Conjectured bound for the first relation degree of trace algebras

Let $n$ and $d$ denote the parameters of the trace algebra considered in the source, and let $N^1(n,d)$ denote the quantity measuring the relevant first relation degree. Bound conjecture.

$$N^1(n,d) \le n(n+1).$$

The surrounding text says that this bound is being proposed as a conjecture and notes that, in the case under discussion, the degree bound for the relations is $12$. The supplied text gives no evidence that the bound has been resolved.