1. An execution order determining device for determining an execution order of concurrently executable tasks, the execution order determining device comprising: a processor; a task control information storing section which stores execution conditions under which an execution of each of the tasks is started, and which stores the execution order of the tasks; a task executing section which executes the tasks in accordance with the execution order stored in the task control information storing section; a task execution administering section which monitors a state of a task being executed by a client including a processor to detect a first task whose state is to be shifted from an execution state indicating that a task is being executed to a process standby state of waiting to receive a second response signal from a second task that is in the execution state and is being executed by a server including a processor, the task execution administering section monitoring the state of the task being executed based on the execution conditions stored in the task control information storing section; and a virtual task administering section which generates a virtual task as a copy of the first task detected by the task execution administering section, wherein the task execution administering section (i) accepts a first request signal from the client for executing the second task and subsequently checks the execution state of the server (ii) generates a first response signal in response to the accepted first request signal, the first response signal being generated based on the execution state of the server, (iii) outputs the generated first response signal to the first task being executed by the client, such that the client continues to execute the first task without waiting for the server to issue the second response and (iv) activates the generated virtual task to issue a second request signal after a start of the execution of the second task by the server, wherein, upon receiving the second response from the server, the generated virtual task checks contents of the first response signal previously output by the task execution administering section and, based on a result of the checking of the contents of the first response signal (a) outputs a result to the client and executes a post-process, (b) executes the post-process without outputting the result to the client, or (c) performs an error process in a case where contents of the second response signal do not agree with the contents of the first response signal, the virtual task administering section adds the generated virtual task to the execution order stored in the task control information storing section to concurrently execute the virtual task with the first task, and the task executing section causes the client to execute the first task whose state is not to be shifted to the process standby state by receiving the second response signal, and causes the virtual task and the second task to be executed concurrently with the first task.