2,X3,X4) -> mark(U133(X1,X2,X3,X4))
U134(mark(X1),X2,X3,X4) -> mark(U134(X1,X2,X3,X4))
U135(mark(X1),X2,X3,X4) -> mark(U135(X1,X2,X3,X4))
U136(mark(X1),X2,X3,X4) -> mark(U136(X1,X2,X3,X4))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
U21(mark(X1),X2) -> mark(U21(X1,X2))
U22(mark(X1),X2) -> mark(U22(X1,X2))
U23(mark(X)) -> mark(U23(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U32(mark(X1),X2) -> mark(U32(X1,X2))
U33(mark(X)) -> mark(U33(X))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
U45(mark(X1),X2) -> mark(U45(X1,X2))
U46(mark(X)) -> mark(U46(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(X)) -> mark(U71(X))
U81(mark(X)) -> mark(U81(X))
U91(mark(X1),X2,X3) -> mark(U91(X1,X2,X3))
U92(mark(X1),X2,X3) -> mark(U92(X1,X2,X3))
U93(mark(X1),X2,X3) -> mark(U93(X1,X2,X3))
U94(mark(X1),X2,X3) -> mark(U94(X1,X2,X3))
U95(mark(X1),X2) -> mark(U95(X1,X2))
U96(mark(X)) -> mark(U96(X))
proper(zeros) -> ok(zeros)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
proper(tt) -> ok(tt)
proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
proper(isNatKind(X)) -> isNatKind(proper(X))
proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
proper(isNat(X)) -> isNat(proper(X))
proper(U106(X)) -> U106(proper(X))
proper(isNatIList(X)) -> isNatIList(proper(X))
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(U111(X1,X2,X3)) -> U111(proper(X1),proper(X2),proper(X3))
proper(U112(X1,X2,X3)) -> U112(proper(X1),proper(X2),proper(X3))
proper(U113(X1,X2,X3)) -> U113(proper(X1),proper(X2),proper(X3))
proper(U114(X1,X2)) -> U114(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(U13(X)) -> U13(proper(X))
proper(isNatList(X)) -> isNatList(proper(X))
proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
proper(U122(X)) -> U122(proper(X))
proper(nil) -> ok(nil)
proper(U131(X1,X2,X3,X4)) -> U131(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U132(X1,X2,X3,X4)) -> U132(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U133(X1,X2,X3,X4)) -> U133(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U134(X1,X2,X3,X4)) -> U134(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U135(X1,X2,X3,X4)) -> U135(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U136(X1,X2,X3,X4)) -> U136(proper(X1),proper(X2),proper(X3),proper(X4))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
proper(U23(X)) -> U23(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
proper(U33(X)) -> U33(proper(X))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
proper(U46(X)) -> U46(proper(X))
proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
proper(U52(X)) -> U52(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X)) -> U62(proper(X))
proper(U71(X)) -> U71(proper(X))
proper(U81(X)) -> U81(proper(X))
proper(U91(X1,X2,X3)) -> U91(proper(X1),proper(X2),proper(X3))
proper(U92(X1,X2,X3)) -> U92(proper(X1),proper(X2),proper(X3))
proper(U93(X1,X2,X3)) -> U93(proper(X1),proper(X2),proper(X3))
proper(U94(X1,X2,X3)) -> U94(proper(X1),proper(X2),proper(X3))
proper(U95(X1,X2)) -> U95(proper(X1),proper(X2))
proper(U96(X)) -> U96(proper(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
isNatKind(ok(X)) -> ok(isNatKind(X))
U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
U106(ok(X)) -> ok(U106(X))
isNatIList(ok(X)) -> ok(isNatIList(X))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
U111(ok(X1),ok(X2),ok(X3)) -> ok(U111(X1,X2,X3))
U112(ok(X1),ok(X2),ok(X3)) -> ok(U112(X1,X2,X3))
U113(ok(X1),ok(X2),ok(X3)) -> ok(U113(X1,X2,X3))
U114(ok(X1),ok(X2)) -> ok(U114(X1,X2))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
U13(ok(X)) -> ok(U13(X))
isNatList(ok(X)) -> ok(isNatList(X))
U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
U122(ok(X)) -> ok(U122(X))
U131(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U131(X1,X2,X3,X4))
U132(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U132(X1,X2,X3,X4))
U133(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U133(X1,X2,X3,X4))
U134(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U134(X1,X2,X3,X4))
U135(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U135(X1,X2,X3,X4))
U136(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U136(X1,X2,X3,X4))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
U23(ok(X)) -> ok(U23(X))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
U33(ok(X)) -> ok(U33(X))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
U46(ok(X)) -> ok(U46(X))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(ok(X)) -> ok(U52(X))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(ok(X)) -> ok(U62(X))
U71(ok(X)) -> ok(U71(X))
U81(ok(X)) -> ok(U81(X))
U91(ok(X1),ok(X2),ok(X3)) -> ok(U91(X1,X2,X3))
U92(ok(X1),ok(X2),ok(X3)) -> ok(U92(X1,X2,X3))
U93(ok(X1),ok(X2),ok(X3)) -> ok(U93(X1,X2,X3))
U94(ok(X1),ok(X2),ok(X3)) -> ok(U94(X1,X2,X3))
U95(ok(X1),ok(X2)) -> ok(U95(X1,X2))
U96(ok(X)) -> ok(U96(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)