ATNoSFERES is a Pittsburgh style Learning Classifier System (LCS) in which the rules are represented as edges of an Augmented Transition Network. Genotypes are strings of tokens of a stack-based language, whose execution builds the labeled graph. The original ATNoSFERES, using a bitstring to represent the language tokens, has been favorably compared in previous work to several Michigan style LCSs architectures in the context of Non Markov problems. Several modifications of ATNoSFERES are proposed here: the most important one conceptually being a representational change: each token is now represented by an integer, hence the genotype is a string of integers; several other modifications of the underlying grammar language are also proposed. The resulting ATNoSFERES-II is validated on several standard animat Non Markov problems, on which it outperforms all previously published results in the LCS literature. The reasons for these improvement are carefully analyzed, and some assumptions are proposed on the underlying mechanisms in order to explain these good results.