An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n + 1) - p(n) ≤ 2

In [Ergodic Theory Dynam. System, 16 (1996) 663–682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S)≤ 3^27. In this paper, we improve this result by giving an S-adic charaterization of these subshifts with a set
S of 5 morphisms, solving by this way the S-adic conjecture for this particular case.