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Sets of solutions to finite systems of equations in a free group, areequivalent to sets of homomorphisms from a fixed f.p. group into a free group.The latter can be encoded in a diagram, the construction of which is valid alsofor f.g. groups. The diagram is known to be canonical for a fixed f.g. groupwith a fixed generating set. In this paper we prove that the constructiondepends on the chosen generating set of the given f.g. group.

Canonicality of Makanin-Razborov Diagrams - Counterexample