Classical likelihood based asymptotically optimal sequential discrimination between two composite classes of distributions with indifference zone (Wald, Chernoff, Kiefer-Sacks, Novikov-Dragalin, Malyutov-Tsitovich et al) is multi-staged. First, a consistent estimate of the distribution is obtained which is tested against the closest alternative(s) in consequent stages. In sixties this natural methodology demonstrated its practical inferiority to asymptotically suboptimal algorithms of Box and Hill. We model the sequential discrimination between Markov Chains with two states and show that for practically meaningful error probabilities the second order optimal Malyutov-Tsitovich's strategies do not attain even the principal term of its asymptotics thus discouraging this classical Wald-Chernoff-et al's approach. Thus the problem of Wald-type asymptotic lower bounds appropriateness for reasonable error probabilities remains open which makes the possibility of replacing the likelihood-based approach interesting. The conditional complexity of universal compression seems to be one of promising candidates, especially in problems of discrimination between distributions of texts which are modeled as stationary ergodic precesses since Shannon. Only a limited amount of asymptotics and extensive simulation results to be presented show a promising performance of the method in addition to the amazing application results for some famous literary cases where the authorship attribution is either unknown or considered established.