This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constrain two-qubit operations to limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. On the basis of a previous work on quantum circuit mapping that leverages gate commutation rules, this paper presents algorithms that utilize both transformation and commutation rules. Results of experiments on a standard benchmark dataset demonstrate the algorithms with more rules can find even better circuit mappings than the previously known best algorithms.