In this study we show how complex creative relations can arise from fairly frequent semantic relations observed in everyday language. By doing this, we reflect on some key cognitive aspects of linguistic and general creativity. In our experimentation, we automated the process of solving a battery of Remote Associates Test tasks. By applying Statistical Natural Language Processing techniques to a large web-based corpus, we perform a frequency and collocation analysis of the test items. Results show that 37% of the 68 tasks were automatically solved, whereas human accuracy reached 43%. Our method outperformed humans in the tasks rated as difficult: 38% and 32%, respectively. Highly relevant is that the novel and adequate relations established in order to solve the RAT were not previously present in the corpus. The frequency based approach pervades all stages of our method: during the divergent stage, highly frequent collocations are listed, while the convergent stage starts by matching each task's triads output, shrinking that list, and finalizing it by choosing the least frequent, therefore more informative and often correct, result. Finally, we discuss the implications of our model in overcoming functional fixedness and understanding cognitive salience in the creative process.