  An incline is an additively idempotent semiring in which the product of two
elements is always less than or equal to either factor. By making use of prime
numbers, this paper proves that A^{11} is less than or equal to A^5 for all 3x3
matrices A over an arbitrary commutative incline, thus giving an answer to an
open problem "For 3x3 matrices over any incline (even noncommutative) is X^5
greater than or equal to X^{11}?", proposed by Cao, Kim and Roush in a
monograph Incline Algebra and Applications, 1984.
