Geodesic
Williams’s conjecture is false for reducible subshifts
Journal of the American Mathematical Society, Tome 05 (1992) no. 1, pp. 213-215

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We show that for two subshifts of finite type having exactly two irreducible components, strong shift equivalence is not the same as shift equivalence. This refutes the Williams conjecture $[{\text {W}}]$ in the reducible case. The irreducible case remains an open problem. 
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Kim, K. H.; Roush, F. W. Williams’s conjecture is false for reducible subshifts. Journal of the American Mathematical Society, Tome 05 (1992) no. 1, pp. 213-215. doi: 10.1090/S0894-0347-1992-1130528-4

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