The solution of the following programs:while(x∈Ω) do {x:〖KG-*3〗=f(x)} end, which was called as Non linear Programs over intervals,was presented,where x was a program variable,Ω(Ω=(a1,b1‖∪‖a2,b2‖∪…∪‖an,bn)，while ‖∈{(,),［,］}，n∈N*) was a set of intervals,and f was a polynomial function.It was proved that, when φ(b1)φ(a2)>0,…,φ(bn－1)φ(an)>0（φ(x)=f(x)－x）,the necessary condition for non-termination of the above program was that there existed fixed point within Ω or on the boundaries of Ω.Furthermore,if there were fixed points within Ω,the above condition was not only necessary but also sufficient.When all fixed points were on the boundaries of Ω,the corresponding necessary and sufficient condition of nontermination was established by introducing more constraints,and a decision algorithm for continuous polynomial function was presented.
