Fundamental group of bouquet of 2 circles not in common point

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I tried to calculate a fundamental group of bouquet of 2 circles not in common point. Let call this point a (see picture). It is different from fundamental group in b or I did some mistake? (Fundamental group in b is: $\left<A,B|\emptyset \right>$, my result of fundamental group in a: $\left<A,B,C|BA=AC\right>$)