As an efficient interconnection network, Network-on-Chip (NoC) provides significant flexibility for increasingly prevalent many-core systems. It is desirable to deploy fault-tolerance in a dependable safety-critical NoC design. However, this process can easily introduce deeply buried flaws that traditional simulation-based NoC design approaches may miss. This paper presents a case study on applying scalable formal verification that detects, corrects, and proves livelock in a dependable fault-tolerant NoC using the IVy verification tool. We formally verify correctness at the routing algorithm level. We first present livelock verification using refutation-based simulation scaled to a 15-by-15 two-dimensional NoC. We then present a novel zone-based approach to livelock verification in which finite coordinate-based routing conditions are abstracted as positional zones relative to a packet’s destination. This abstraction allows us to detect and remove livelock patterns on an arbitrarily large network. The resultant improved routing algorithm is free of livelock and maintains a high level of fault tolerance.