Determination as to whether a nondecreasing sequence exists or not is efficiently made. A sorting part sorts elements of a set Pi in ascending order to generate vectors ti,i+1 and bi,i+1. A merging part generates vectors t0,m and b0,m by repeating the process of merging vectors (ti,j, bi,j) and (tj,k, bj,k) to generate (ti,k, bi,k). A stable-sorting part generates a vector e by coupling and stably sorting vectors bi,j and tj,k. A searching part searches for sets of (λ, x, y) in which e[λ] is bi,j[x] and e[λ+1] is tj,k[y] and generates a set X including all x and a set Y including all y. An extracting part sorts ti,j[x] (x∈X) in ascending order to generate a vector ti,k and sorts bj,k[y] (y∈Y) in ascending order to generate a vector bi,k. If the length of a vector t0,m is 0, a determining part outputs a result of determination that indicates the absence of a nondecreasing sequence.