Example of attribute grammar that is NOT l-ORD but non-circular

I am wondering if there exists an example attribute grammar that is non-circular but not l-ordered (l-ORD) as well.

The reason I am asking this is one can find an attribute grammar that is circular, then it will obviously not be an l-ORD. But I am wondering if there even exists a non-circular AG that is also not l-ORD.