org.jboss.cdi.tck.tests.implementation.enterprise.newBean.Wizard has a cycle which is very similar to the constellation of CDITCK-427.

@RequestScoped
public class Wizard {
    @Inject
    @Tame
    private Dragon dragon;

    @Produces
    @Tame
    public Dragon summon(@New Dragon dragon) {
        return dragon;
    }
}

For calling the producer method we would need to create the bean upfront, which we cannot as @Tame Dragon is not yet produced. This is essentially a dependency cycle which is illegal.