Growth of nonsymmetric operads

The paper concerns the Gelfand-Kirillov dimension and generating series of nonsymmetric operads. An analogue Bergman's gap theorem is proved, namely, no finitely generated locally finite operad has strictly between $1$ $2$. For every $r\in \{0\}\cup \{1\}\cup [2,\infty)$ or $r=\infty$, we construct a single-element with $r$. We also provide counterexamples to two expectations Khoroshkin Piontkovski about