The complexity class $PR$ is the set of all formal languages that can be decided by a primitive recursive function. Is there any language $l$ known to be complete for this class, i.e., for every language in $PR$ there is a primitive-recursive reduction from it to $l$?

Perhaps this notion is trivial, or it trivially does not exist (thus it is not worth appearing explicitly in the literature, at least not in this form) and I am simply thinking too hard about it. A reasonable candidate for $l$ would seem to be {<$p,x,y$> | $p$ is an encoding of a p.r. function which maps $x$ to $y$}, but that set would not appear to be itself primitive recursive, as there is no universal p.r. function to accept it.