(VAR IL L M N V V1 V2 X X1 X2 X3 X4 )
(RULES 
        active(zeros) -> mark(cons(0, zeros))
        active(U11(tt, L)) -> mark(s(length(L)))
        active(U21(tt)) -> mark(nil)
        active(U31(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
        active(and(tt, X)) -> mark(X)
        active(isNat(0)) -> mark(tt)
        active(isNat(length(V1))) -> mark(isNatList(V1))
        active(isNat(s(V1))) -> mark(isNat(V1))
        active(isNatIList(V)) -> mark(isNatList(V))
        active(isNatIList(zeros)) -> mark(tt)
        active(isNatIList(cons(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2)))
        active(isNatList(nil)) -> mark(tt)
        active(isNatList(cons(V1, V2))) -> mark(and(isNat(V1), isNatList(V2)))
        active(isNatList(take(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2)))
        active(length(nil)) -> mark(0)
        active(length(cons(N, L))) -> mark(U11(and(isNatList(L), isNat(N)), L))
        active(take(0, IL)) -> mark(U21(isNatIList(IL)))
        active(take(s(M), cons(N, IL))) -> mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N))
        mark(zeros) -> active(zeros)
        mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
        mark(0) -> active(0)
        mark(U11(X1, X2)) -> active(U11(mark(X1), X2))
        mark(tt) -> active(tt)
        mark(s(X)) -> active(s(mark(X)))
        mark(length(X)) -> active(length(mark(X)))
        mark(U21(X)) -> active(U21(mark(X)))
        mark(nil) -> active(nil)
        mark(U31(X1, X2, X3, X4)) -> active(U31(mark(X1), X2, X3, X4))
        mark(take(X1, X2)) -> active(take(mark(X1), mark(X2)))
        mark(and(X1, X2)) -> active(and(mark(X1), X2))
        mark(isNat(X)) -> active(isNat(X))
        mark(isNatList(X)) -> active(isNatList(X))
        mark(isNatIList(X)) -> active(isNatIList(X))
        cons(mark(X1), X2) -> cons(X1, X2)
        cons(X1, mark(X2)) -> cons(X1, X2)
        cons(active(X1), X2) -> cons(X1, X2)
        cons(X1, active(X2)) -> cons(X1, X2)
        U11(mark(X1), X2) -> U11(X1, X2)
        U11(X1, mark(X2)) -> U11(X1, X2)
        U11(active(X1), X2) -> U11(X1, X2)
        U11(X1, active(X2)) -> U11(X1, X2)
        s(mark(X)) -> s(X)
        s(active(X)) -> s(X)
        length(mark(X)) -> length(X)
        length(active(X)) -> length(X)
        U21(mark(X)) -> U21(X)
        U21(active(X)) -> U21(X)
        U31(mark(X1), X2, X3, X4) -> U31(X1, X2, X3, X4)
        U31(X1, mark(X2), X3, X4) -> U31(X1, X2, X3, X4)
        U31(X1, X2, mark(X3), X4) -> U31(X1, X2, X3, X4)
        U31(X1, X2, X3, mark(X4)) -> U31(X1, X2, X3, X4)
        U31(active(X1), X2, X3, X4) -> U31(X1, X2, X3, X4)
        U31(X1, active(X2), X3, X4) -> U31(X1, X2, X3, X4)
        U31(X1, X2, active(X3), X4) -> U31(X1, X2, X3, X4)
        U31(X1, X2, X3, active(X4)) -> U31(X1, X2, X3, X4)
        take(mark(X1), X2) -> take(X1, X2)
        take(X1, mark(X2)) -> take(X1, X2)
        take(active(X1), X2) -> take(X1, X2)
        take(X1, active(X2)) -> take(X1, X2)
        and(mark(X1), X2) -> and(X1, X2)
        and(X1, mark(X2)) -> and(X1, X2)
        and(active(X1), X2) -> and(X1, X2)
        and(X1, active(X2)) -> and(X1, X2)
        isNat(mark(X)) -> isNat(X)
        isNat(active(X)) -> isNat(X)
        isNatList(mark(X)) -> isNatList(X)
        isNatList(active(X)) -> isNatList(X)
        isNatIList(mark(X)) -> isNatIList(X)
        isNatIList(active(X)) -> isNatIList(X)
        
)