YES(?,O(n^1))

Problem:
 f(x,x) -> a()
 f(g(x),y) -> f(x,y)

Proof:
 RT Transformation Processor:
  strict:
   f(x,x) -> a()
   f(g(x),y) -> f(x,y)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [g](x0) = x0 + 2,
    
    [a] = 0,
    
    [f](x0, x1) = x0 + x1
   orientation:
    f(x,x) = 2x >= 0 = a()
    
    f(g(x),y) = x + y + 2 >= x + y = f(x,y)
   problem:
    strict:
     f(x,x) -> a()
    weak:
     f(g(x),y) -> f(x,y)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [g](x0) = x0,
     
     [a] = 0,
     
     [f](x0, x1) = x0 + x1 + 1
    orientation:
     f(x,x) = 2x + 1 >= 0 = a()
     
     f(g(x),y) = x + y + 1 >= x + y + 1 = f(x,y)
    problem:
     strict:
      
     weak:
      f(x,x) -> a()
      f(g(x),y) -> f(x,y)
    Qed