The diagram above shows the refinement of the useability requirement "Autosolve". In step 1 the actor asks the sudoku object, which represents the UI (User Interface), to solve the sudoku puzzle. In step 1.1 the sudoku object activates the board object to manage the work to be done. The first time AutoSolve is called without parameters, therefore 1.1.1 GetCell, 1.1.2 SetDigit and 1.1.3 UpdateSibling are skipped. In the first loop the board evaluates the 6 basic rules and accepts resulting singles until there are no more singles to accept. In step 1.1.6 the board checks whether the puzzle has already been solved or not. If solved, the board returns in 1.1.11 "solved". In step 1.1.7 the board looks up the cell with the fewest candidates. For each candidate the board creates in 1.1.8 a new board and sends the message AutoSolve to this new board object. Now  AutoSolve is sent with 2 parameters, the location of the cell with the fewest candidates and the candidate value. The new board gets in 1.1.1 the cell with the given location, sets in 1.1.2 the candidate value and removes in 1.1.3 the candidate form all siblings in the row, the column and the box. Then the other steps are repeated over and over again until the puzzle has been solved or an invalid state occured.

Note that during the phase analysis a UML sequence diagram diagram doesn't contain implementation details. Implementation details are added during the phase design.