The design of computer instruction sets has been mostly considered as being a manual process, due to complications between hardware and software, and the lack of suitable design tools. The manual process limits understanding of the hardware/software interface and tradeoffs. Motivated by this limitation, the design automation system ASIA (Automatic Synthesis for Instruction-set Architecture) was developed to systematize the design process for instruction sets. This paper presents a case study of using ASIA in synthesis and design exploration for application specific Symbolic (Prolog) computing. Instruction sets are optimized for given applications while maintaining their support for general Prolog execution. The results are compared with the VLSI-BAM processor, a manually-designed, general purpose instruction set processor for Prolog. The experiments show that: (1) the systematic and quantitative approach to instruction set design is feasible; (2) the design space of application-specific instruction sets consists of multiple dimensions across hardware and software, and ASIA is capable of exploiting such a complex design space and managing the hardware/software interactions; (3) the architectural properties of software applications vary significantly; therefore, (4) application specific instruction sets can provide better performance/cost tradeoff than can the general purpose instruction set processor in the context of specific application domains.