Determination as to whether a nondecreasing sequence exists or not is efficiently made. A sorting part 10 sorts elements of a set P i in ascending order to generate vectors t i,i+1 and b i,i+1 . A merging part 20 generates vectors t 0,m and b 0,m by repeating the process of merging vectors (t i,j , b i,j ) and (t j,k , b j,k ) to generate (t i,k , b i,k ). A stable-sorting part 21 generates a vector e by coupling and stably sorting vectors b i,j and t j,k . A searching part 22 searches for sets of (», x, y) in which e[»] is b i,j [x] and e[» + 1] is t j,k [y] and generates a set X including all x and a set Y including all y. An extracting part 23 sorts t i,j [x] (x ˆˆ X) in ascending order to generate a vector t i,k and sorts b j,k [y] (y ˆˆ Y) in ascending order to generate a vector b j,k . If the length of a vector t 0,m is 0, a determining part 30 outputs a result of determination that indicates the absence of a nondecreasing sequence.