For single-ended sets of tuples in free groups, and related algebraic categories, a canonical minimal-complexity Makanin-Razborov diagram exists and is unique up to isomorphism of trimmed reduced completions.
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A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples in free groups, semigroups, associative algebras and Lie algebras I
For single-ended sets of tuples in free groups, and related algebraic categories, a canonical minimal-complexity Makanin-Razborov diagram exists and is unique up to isomorphism of trimmed reduced completions.