NO

Problem:
 f(X,g(X)) -> f(1(),g(X))
 g(1()) -> g(0())

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
         [1]
   [0] = [1],
   
         [0]
   [1] = [2],
   
                 [2 0]     [1 0]     [2]
   [f](x0, x1) = [1 0]x0 + [1 2]x1 + [1],
   
             [1 2]     [2]
   [g](x0) = [1 2]x0 + [1]
  orientation:
               [3 2]    [4]    [1 2]    [4]              
   f(X,g(X)) = [4 6]X + [5] >= [3 6]X + [5] = f(1(),g(X))
   
            [6]    [5]         
   g(1()) = [5] >= [4] = g(0())
  problem:
   f(X,g(X)) -> f(1(),g(X))
  Unfolding Processor:
   loop length: 1
   terms:
    f(1(),g(1()))
   context: []
   substitution:
    
   Qed