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We prove that the presentations $\langle x,y | [x,y],1 \rangle$ and $\langlex,y | [x,[x,y^{-1}]]^2y[y^{-1},x]y^{-1},[x,[[y^{-1},x],x]] \rangle$ are not$Q^*$-equivalent even though their standard complexes have the same simplehomotopy type.

A counterexample to a strong version of the Andrews-Curtis conjecture