Termination analysis of programs over the set of intervals

The termination problem of simple while program: While (constraints) {updates} is undecidable in general. Sometimes it can be decided by computing fixed point of nonlinear updating function. For some loops which cannot be determined by fixed point, we transformed them into loops whose termination problem can be determined by periodic orbit of the updating function. The case that termination problem can be determined by existence of fixed point is a special case of our result.