YES

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

Proof:
 Church Rosser Transformation Processor (kb):
  f(f(x)) -> f(g(f(x)))
  critical peaks: joinable
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [1 0]     [0]
     [g](x0) = [0 0]x0 + [1],
     
               [1 1]     [1]
     [f](x0) = [2 0]x0 + [2]
    orientation:
               [3 1]    [4]    [1 1]    [3]             
     f(f(x)) = [2 2]x + [4] >= [2 2]x + [4] = f(g(f(x)))
    problem:
     
    Qed