YES(?,O(n^2))

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:
  dimension: 2
  interpretation:
         [1]
   [v] = [2],
   
         [1]
   [u] = [1],
   
                  [1 5]          [0]
   [++](x0, x1) = [0 0]x0 + x1 + [1],
   
                     [1 2]     [1 3]  
   [merge](x0, x1) = [0 1]x0 + [0 1]x1,
   
           [1]
   [nil] = [5]
  orientation:
                    [1 2]    [16]         
   merge(x,nil()) = [0 1]x + [5 ] >= x = x
   
                    [1 3]    [11]         
   merge(nil(),y) = [0 1]y + [5 ] >= y = y
   
                                [1 5]    [1 2]    [18]    [1 5]    [1 2]    [16]                             
   merge(++(x,y),++(u(),v())) = [0 0]x + [0 1]y + [4 ] >= [0 0]x + [0 1]y + [4 ] = ++(x,merge(y,++(u(),v())))
   
                                [1 5]    [1 2]    [18]    [1 5]    [1 2]    [15]                             
   merge(++(x,y),++(u(),v())) = [0 0]x + [0 1]y + [4 ] >= [0 0]x + [0 1]y + [4 ] = ++(u(),merge(++(x,y),v()))
  problem:
   
  Qed