(VAR IL L M N V V1 V2 X X1 X2 X3 X4 )
(RULES 
        a__zeros -> cons(0, zeros)
        a__U11(tt, V1) -> a__U12(a__isNatList(V1))
        a__U12(tt) -> tt
        a__U21(tt, V1) -> a__U22(a__isNat(V1))
        a__U22(tt) -> tt
        a__U31(tt, V) -> a__U32(a__isNatList(V))
        a__U32(tt) -> tt
        a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2)
        a__U42(tt, V2) -> a__U43(a__isNatIList(V2))
        a__U43(tt) -> tt
        a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2)
        a__U52(tt, V2) -> a__U53(a__isNatList(V2))
        a__U53(tt) -> tt
        a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2)
        a__U62(tt, V2) -> a__U63(a__isNatIList(V2))
        a__U63(tt) -> tt
        a__U71(tt, L) -> s(a__length(mark(L)))
        a__U81(tt) -> nil
        a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL))
        a__and(tt, X) -> mark(X)
        a__isNat(0) -> tt
        a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
        a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
        a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
        a__isNatIList(zeros) -> tt
        a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
        a__isNatIListKind(nil) -> tt
        a__isNatIListKind(zeros) -> tt
        a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
        a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
        a__isNatKind(0) -> tt
        a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
        a__isNatKind(s(V1)) -> a__isNatKind(V1)
        a__isNatList(nil) -> tt
        a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
        a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
        a__length(nil) -> 0
        a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)
        a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
        a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N)
        mark(zeros) -> a__zeros
        mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
        mark(U12(X)) -> a__U12(mark(X))
        mark(isNatList(X)) -> a__isNatList(X)
        mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
        mark(U22(X)) -> a__U22(mark(X))
        mark(isNat(X)) -> a__isNat(X)
        mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
        mark(U32(X)) -> a__U32(mark(X))
        mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
        mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
        mark(U43(X)) -> a__U43(mark(X))
        mark(isNatIList(X)) -> a__isNatIList(X)
        mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
        mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
        mark(U53(X)) -> a__U53(mark(X))
        mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
        mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
        mark(U63(X)) -> a__U63(mark(X))
        mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
        mark(length(X)) -> a__length(mark(X))
        mark(U81(X)) -> a__U81(mark(X))
        mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
        mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
        mark(and(X1, X2)) -> a__and(mark(X1), X2)
        mark(isNatIListKind(X)) -> a__isNatIListKind(X)
        mark(isNatKind(X)) -> a__isNatKind(X)
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(0) -> 0
        mark(tt) -> tt
        mark(s(X)) -> s(mark(X))
        mark(nil) -> nil
        a__zeros -> zeros
        a__U11(X1, X2) -> U11(X1, X2)
        a__U12(X) -> U12(X)
        a__isNatList(X) -> isNatList(X)
        a__U21(X1, X2) -> U21(X1, X2)
        a__U22(X) -> U22(X)
        a__isNat(X) -> isNat(X)
        a__U31(X1, X2) -> U31(X1, X2)
        a__U32(X) -> U32(X)
        a__U41(X1, X2, X3) -> U41(X1, X2, X3)
        a__U42(X1, X2) -> U42(X1, X2)
        a__U43(X) -> U43(X)
        a__isNatIList(X) -> isNatIList(X)
        a__U51(X1, X2, X3) -> U51(X1, X2, X3)
        a__U52(X1, X2) -> U52(X1, X2)
        a__U53(X) -> U53(X)
        a__U61(X1, X2, X3) -> U61(X1, X2, X3)
        a__U62(X1, X2) -> U62(X1, X2)
        a__U63(X) -> U63(X)
        a__U71(X1, X2) -> U71(X1, X2)
        a__length(X) -> length(X)
        a__U81(X) -> U81(X)
        a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
        a__take(X1, X2) -> take(X1, X2)
        a__and(X1, X2) -> and(X1, X2)
        a__isNatIListKind(X) -> isNatIListKind(X)
        a__isNatKind(X) -> isNatKind(X)
        
)