(VAR L N V V1 V2 X X1 X2 X3 )
(RULES 
        a__zeros -> cons(0, zeros)
        a__U11(tt, V1) -> a__U12(a__isNatIListKind(V1), V1)
        a__U12(tt, V1) -> a__U13(a__isNatList(V1))
        a__U13(tt) -> tt
        a__U21(tt, V1) -> a__U22(a__isNatKind(V1), V1)
        a__U22(tt, V1) -> a__U23(a__isNat(V1))
        a__U23(tt) -> tt
        a__U31(tt, V) -> a__U32(a__isNatIListKind(V), V)
        a__U32(tt, V) -> a__U33(a__isNatList(V))
        a__U33(tt) -> tt
        a__U41(tt, V1, V2) -> a__U42(a__isNatKind(V1), V1, V2)
        a__U42(tt, V1, V2) -> a__U43(a__isNatIListKind(V2), V1, V2)
        a__U43(tt, V1, V2) -> a__U44(a__isNatIListKind(V2), V1, V2)
        a__U44(tt, V1, V2) -> a__U45(a__isNat(V1), V2)
        a__U45(tt, V2) -> a__U46(a__isNatIList(V2))
        a__U46(tt) -> tt
        a__U51(tt, V2) -> a__U52(a__isNatIListKind(V2))
        a__U52(tt) -> tt
        a__U61(tt) -> tt
        a__U71(tt) -> tt
        a__U81(tt, V1, V2) -> a__U82(a__isNatKind(V1), V1, V2)
        a__U82(tt, V1, V2) -> a__U83(a__isNatIListKind(V2), V1, V2)
        a__U83(tt, V1, V2) -> a__U84(a__isNatIListKind(V2), V1, V2)
        a__U84(tt, V1, V2) -> a__U85(a__isNat(V1), V2)
        a__U85(tt, V2) -> a__U86(a__isNatList(V2))
        a__U86(tt) -> tt
        a__U91(tt, L, N) -> a__U92(a__isNatIListKind(L), L, N)
        a__U92(tt, L, N) -> a__U93(a__isNat(N), L, N)
        a__U93(tt, L, N) -> a__U94(a__isNatKind(N), L)
        a__U94(tt, L) -> s(a__length(mark(L)))
        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__isNatKind(V1), V1, V2)
        a__isNatIListKind(nil) -> tt
        a__isNatIListKind(zeros) -> tt
        a__isNatIListKind(cons(V1, V2)) -> a__U51(a__isNatKind(V1), V2)
        a__isNatKind(0) -> tt
        a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1))
        a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1))
        a__isNatList(nil) -> tt
        a__isNatList(cons(V1, V2)) -> a__U81(a__isNatKind(V1), V1, V2)
        a__length(nil) -> 0
        a__length(cons(N, L)) -> a__U91(a__isNatList(L), L, N)
        mark(zeros) -> a__zeros
        mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
        mark(U12(X1, X2)) -> a__U12(mark(X1), X2)
        mark(isNatIListKind(X)) -> a__isNatIListKind(X)
        mark(U13(X)) -> a__U13(mark(X))
        mark(isNatList(X)) -> a__isNatList(X)
        mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
        mark(U22(X1, X2)) -> a__U22(mark(X1), X2)
        mark(isNatKind(X)) -> a__isNatKind(X)
        mark(U23(X)) -> a__U23(mark(X))
        mark(isNat(X)) -> a__isNat(X)
        mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
        mark(U32(X1, X2)) -> a__U32(mark(X1), X2)
        mark(U33(X)) -> a__U33(mark(X))
        mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
        mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
        mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
        mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
        mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
        mark(U46(X)) -> a__U46(mark(X))
        mark(isNatIList(X)) -> a__isNatIList(X)
        mark(U51(X1, X2)) -> a__U51(mark(X1), X2)
        mark(U52(X)) -> a__U52(mark(X))
        mark(U61(X)) -> a__U61(mark(X))
        mark(U71(X)) -> a__U71(mark(X))
        mark(U81(X1, X2, X3)) -> a__U81(mark(X1), X2, X3)
        mark(U82(X1, X2, X3)) -> a__U82(mark(X1), X2, X3)
        mark(U83(X1, X2, X3)) -> a__U83(mark(X1), X2, X3)
        mark(U84(X1, X2, X3)) -> a__U84(mark(X1), X2, X3)
        mark(U85(X1, X2)) -> a__U85(mark(X1), X2)
        mark(U86(X)) -> a__U86(mark(X))
        mark(U91(X1, X2, X3)) -> a__U91(mark(X1), X2, X3)
        mark(U92(X1, X2, X3)) -> a__U92(mark(X1), X2, X3)
        mark(U93(X1, X2, X3)) -> a__U93(mark(X1), X2, X3)
        mark(U94(X1, X2)) -> a__U94(mark(X1), X2)
        mark(length(X)) -> a__length(mark(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(X1, X2) -> U12(X1, X2)
        a__isNatIListKind(X) -> isNatIListKind(X)
        a__U13(X) -> U13(X)
        a__isNatList(X) -> isNatList(X)
        a__U21(X1, X2) -> U21(X1, X2)
        a__U22(X1, X2) -> U22(X1, X2)
        a__isNatKind(X) -> isNatKind(X)
        a__U23(X) -> U23(X)
        a__isNat(X) -> isNat(X)
        a__U31(X1, X2) -> U31(X1, X2)
        a__U32(X1, X2) -> U32(X1, X2)
        a__U33(X) -> U33(X)
        a__U41(X1, X2, X3) -> U41(X1, X2, X3)
        a__U42(X1, X2, X3) -> U42(X1, X2, X3)
        a__U43(X1, X2, X3) -> U43(X1, X2, X3)
        a__U44(X1, X2, X3) -> U44(X1, X2, X3)
        a__U45(X1, X2) -> U45(X1, X2)
        a__U46(X) -> U46(X)
        a__isNatIList(X) -> isNatIList(X)
        a__U51(X1, X2) -> U51(X1, X2)
        a__U52(X) -> U52(X)
        a__U61(X) -> U61(X)
        a__U71(X) -> U71(X)
        a__U81(X1, X2, X3) -> U81(X1, X2, X3)
        a__U82(X1, X2, X3) -> U82(X1, X2, X3)
        a__U83(X1, X2, X3) -> U83(X1, X2, X3)
        a__U84(X1, X2, X3) -> U84(X1, X2, X3)
        a__U85(X1, X2) -> U85(X1, X2)
        a__U86(X) -> U86(X)
        a__U91(X1, X2, X3) -> U91(X1, X2, X3)
        a__U92(X1, X2, X3) -> U92(X1, X2, X3)
        a__U93(X1, X2, X3) -> U93(X1, X2, X3)
        a__U94(X1, X2) -> U94(X1, X2)
        a__length(X) -> length(X)
        
)