  The associative operad is the quotient of the magmatic operad by the operad
congruence identifying the two binary trees of degree $2$. We introduce here a
generalization of the associative operad depending on a nonnegative integer
$d$, called $d$-comb associative operad, as the quotient of the magmatic operad
by the operad congruence identifying the left and the right comb binary trees
of degree $d$. We study the case $d = 3$ and provide an orientation of its
space of relations by using rewrite systems on trees and the Buchberger
algorithm for operads to obtain a convergent rewrite system.
