$\textbf{Definition: }$Let $\mathcal{A}$ be a unital $C^*$-algebra and $$\mathcal{T}(\mathcal{A})=Tracial~States~of~\mathcal{A}$$ $\mathcal{A}$ has strict comparison for projections if for all projections $p,q \in \mathcal{A}$ $$\tau({p})<\tau(q)~~~~~~\forall~\tau \in \mathcal{T}(\mathcal{A}) \implies p\leq q$$
I am trying to find a $C^*$-algebra which does not have strict comparison for projections. I want to find a simple , unital AF algebra without strict comparison that is
$\textbf{GOAL:}~~~~~$Find a simple unital AF-algebra $\mathcal{A}$ and $p,q \in \mathcal{A}$ projections such that $\tau(p)=\tau(q)$ for all $\tau \in \mathcal{T}(\mathcal{A})$ but $p \not\sim q$.
Thanks in advance for your help.