YES(?,O(n^1))

Problem:
 f(f(x)) -> g(f(x))
 g(g(x)) -> f(x)

Proof:
 RT Transformation Processor:
  strict:
   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [g](x0) = x0 + 16,
    
    [f](x0) = x0 + 1
   orientation:
    f(f(x)) = x + 2 >= x + 17 = g(f(x))
    
    g(g(x)) = x + 32 >= x + 1 = f(x)
   problem:
    strict:
     f(f(x)) -> g(f(x))
    weak:
     g(g(x)) -> f(x)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [g](x0) = x0 + 12,
     
     [f](x0) = x0 + 16
    orientation:
     f(f(x)) = x + 32 >= x + 28 = g(f(x))
     
     g(g(x)) = x + 24 >= x + 16 = f(x)
    problem:
     strict:
      
     weak:
      f(f(x)) -> g(f(x))
      g(g(x)) -> f(x)
    Qed