YES(?,O(n^1))

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

Proof:
 RT Transformation Processor:
  strict:
   f(a(),x) -> g(a(),x)
   g(a(),x) -> f(b(),x)
   f(a(),x) -> f(b(),x)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b] = 2,
    
    [g](x0, x1) = x0 + x1 + 25,
    
    [f](x0, x1) = x0 + x1 + 14,
    
    [a] = 3
   orientation:
    f(a(),x) = x + 17 >= x + 28 = g(a(),x)
    
    g(a(),x) = x + 28 >= x + 16 = f(b(),x)
    
    f(a(),x) = x + 17 >= x + 16 = f(b(),x)
   problem:
    strict:
     f(a(),x) -> g(a(),x)
    weak:
     g(a(),x) -> f(b(),x)
     f(a(),x) -> f(b(),x)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b] = 1,
     
     [g](x0, x1) = x0 + x1,
     
     [f](x0, x1) = x0 + x1 + 1,
     
     [a] = 2
    orientation:
     f(a(),x) = x + 3 >= x + 2 = g(a(),x)
     
     g(a(),x) = x + 2 >= x + 2 = f(b(),x)
     
     f(a(),x) = x + 3 >= x + 2 = f(b(),x)
    problem:
     strict:
      
     weak:
      f(a(),x) -> g(a(),x)
      g(a(),x) -> f(b(),x)
      f(a(),x) -> f(b(),x)
    Qed