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

Recently Ott, Tomforde and Willis proposed a new approach for one sided shift spaces over infinite alphabets. In this new approach the conjugacy classes of shifts of finite type, edge shifts, and M  -step shifts are distinct and the authors conjecture that for each M∈N∪{0}M∈N∪{0} there exists an (M+1)(M+1)-step shift space that is not conjugate to any M  -step shift. In this short paper we build a class of (M+1)(M+1)-step shifts that are not conjugate to any M-step shift and hence show that their conjecture is correct.