Roots question

We have a wonderful philodendron (spelling ?) in the house which is about 2 years old. It is doing wonderful and we keep it shaped by cutting off the long new stems. We are wondering if its root system because of its age are getting bound up in the 9" pot it is in. Our reasoning is if we keep it trimmed the roots should not multiply and it should not be root bound. Is this true or do the roots keep growing and it should be transplanted into a larger pot? How will we know when to transplant?
Thanks In Advance, Kathy

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