  Drew, Johnson and Loewy conjectured that for $n \geq 4$, the CP-rank of every
$n \times n$ completely positive real matrix is at most $\left[n^{2}/4\right]$.
While this conjecture is false for completely positive real matrices, we show
that this conjecture is true for $n \times n$ completely positive matrices over
certain special types of inclines. In addition, we prove an incline version of
Markham's theorems which gives sufficient conditions for completely positive
matrices over special inclines to have triangular factorizations.
