In this paper, we prove that a valuation ring $R$ is archimedean if and only if for any finitely generated ideal I of R[x], the ideal LT}(I) generated by the leading terms of the elements of I is also finitely generated. This proves the archimedean conjecture in one variable. We also give a negative answer to the open question of whether if a 1- Groebner valuation ring is coherent.