YES

Problem:
 a__f(f(a())) -> c(f(g(f(a()))))
 mark(f(X)) -> a__f(mark(X))
 mark(a()) -> a()
 mark(c(X)) -> c(X)
 mark(g(X)) -> g(mark(X))
 a__f(X) -> f(X)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]  
   [c](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]     [0]
   [f](x0) = [0 0 0]x0 + [1]
             [0 1 1]     [0],
   
               
   [g](x0) = x0
               ,
   
                [1 1 1]     [0]
   [mark](x0) = [0 1 0]x0 + [0]
                [0 0 1]     [1],
   
         [0]
   [a] = [0]
         [0],
   
                [1 0 0]     [1]
   [a__f](x0) = [0 0 0]x0 + [1]
                [0 1 1]     [0]
  orientation:
                  [1]    [0]                  
   a__f(f(a())) = [1] >= [0] = c(f(g(f(a()))))
                  [1]    [0]                  
   
                [1 1 1]    [1]    [1 1 1]    [1]                
   mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__f(mark(X))
                [0 1 1]    [1]    [0 1 1]    [1]                
   
               [0]    [0]      
   mark(a()) = [0] >= [0] = a()
               [1]    [0]      
   
                [1 0 0]    [0]    [1 0 0]        
   mark(c(X)) = [0 0 0]X + [0] >= [0 0 0]X = c(X)
                [0 0 0]    [1]    [0 0 0]        
   
                [1 1 1]    [0]    [1 1 1]    [0]             
   mark(g(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = g(mark(X))
                [0 0 1]    [1]    [0 0 1]    [1]             
   
             [1 0 0]    [1]    [1 0 0]    [0]       
   a__f(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
             [0 1 1]    [0]    [0 1 1]    [0]       
  problem:
   mark(f(X)) -> a__f(mark(X))
   mark(a()) -> a()
   mark(c(X)) -> c(X)
   mark(g(X)) -> g(mark(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c](x0) = x0,
    
    [f](x0) = 4x0,
    
    [g](x0) = 4x0 + 1,
    
    [mark](x0) = 2x0,
    
    [a] = 0,
    
    [a__f](x0) = 4x0
   orientation:
    mark(f(X)) = 8X >= 8X = a__f(mark(X))
    
    mark(a()) = 0 >= 0 = a()
    
    mark(c(X)) = 2X >= X = c(X)
    
    mark(g(X)) = 8X + 2 >= 8X + 1 = g(mark(X))
   problem:
    mark(f(X)) -> a__f(mark(X))
    mark(a()) -> a()
    mark(c(X)) -> c(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [0]
     [c](x0) = [0 0 1]x0 + [0]
               [0 0 0]     [1],
     
               [1 0 0]     [1]
     [f](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [0],
     
                  [1 0 1]  
     [mark](x0) = [0 1 0]x0
                  [0 0 1]  ,
     
           [0]
     [a] = [0]
           [1],
     
                  [1 0 0]  
     [a__f](x0) = [0 0 0]x0
                  [0 0 1]  
    orientation:
                  [1 0 1]    [1]    [1 0 1]                 
     mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__f(mark(X))
                  [0 0 1]    [0]    [0 0 1]                 
     
                 [1]    [0]      
     mark(a()) = [0] >= [0] = a()
                 [1]    [1]      
     
                  [1 0 0]    [1]    [1 0 0]    [0]       
     mark(c(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = c(X)
                  [0 0 0]    [1]    [0 0 0]    [1]       
    problem:
     
    Qed