NO

Problem:
 f(a()) -> f(g(b(),b()))
 a() -> g(c(),c())
 c() -> d()
 d() -> b()
 b() -> d()

Proof:
 Matrix Interpretation Processor:
  dimension: 3
  interpretation:
         [0]
   [d] = [0]
         [0],
   
         [0]
   [c] = [0]
         [0],
   
                 [1 0 0]     [1 0 0]  
   [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
         [0]
   [b] = [0]
         [0],
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  ,
   
         [1]
   [a] = [0]
         [0]
  orientation:
            [1]    [0]                
   f(a()) = [0] >= [0] = f(g(b(),b()))
            [0]    [0]                
   
         [1]    [0]             
   a() = [0] >= [0] = g(c(),c())
         [0]    [0]             
   
         [0]    [0]      
   c() = [0] >= [0] = d()
         [0]    [0]      
   
         [0]    [0]      
   d() = [0] >= [0] = b()
         [0]    [0]      
   
         [0]    [0]      
   b() = [0] >= [0] = d()
         [0]    [0]      
  problem:
   c() -> d()
   d() -> b()
   b() -> d()
  Matrix Interpretation Processor:
   dimension: 3
   interpretation:
          [0]
    [d] = [0]
          [0],
    
          [1]
    [c] = [1]
          [0],
    
          [0]
    [b] = [0]
          [0]
   orientation:
          [1]    [0]      
    c() = [1] >= [0] = d()
          [0]    [0]      
    
          [0]    [0]      
    d() = [0] >= [0] = b()
          [0]    [0]      
    
          [0]    [0]      
    b() = [0] >= [0] = d()
          [0]    [0]      
   problem:
    d() -> b()
    b() -> d()
   Unfolding Processor:
    loop length: 2
    terms:
     d()
     b()
    context: []
    substitution:
     
    Qed