(VAR IL L M N X X1 X2 X3 X4 )
(RULES 
        active(zeros) -> mark(cons(0, zeros))
        active(U11(tt, L)) -> mark(U12(tt, L))
        active(U12(tt, L)) -> mark(s(length(L)))
        active(U21(tt, IL, M, N)) -> mark(U22(tt, IL, M, N))
        active(U22(tt, IL, M, N)) -> mark(U23(tt, IL, M, N))
        active(U23(tt, IL, M, N)) -> mark(cons(N, take(M, IL)))
        active(length(nil)) -> mark(0)
        active(length(cons(N, L))) -> mark(U11(tt, L))
        active(take(0, IL)) -> mark(nil)
        active(take(s(M), cons(N, IL))) -> mark(U21(tt, IL, M, 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(s(X)) -> s(active(X))
        active(length(X)) -> length(active(X))
        active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4)
        active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4)
        active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4)
        active(take(X1, X2)) -> take(active(X1), X2)
        active(take(X1, X2)) -> take(X1, active(X2))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        U11(mark(X1), X2) -> mark(U11(X1, X2))
        U12(mark(X1), X2) -> mark(U12(X1, X2))
        s(mark(X)) -> mark(s(X))
        length(mark(X)) -> mark(length(X))
        U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4))
        U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4))
        U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4))
        take(mark(X1), X2) -> mark(take(X1, X2))
        take(X1, mark(X2)) -> mark(take(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(X1, X2)) -> U12(proper(X1), proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(length(X)) -> length(proper(X))
        proper(U21(X1, X2, X3, X4)) -> U21(proper(X1), proper(X2), proper(X3), proper(X4))
        proper(U22(X1, X2, X3, X4)) -> U22(proper(X1), proper(X2), proper(X3), proper(X4))
        proper(U23(X1, X2, X3, X4)) -> U23(proper(X1), proper(X2), proper(X3), proper(X4))
        proper(take(X1, X2)) -> take(proper(X1), proper(X2))
        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))
        s(ok(X)) -> ok(s(X))
        length(ok(X)) -> ok(length(X))
        U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4))
        U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4))
        U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4))
        take(ok(X1), ok(X2)) -> ok(take(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)