Dog swallowed some of his rope toy. Please help.

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It is a toy like this. I NEVER leave him alone with it because he is a big chewer, but I got distracted this time I noticed that he ate some of the strings on the end of it. I can't really explain how much he ate...it's difficult to explain. Do you think he's going to be alright? What should I look for? Has this ever happened to your dog?

I'm very nervous.