Let us call *primitive* an interaction system with the signature

$\Sigma = \{(\rho, 0), (\xi, n)\}, \quad n \geq 2;$

and the only rule being of the form

$\rho \bowtie \xi[\rho, \xi(a_1, \dots , a_n), a_{n + 1}, a_{2n - 2}],$

where $(a_1, \dots , a_{2n - 2})$ defines a wiring.

Are there any Turing-complete primitive interaction systems?