YES(?,O(n^3))

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 mark(f(X)) -> active(f(X))
 mark(a()) -> active(a())
 mark(g(X)) -> active(g(mark(X)))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)

Proof:
 RT Transformation Processor:
  strict:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   mark(f(X)) -> active(f(X))
   mark(a()) -> active(a())
   mark(g(X)) -> active(g(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [mark](x0) = x0,
    
    [g](x0) = x0,
    
    [active](x0) = x0 + 29,
    
    [f](x0) = x0,
    
    [a] = 2
   orientation:
    active(f(f(a()))) = 31 >= 2 = mark(f(g(f(a()))))
    
    mark(f(X)) = X >= X + 29 = active(f(X))
    
    mark(a()) = 2 >= 31 = active(a())
    
    mark(g(X)) = X >= X + 29 = active(g(mark(X)))
    
    f(mark(X)) = X >= X = f(X)
    
    f(active(X)) = X + 29 >= X = f(X)
    
    g(mark(X)) = X >= X = g(X)
    
    g(active(X)) = X + 29 >= X = g(X)
   problem:
    strict:
     mark(f(X)) -> active(f(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     g(mark(X)) -> g(X)
    weak:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     f(active(X)) -> f(X)
     g(active(X)) -> g(X)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [mark](x0) = x0 + 8,
     
     [g](x0) = x0 + 2,
     
     [active](x0) = x0 + 17,
     
     [f](x0) = x0,
     
     [a] = 6
    orientation:
     mark(f(X)) = X + 8 >= X + 17 = active(f(X))
     
     mark(a()) = 14 >= 23 = active(a())
     
     mark(g(X)) = X + 10 >= X + 27 = active(g(mark(X)))
     
     f(mark(X)) = X + 8 >= X = f(X)
     
     g(mark(X)) = X + 10 >= X + 2 = g(X)
     
     active(f(f(a()))) = 23 >= 16 = mark(f(g(f(a()))))
     
     f(active(X)) = X + 17 >= X = f(X)
     
     g(active(X)) = X + 19 >= X + 2 = g(X)
    problem:
     strict:
      mark(f(X)) -> active(f(X))
      mark(a()) -> active(a())
      mark(g(X)) -> active(g(mark(X)))
     weak:
      f(mark(X)) -> f(X)
      g(mark(X)) -> g(X)
      active(f(f(a()))) -> mark(f(g(f(a()))))
      f(active(X)) -> f(X)
      g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 2
     interpretation:
                        [11]
      [mark](x0) = x0 + [0 ],
      
                [1 0]     [3]
      [g](x0) = [0 0]x0 + [0],
      
                     [1 2]  
      [active](x0) = [0 1]x0,
      
                [1 2]     [0]
      [f](x0) = [0 0]x0 + [5],
      
            [0]
      [a] = [4]
     orientation:
                   [1 2]    [11]    [1 2]    [10]               
      mark(f(X)) = [0 0]X + [5 ] >= [0 0]X + [5 ] = active(f(X))
      
                  [11]    [8]              
      mark(a()) = [4 ] >= [4] = active(a())
      
                   [1 0]    [14]    [1 0]    [14]                     
      mark(g(X)) = [0 0]X + [0 ] >= [0 0]X + [0 ] = active(g(mark(X)))
      
                   [1 2]    [11]    [1 2]    [0]       
      f(mark(X)) = [0 0]X + [5 ] >= [0 0]X + [5] = f(X)
      
                   [1 0]    [14]    [1 0]    [3]       
      g(mark(X)) = [0 0]X + [0 ] >= [0 0]X + [0] = g(X)
      
                          [28]    [22]                     
      active(f(f(a()))) = [5 ] >= [5 ] = mark(f(g(f(a()))))
      
                     [1 4]    [0]    [1 2]    [0]       
      f(active(X)) = [0 0]X + [5] >= [0 0]X + [5] = f(X)
      
                     [1 2]    [3]    [1 0]    [3]       
      g(active(X)) = [0 0]X + [0] >= [0 0]X + [0] = g(X)
     problem:
      strict:
       mark(g(X)) -> active(g(mark(X)))
      weak:
       mark(f(X)) -> active(f(X))
       mark(a()) -> active(a())
       f(mark(X)) -> f(X)
       g(mark(X)) -> g(X)
       active(f(f(a()))) -> mark(f(g(f(a()))))
       f(active(X)) -> f(X)
       g(active(X)) -> g(X)
     Matrix Interpretation Processor:
      dimension: 3
      interpretation:
                    [1 4 4]     [1]
       [mark](x0) = [0 0 0]x0 + [0]
                    [0 0 1]     [0],
       
                 [1 4 0]     [0]
       [g](x0) = [0 0 2]x0 + [0]
                 [0 0 1]     [1],
       
                      [1 4 0]     [1]
       [active](x0) = [0 0 0]x0 + [0]
                      [0 0 1]     [0],
       
                 [1 4 0]  
       [f](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
             [3]
       [a] = [2]
             [0]
      orientation:
                    [1  4  12]    [5]    [1  4  12]    [2]                     
       mark(g(X)) = [0  0  0 ]X + [0] >= [0  0  0 ]X + [0] = active(g(mark(X)))
                    [0  0  1 ]    [1]    [0  0  1 ]    [1]                     
       
                    [1 4 0]    [1]    [1 4 0]    [1]               
       mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(f(X))
                    [0 0 0]    [0]    [0 0 0]    [0]               
       
                   [12]    [12]              
       mark(a()) = [0 ] >= [0 ] = active(a())
                   [0 ]    [0 ]              
       
                    [1 4 4]    [1]    [1 4 0]        
       f(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X)
                    [0 0 0]    [0]    [0 0 0]        
       
                    [1 4 4]    [1]    [1 4 0]    [0]       
       g(mark(X)) = [0 0 2]X + [0] >= [0 0 2]X + [0] = g(X)
                    [0 0 1]    [1]    [0 0 1]    [1]       
       
                           [12]    [12]                     
       active(f(f(a()))) = [0 ] >= [0 ] = mark(f(g(f(a()))))
                           [0 ]    [0 ]                     
       
                      [1 4 0]    [1]    [1 4 0]        
       f(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X)
                      [0 0 0]    [0]    [0 0 0]        
       
                      [1 4 0]    [1]    [1 4 0]    [0]       
       g(active(X)) = [0 0 2]X + [0] >= [0 0 2]X + [0] = g(X)
                      [0 0 1]    [1]    [0 0 1]    [1]       
      problem:
       strict:
        
       weak:
        mark(g(X)) -> active(g(mark(X)))
        mark(f(X)) -> active(f(X))
        mark(a()) -> active(a())
        f(mark(X)) -> f(X)
        g(mark(X)) -> g(X)
        active(f(f(a()))) -> mark(f(g(f(a()))))
        f(active(X)) -> f(X)
        g(active(X)) -> g(X)
      Qed