(VAR L N V V1 V2 X X1 X2 X3 )
(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, L)) -> mark(s(length(L)))
        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(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(length(nil)) -> mark(0)
        active(length(cons(N, L))) -> mark(U61(and(and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L))
        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)) -> U61(active(X1), X2)
        active(s(X)) -> s(active(X))
        active(length(X)) -> length(active(X))
        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) -> mark(U61(X1, X2))
        s(mark(X)) -> mark(s(X))
        length(mark(X)) -> mark(length(X))
        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)) -> U61(proper(X1), proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(and(X1, X2)) -> and(proper(X1), proper(X2))
        proper(isNatIListKind(X)) -> isNatIListKind(proper(X))
        proper(isNatKind(X)) -> isNatKind(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(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(U61(X1, X2))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        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))
        
)