YES

Problem:
 merge(x,nil()) -> x
 merge(nil(),y) -> y
 merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
 merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [v] = [0]
         [0],
   
                     [1 1 0]       
   [merge](x0, x1) = [0 1 0]x0 + x1
                     [0 0 1]       ,
   
         [0]
   [u] = [0]
         [0],
   
           [1]
   [nil] = [0]
           [0],
   
                  [1 0 0]     [1 0 0]  
   [++](x0, x1) = [0 0 0]x0 + [0 1 1]x1
                  [0 0 0]     [0 0 0]  
  orientation:
                    [1 1 0]    [1]         
   merge(x,nil()) = [0 1 0]x + [0] >= x = x
                    [0 0 1]    [0]         
   
                        [1]         
   merge(nil(),y) = y + [0] >= y = y
                        [0]         
   
                                [1 0 0]    [1 1 1]     [1 0 0]    [1 1 0]                              
   merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 1]y >= [0 0 0]x + [0 1 1]y = ++(x,merge(y,++(u(),v())))
                                [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                              
   
                                [1 0 0]    [1 1 1]     [1 0 0]    [1 1 1]                              
   merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 1]y >= [0 0 0]x + [0 1 1]y = ++(u(),merge(++(x,y),v()))
                                [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                              
  problem:
   merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
   merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
          [0]
    [v] = [0]
          [0],
    
                      [1 1 1]     [1 0 0]  
    [merge](x0, x1) = [0 1 0]x0 + [0 0 1]x1
                      [0 0 1]     [0 0 0]  ,
    
          [0]
    [u] = [0]
          [0],
    
                   [1 0 0]     [1 0 0]     [0]
    [++](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [0]
                   [0 0 0]     [0 0 0]     [1]
   orientation:
                                 [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [0]                             
    merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 1]y + [1] >= [0 0 0]x + [0 1 1]y + [1] = ++(x,merge(y,++(u(),v())))
                                 [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                             
    
                                 [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [1]                             
    merge(++(x,y),++(u(),v())) = [0 0 0]x + [0 1 1]y + [1] >= [0 0 0]x + [0 1 1]y + [1] = ++(u(),merge(++(x,y),v()))
                                 [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]                             
   problem:
    merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [v] = [0]
           [1],
     
                       [1 0 0]     [1 1 0]  
     [merge](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                       [0 0 0]     [0 0 0]  ,
     
           [0]
     [u] = [0]
           [0],
     
                    [1 0 0]     [1 0 0]  
     [++](x0, x1) = [0 0 0]x0 + [0 1 1]x1
                    [0 1 0]     [0 0 0]  
    orientation:
                                  [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                              
     merge(++(x,y),++(u(),v())) = [0 1 0]x + [0 0 0]y + [0] >= [0 1 0]x + [0 0 0]y = ++(u(),merge(++(x,y),v()))
                                  [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                              
    problem:
     
    Qed