Must a complex system be adaptive to be of interest in the field of complexity? Give an example to support your answer.

A system is roughly described as complex if it is made up of a large number of interconnected elements with emergent global dynamics that are qualitatively distinct from the dynamics of each individual component.

Yes, since a non-adaptive system would continue to respond in the same way after receiving input information (a change in the environment). Its "capacity to stay alive" would be determined purely by the consistency of the environment. This type of system will very probably be terminated if the environment changes. Examining the "balance" of the ball in a labile equilibrium, which is actually no balance at all because any disturbance in the ball will tip it off, rendering it completely uninteresting. A stable equilibrium, on the other hand (a basic example of an adaptive system), would have many additional traits that would be more fascinating to investigate.

Therefore, Yes, in the study of complexity, non-adaptive complex systems are not of interest.