Can I take Flexeril if I'm also taking Coumadin?

I ran an interaction check and they do not interact:

"Drug Interactions Checker Search Report

This report displays the potential drug interactions for the following 2 drugs:

Flexeril (cyclobenzaprine)
Coumadin (warfarin)

Interactions between your drugs
No interactions were found between your selected drugs. This does not necessarily mean no interactions exist. Always consult your health care provider.

Drug and food interactions
Moderate
warfarin food
Applies to: Coumadin (warfarin)

Nutrition and diet can affect your treatment with warfarin. Therefore, it is important to keep your vitamin supplement and food intake steady throughout treatment. For example, increasing vitamin K levels in the body can promote clotting and reduce the effectiveness of warfarin. While there is no need to avoid products that contain vitamin K, you should maintain a consistent level of consumption of these products. Foods rich in vitamin K include beef liver, broccoli, Brussels sprouts, cabbage, collard greens, endive, kale, lettuce, mustard greens, parsley, soy beans, spinach, Swiss chard, turnip greens, watercress, and other green leafy vegetables. Moderate to high levels of vitamin K are also found in other foods such as asparagus, avocados, dill pickles, green peas, green tea, canola oil, margarine, mayonnaise, olive oil, and soybean oil. However, even foods that do not contain much vitamin K may occasionally affect the action of warfarin. There have been reports of patients who experienced bleeding complications and increased INR or bleeding times after consuming large quantities of cranberry juice, mangos, grapefruit, grapefruit juice, grapefruit seed extract, or pomegranate juice. Again, you do not need to avoid these foods completely, but it may be preferable to limit their consumption, or at least maintain the same level of use while you are receiving warfarin. Talk to a health care provider if you are uncertain about what foods or medications you take that may interact with warfarin. It is important to tell your doctor about all medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.

When warfarin is given with enteral (tube) feedings, you may interrupt the feeding for one hour before and one hour after the warfarin dose to minimize potential for interaction. Feeding formulas containing soy protein should be avoided.

Moderate
cyclobenzaprine food
Applies to: Flexeril (cyclobenzaprine)

Alcohol can increase the nervous system side effects of cyclobenzaprine such as dizziness, drowsiness, and difficulty concentrating. Some people may also experience impairment in thinking and judgment. You should avoid or limit the use of alcohol while being treated with cyclobenzaprine. Do not use more than the recommended dose of cyclobenzaprine, and avoid activities requiring mental alertness such as driving or operating hazardous machinery until you know how the medication affects you. Talk to your doctor or pharmacist if you have any questions or concerns.

Therapeutic duplication warnings
No warnings were found for your selected drugs.

Therapeutic duplication warnings are only returned when drugs within the same group exceed the recommended therapeutic duplication maximum.

Drug Interaction Classification
These classifications are only a guideline. The relevance of a particular drug interaction to a specific individual is difficult to determine. Always consult your health care provider before starting or stopping any medication.
Major
Highly clinically significant. Avoid combinations; the risk of the interaction outweighs the benefit.
Moderate
Moderately clinically significant. Usually avoid combinations; use it only under special circumstances.
Minor
Minimally clinically significant. Minimize risk; assess risk and consider an alternative drug, take steps to circumvent the interaction risk and/or institute a monitoring plan.
Unknown
No interaction information available."