YES(?,O(n^1))

Problem:
 f(0()) -> s(0())
 f(s(x)) -> g(s(s(x)))
 g(0()) -> s(0())
 g(s(0())) -> s(0())
 g(s(s(x))) -> f(x)

Proof:
 RT Transformation Processor:
  strict:
   f(0()) -> s(0())
   f(s(x)) -> g(s(s(x)))
   g(0()) -> s(0())
   g(s(0())) -> s(0())
   g(s(s(x))) -> f(x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [g](x0) = x0 + 19,
    
    [s](x0) = x0,
    
    [f](x0) = x0 + 18,
    
    [0] = 0
   orientation:
    f(0()) = 18 >= 0 = s(0())
    
    f(s(x)) = x + 18 >= x + 19 = g(s(s(x)))
    
    g(0()) = 19 >= 0 = s(0())
    
    g(s(0())) = 19 >= 0 = s(0())
    
    g(s(s(x))) = x + 19 >= x + 18 = f(x)
   problem:
    strict:
     f(s(x)) -> g(s(s(x)))
    weak:
     f(0()) -> s(0())
     g(0()) -> s(0())
     g(s(0())) -> s(0())
     g(s(s(x))) -> f(x)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [g](x0) = x0 + 4,
     
     [s](x0) = x0 + 2,
     
     [f](x0) = x0 + 8,
     
     [0] = 2
    orientation:
     f(s(x)) = x + 10 >= x + 8 = g(s(s(x)))
     
     f(0()) = 10 >= 4 = s(0())
     
     g(0()) = 6 >= 4 = s(0())
     
     g(s(0())) = 8 >= 4 = s(0())
     
     g(s(s(x))) = x + 8 >= x + 8 = f(x)
    problem:
     strict:
      
     weak:
      f(s(x)) -> g(s(s(x)))
      f(0()) -> s(0())
      g(0()) -> s(0())
      g(s(0())) -> s(0())
      g(s(s(x))) -> f(x)
    Qed