Dexecutor can be used very easily for workflow like cases as depicted in the following diagram.

Dexecutor instance is created using DexecutorConfig, which in turn requires ExecutionEngine and TaskProvider, Default Implementation of ExecutionEngine uses ExecutorService, so lets create a Dexecutor Instance first (source code can be found here):

private static ExecutorService buildExecutor() {
   ExecutorService executorService = Executors.newFixedThreadPool(ThreadPoolUtil.ioIntesivePoolSize());
   return executorService;
 }

private Dexecutor<String, Boolean> buildDexecutor(final ExecutorService executorService) {
   DexecutorConfig<String, Boolean> config = new DexecutorConfig<>(executorService, new WorkFlowTaskProvider());
   return new DefaultDexecutor<>(config);
 }

TaskProvider comes into action, when it is the time to execute the task, for this example we will have simple implementation WorkFlowTaskProvider

public class WorkFlowTaskProvider implements TaskProvider<String, Boolean> {

    private final Map<String, Task<String, Boolean>> tasks = new HashMap<String, Task<String, Boolean>>() {

        private static final long serialVersionUID = 1L;
        {
            put(TaskOne.NAME, new TaskOne());
            put(TaskTwo.NAME, new TaskTwo());
            put(TaskThree.NAME, new TaskThree());
            put(TaskFour.NAME, new TaskFour());
            put(TaskFive.NAME, new TaskFive());
            put(TaskSix.NAME, new TaskSix());
            put(TaskSeven.NAME, new TaskSeven());
        }    
    };

    @Override
    public Task<String, Boolean> provideTask(final String id) {
        return this.tasks.get(id);
    }
}

For simplicity, we have implemented Task for each of the tasks (1..7), those can be found here, Most of the task implementations are same except for TaskTwo (if task 2 result is TRUE then tasks 3 and 4 would be executed otherwise task 5 would be executed) and TaskFive (If task 5 is executed (not skipped) then task task 6 would be executed).

TaskFive (TaskThree, TaskFour and TaskSix) overrides shouldExecute() method, to signal if the task should be executed or skipped.

Next step is to build the graph:

If WorkFlowApplication is executed, the following output can be observed.

Output if TaskTwo Is False

Executing TaskOne , result : true
Executing TaskTwo , result : false
Executing TaskFive , result : true
Executing TaskSix , result : true
Executing TaskSeven , result : true

Output if TaskTwo Is True

Executing TaskOne , result : true
Executing TaskTwo , result : true
Executing TaskFour , result : true
Executing TaskThree , result : true
Executing TaskSeven , result : true