CSP for binary conservative relational structures

We prove that whenever $${\mathbb {A}}$$A is a 3-conservative relational structure with only binary and unary relations, then the algebra of polymorphisms of $${\mathbb {A}}$$A either has no Taylor operation (i.e., CSP($${\mathbb {A}}$$A) is NP-complete), or it generates an SD($${\wedge}$$∧) variety (i.e., CSP($${\mathbb {A}}$$A) has bounded width).

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