Huet showed in 1973 that 3rd order unification is undecidable .
This was improved upon by Baxter in 1978 then by Goldfarb in 1981 by showing that 2nd order unification is already undecidable .
Huet showed in 1973 that 3rd order unification is undecidable and this was improved upon by Baxter in 1978 then by Goldfarb in 1981 by showing that 2nd order unification is already undecidable .