Fund Project:Supported by the National Key Basic Research Project of China (Grant No.2011CB302402) and the Fundamental Research Funds for the Central Universities, Southwest University for Nationalities (Grant No.12NZYTH04).
We introduce a concept for the majorization order on monomials. With the help of this order, we derive a necessary condition on the positive termination of a general successive difference substitution algorithm (KSDS) for an input form $f$.