(VAR V1 V V2 L N X1 X2 X3 X)
(RULES 
active(zeros) -> mark(cons(0,zeros))
active(U11(tt,V1)) -> mark(U12(isNatIListKind(V1),V1))
active(U12(tt,V1)) -> mark(U13(isNatList(V1)))
active(U13(tt)) -> mark(tt)
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)) -> mark(tt)
active(U71(tt)) -> mark(tt)
active(U81(tt,V1,V2)) -> mark(U82(isNatKind(V1),V1,V2))
active(U82(tt,V1,V2)) -> mark(U83(isNatIListKind(V2),V1,V2))
active(U83(tt,V1,V2)) -> mark(U84(isNatIListKind(V2),V1,V2))
active(U84(tt,V1,V2)) -> mark(U85(isNat(V1),V2))
active(U85(tt,V2)) -> mark(U86(isNatList(V2)))
active(U86(tt)) -> mark(tt)
active(U91(tt,L,N)) -> mark(U92(isNatIListKind(L),L,N))
active(U92(tt,L,N)) -> mark(U93(isNat(N),L,N))
active(U93(tt,L,N)) -> mark(U94(isNatKind(N),L))
active(U94(tt,L)) -> mark(s(length(L)))
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(isNatKind(0)) -> mark(tt)
active(isNatKind(length(V1))) -> mark(U61(isNatIListKind(V1)))
active(isNatKind(s(V1))) -> mark(U71(isNatKind(V1)))
active(isNatList(nil)) -> mark(tt)
active(isNatList(cons(V1,V2))) -> mark(U81(isNatKind(V1),V1,V2))
active(length(nil)) -> mark(0)
active(length(cons(N,L))) -> mark(U91(isNatList(L),L,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(U13(X)) -> U13(active(X))
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(X)) -> U61(active(X))
active(U71(X)) -> U71(active(X))
active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
active(U85(X1,X2)) -> U85(active(X1),X2)
active(U86(X)) -> U86(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)) -> U94(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
U13(mark(X)) -> mark(U13(X))
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(X)) -> mark(U61(X))
U71(mark(X)) -> mark(U71(X))
U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
U85(mark(X1),X2) -> mark(U85(X1,X2))
U86(mark(X)) -> mark(U86(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) -> mark(U94(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
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(X1,X2)) -> U12(proper(X1),proper(X2))
proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
proper(U13(X)) -> U13(proper(X))
proper(isNatList(X)) -> isNatList(proper(X))
proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
proper(isNatKind(X)) -> isNatKind(proper(X))
proper(U23(X)) -> U23(proper(X))
proper(isNat(X)) -> isNat(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(isNatIList(X)) -> isNatIList(proper(X))
proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
proper(U52(X)) -> U52(proper(X))
proper(U61(X)) -> U61(proper(X))
proper(U71(X)) -> U71(proper(X))
proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
proper(U85(X1,X2)) -> U85(proper(X1),proper(X2))
proper(U86(X)) -> U86(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)) -> U94(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(nil) -> ok(nil)
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
isNatIListKind(ok(X)) -> ok(isNatIListKind(X))
U13(ok(X)) -> ok(U13(X))
isNatList(ok(X)) -> ok(isNatList(X))
U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
isNatKind(ok(X)) -> ok(isNatKind(X))
U23(ok(X)) -> ok(U23(X))
isNat(ok(X)) -> ok(isNat(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))
isNatIList(ok(X)) -> ok(isNatIList(X))
U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
U52(ok(X)) -> ok(U52(X))
U61(ok(X)) -> ok(U61(X))
U71(ok(X)) -> ok(U71(X))
U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
U85(ok(X1),ok(X2)) -> ok(U85(X1,X2))
U86(ok(X)) -> ok(U86(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(U94(X1,X2))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)