1. An information-processing device comprising: a memory; an execution means for assigning a storage area of the memory to each of a plurality of application programs, to execute the application program; a storage means for storing first identification information that represents a state in which an application program is running, or second identification information that represents a state in which execution of an application program is suspended, for each application program, wherein: (a) in a case where at least one first application program is running, a total number of the first identification information stored in the storage means is smaller than an allowable number of application programs, and a second application program is to be executed, the execution means: suspends execution of the at least one first application program, and rewrites identification information of the at least one first application program that is stored in the storage means, as the second identification information, assigns a first amount of the storage area to the second application program, to execute the second application program, and when the second application program is running, and an instruction to execute the first application program has been received, reassigns to the second application program a second amount of the storage area smaller than the first amount of the storage area, and assigns the second amount of the storage area to the at least one first application program, to execute the first application program and the second application program in parallel, and rewrites identification information of each of the at least one first application program and the second application program, as the first identification; and (b) in a case where the at least one first application program is running, a total number of the first identification information stored in the storage means is equal to the allowable number, and the second application program is to be executed, the execution means: suspends execution of the at least one first application program, and rewrites identification information of the first application program that is stored in the storage means, as the second identification information, assigns the first amount of the storage area of the memory to the second application program, to execute the second application program, when the second application program is running, and an instruction to execute the at least one first application program has been received, ends the second application program, and assigns the second amount of the storage area to each of the at least one first application program, to execute the first application program in parallel with other running applications, and rewrites identification information of the at least one first application program, as the first identification information, and the second application program is an application program for implementing a full function when the first amount of the storage area is assigned to the application program, and for implementing a part of the function when the second amount of the storage area is assigned to the application program.