YES

Problem:
 f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())

Proof:
 Uncurry Processor (mirror):
  a2(a1(x),x6) -> a2(f(x,a2(a(),a())),x6)
  a1(a1(x)) -> a1(f(x,a2(a(),a())))
  f(a1(x4),x5) -> a2(x4,x5)
  f(a(),x5) -> a1(x5)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 1]     [0]
    [a1](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
    
                   [1 0 1]     [1 0 0]     [0]
    [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                   [0 0 0]     [0 0 0]     [0],
    
                  [1 0 1]     [1 0 1]     [0]
    [f](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [0]
                  [0 0 0]     [0 0 0]     [1],
    
          [0]
    [a] = [0]
          [0]
   orientation:
                   [1 0 1]    [1 0 0]     [1]    [1 0 1]    [1 0 0]     [1]                          
    a2(a1(x),x6) = [0 0 0]x + [0 0 0]x6 + [1] >= [0 0 0]x + [0 0 0]x6 + [1] = a2(f(x,a2(a(),a())),x6)
                   [0 0 0]    [0 0 0]     [0]    [0 0 0]    [0 0 0]     [0]                          
    
                [1 0 1]    [1]    [1 0 1]    [1]                       
    a1(a1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = a1(f(x,a2(a(),a())))
                [0 0 0]    [1]    [0 0 0]    [1]                       
    
                   [1 0 1]     [1 0 1]     [1]    [1 0 1]     [1 0 0]     [0]            
    f(a1(x4),x5) = [0 0 0]x4 + [0 1 0]x5 + [1] >= [0 0 0]x4 + [0 0 0]x5 + [1] = a2(x4,x5)
                   [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [0]            
    
                [1 0 1]     [0]    [1 0 1]     [0]         
    f(a(),x5) = [0 1 0]x5 + [0] >= [0 0 0]x5 + [0] = a1(x5)
                [0 0 0]     [1]    [0 0 0]     [1]         
   problem:
    a2(a1(x),x6) -> a2(f(x,a2(a(),a())),x6)
    a1(a1(x)) -> a1(f(x,a2(a(),a())))
    f(a(),x5) -> a1(x5)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 0]     [0]
     [a1](x0) = [0 1 0]x0 + [0]
                [0 1 0]     [1],
     
                    [1 0 1]     [1 0 0]     [0]
     [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [1],
     
                   [1 0 0]     [1 0 0]  
     [f](x0, x1) = [0 1 0]x0 + [0 1 0]x1
                   [0 1 0]     [0 1 0]  ,
     
           [0]
     [a] = [1]
           [0]
    orientation:
                    [1 1 0]    [1 0 0]     [1]    [1 1 0]    [1 0 0]     [0]                          
     a2(a1(x),x6) = [0 0 0]x + [0 0 0]x6 + [0] >= [0 0 0]x + [0 0 0]x6 + [0] = a2(f(x,a2(a(),a())),x6)
                    [0 0 0]    [0 0 0]     [1]    [0 0 0]    [0 0 0]     [1]                          
     
                 [1 0 0]    [0]    [1 0 0]    [0]                       
     a1(a1(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = a1(f(x,a2(a(),a())))
                 [0 1 0]    [1]    [0 1 0]    [1]                       
     
                 [1 0 0]     [0]    [1 0 0]     [0]         
     f(a(),x5) = [0 1 0]x5 + [1] >= [0 1 0]x5 + [0] = a1(x5)
                 [0 1 0]     [1]    [0 1 0]     [1]         
    problem:
     a1(a1(x)) -> a1(f(x,a2(a(),a())))
     f(a(),x5) -> a1(x5)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                 [1 1 0]     [0]
      [a1](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
      
                     [1 0 0]     [1 0 0]  
      [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
      
                    [1 0 0]     [1 1 0]  
      [f](x0, x1) = [0 1 0]x0 + [0 0 1]x1
                    [0 0 0]     [0 0 0]  ,
      
            [0]
      [a] = [1]
            [0]
     orientation:
                  [1 1 0]    [1]    [1 1 0]    [0]                       
      a1(a1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a1(f(x,a2(a(),a())))
                  [0 0 0]    [0]    [0 0 0]    [0]                       
      
                  [1 1 0]     [0]    [1 1 0]     [0]         
      f(a(),x5) = [0 0 1]x5 + [1] >= [0 0 0]x5 + [1] = a1(x5)
                  [0 0 0]     [0]    [0 0 0]     [0]         
     problem:
      f(a(),x5) -> a1(x5)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                  [1 0 0]  
       [a1](x0) = [0 0 0]x0
                  [0 0 0]  ,
       
                     [1 1 0]     [1 0 0]  
       [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
       
             [0]
       [a] = [1]
             [0]
      orientation:
                   [1 0 0]     [1]    [1 0 0]           
       f(a(),x5) = [0 0 0]x5 + [0] >= [0 0 0]x5 = a1(x5)
                   [0 0 0]     [0]    [0 0 0]           
      problem:
       
      Qed