The main purpose of this thread is to show that the argument (from observed complexity) for the necessity of an intelligent designer if properly stated need not also necessarily require any logical problem- such as an inifinite regression. Before digressing more into the issue of what is meant specifically by "complexity", it needs to be pointed out that even if an intelligent desginer itself had to also be complex [which I don't nesessarily accept], the fact remains that the initial ID statement given in the OP here would still not necessarilry also require the designer to themself have a designer. This is due to the fact that the statement in the OP is referring only to complexity that has an origin being best explained as the result of a designer rather that as the result of natural processes. "The origin of complexity from non-complexity is best explained as the result of an intelligent designer, rather than as the result non-intelligently guided natural processes". Given that there is nothing in the above statement that also requires the desginer to themself have an origin, there is no requirement in the above for them to also have a designer themself. This is true even if the designer were also defined as being complex.
It also needs to be remembered that even anti-creationists already accept intelligent design as logicallly valid science in other instances. As I pointed out in the first post: "To use an analogy the origin of the multiple componet complexity of a sophisticated "watch like device" if found on Mars would be taken as strong evidence of being the result of an intelligent designer, rather than as the result of natural processes. (In this case no one-not even anti-creationists would object to complexity as evidence for design)." So then how can they turn around and then claim that the arguemt for a designer from complex design is somehow necessarily illogical?