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Recently Ott, Tomforde and Willis proposed a new approach for one sided shiftspaces over infinite alphabets. In this new approach the conjugacy classes ofshifts of finite type, edge shifts, and M-step shifts are distinct and theauthors conjecture that for each non-negative integer M there exist an(M+1)-step shift space that is not conjugate to any M-step shift. In this shortpaper we build a class of (M+1)-step shifts that are not conjugate to anyM-step shift and hence show that their conjecture is correct.

(M + 1)-step shift spaces that are not conjugate to M-step shift spaces