YES(?,O(n^2))

Problem:
 add(0(),x) -> x
 add(s(x),y) -> s(add(x,y))

Proof:
 RT Transformation Processor:
  strict:
   add(0(),x) -> x
   add(s(x),y) -> s(add(x,y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [s](x0) = x0 + 12,
    
    [add](x0, x1) = x0 + x1 + 24,
    
    [0] = 0
   orientation:
    add(0(),x) = x + 24 >= x = x
    
    add(s(x),y) = x + y + 36 >= x + y + 36 = s(add(x,y))
   problem:
    strict:
     add(s(x),y) -> s(add(x,y))
    weak:
     add(0(),x) -> x
   Matrix Interpretation Processor:
    dimension: 2
    interpretation:
                    [1]
     [s](x0) = x0 + [2],
     
                     [1 2]     [1 1]  
     [add](x0, x1) = [0 1]x0 + [0 1]x1,
     
           [0]
     [0] = [0]
    orientation:
                   [1 2]    [1 1]    [5]    [1 2]    [1 1]    [1]              
     add(s(x),y) = [0 1]x + [0 1]y + [2] >= [0 1]x + [0 1]y + [2] = s(add(x,y))
     
                  [1 1]          
     add(0(),x) = [0 1]x >= x = x
    problem:
     strict:
      
     weak:
      add(s(x),y) -> s(add(x,y))
      add(0(),x) -> x
    Qed