1. An automatic designing system for automatically designing an architecture for components in a system, the automatic designing system comprising: a rule storage unit which stores a set of rewrite rules each used for rewriting a variable node of a hierarchically structured graph in a design architecture for the system, a rewritable part of the rewrite rules being taken as a variable node and a non-rewritable part being taken as a fixed node in a previously-designed design architecture for the system; a search unit (i) which sequentially determines variable nodes to be application targets for the rewrite rules by repeatedly searching the graph including components in the design architecture for the system to be designed using a search tree for the graph until an undefined variable node no longer exists in the graph and (ii) which performs backtracking on condition that no variable node to be the application target is found; a judgment unit which reads one of the rewrite rules corresponding to the determined variable node from the rule storage unit and judges whether or not the rewrite rule is applicable to the determined variable node; and a rule application unit which replaces the determined variable node with a partial graph in accordance with the read rewrite rule in response to a judgment result that the read rewrite rule is applicable, the partial graph including at least one of the fixed node and the variable node.