YES

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

Proof:
 Uncurry Processor (mirror):
  a3(x,a(),x6) -> f(a3(a(),f(x,a()),a()),x6)
  a2(x,a()) -> a3(a(),f(x,a()),a())
  f(a2(x4,x3),x5) -> a3(x4,x3,x5)
  f(a1(x4),x5) -> a2(x4,x5)
  f(a(),x5) -> a1(x5)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 1 0]     [1 0 1]     [1 1 0]  
    [a3](x0, x1, x2) = [1 1 0]x0 + [0 0 0]x1 + [0 0 1]x2
                       [0 0 0]     [0 0 0]     [1 0 0]  ,
    
                   [1 1 0]     [1 1 0]  
    [a2](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                   [0 0 0]     [0 0 0]  ,
    
               [1 1 0]     [0]
    [a1](x0) = [0 0 1]x0 + [1]
               [0 0 0]     [0],
    
                  [1 1 0]     [1 1 0]  
    [f](x0, x1) = [1 0 1]x0 + [0 0 1]x1
                  [0 0 0]     [1 0 0]  ,
    
          [0]
    [a] = [0]
          [1]
   orientation:
                   [1 1 0]    [1 1 0]     [1]    [1 1 0]    [1 1 0]     [1]                             
    a3(x,a(),x6) = [1 1 0]x + [0 0 1]x6 + [0] >= [1 1 0]x + [0 0 1]x6 + [0] = f(a3(a(),f(x,a()),a()),x6)
                   [0 0 0]    [1 0 0]     [0]    [0 0 0]    [1 0 0]     [0]                             
    
                [1 1 0]    [0]    [1 1 0]    [0]                       
    a2(x,a()) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a3(a(),f(x,a()),a())
                [0 0 0]    [0]    [0 0 0]    [0]                       
    
                      [1 1 1]     [1 1 0]     [1 1 0]      [1 0 1]     [1 1 0]     [1 1 0]                 
    f(a2(x4,x3),x5) = [1 1 0]x3 + [1 1 0]x4 + [0 0 1]x5 >= [0 0 0]x3 + [1 1 0]x4 + [0 0 1]x5 = a3(x4,x3,x5)
                      [0 0 0]     [0 0 0]     [1 0 0]      [0 0 0]     [0 0 0]     [1 0 0]                 
    
                   [1 1 1]     [1 1 0]     [1]    [1 1 0]     [1 1 0]              
    f(a1(x4),x5) = [1 1 0]x4 + [0 0 1]x5 + [0] >= [0 0 0]x4 + [0 0 1]x5 = a2(x4,x5)
                   [0 0 0]     [1 0 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 1]x5 + [1] = a1(x5)
                [1 0 0]     [0]    [0 0 0]     [0]         
   problem:
    a3(x,a(),x6) -> f(a3(a(),f(x,a()),a()),x6)
    a2(x,a()) -> a3(a(),f(x,a()),a())
    f(a2(x4,x3),x5) -> a3(x4,x3,x5)
    f(a(),x5) -> a1(x5)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                        [1 1 0]     [1 0 1]     [1 0 0]  
     [a3](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                        [0 0 0]     [0 0 0]     [0 0 0]  ,
     
                    [1 1 0]     [1 0 1]  
     [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 1]  ,
     
                [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] = [0]
           [1]
    orientation:
                    [1 1 0]    [1 0 0]     [1]    [1 1 0]    [1 0 0]                               
     a3(x,a(),x6) = [0 0 0]x + [0 0 0]x6 + [0] >= [0 0 0]x + [0 0 0]x6 = f(a3(a(),f(x,a()),a()),x6)
                    [0 0 0]    [0 0 0]     [0]    [0 0 0]    [0 0 0]                               
     
                 [1 1 0]    [1]    [1 1 0]                        
     a2(x,a()) = [0 0 0]x + [0] >= [0 0 0]x = a3(a(),f(x,a()),a())
                 [0 0 0]    [1]    [0 0 0]                        
     
                       [1 0 1]     [1 1 0]     [1 0 0]      [1 0 1]     [1 1 0]     [1 0 0]                 
     f(a2(x4,x3),x5) = [0 0 0]x3 + [0 0 0]x4 + [0 0 0]x5 >= [0 0 0]x3 + [0 0 0]x4 + [0 0 0]x5 = a3(x4,x3,x5)
                       [0 0 0]     [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]     [0 0 0]                 
     
                 [1 0 0]      [1 0 0]           
     f(a(),x5) = [0 0 0]x5 >= [0 0 0]x5 = a1(x5)
                 [0 0 0]      [0 0 0]           
    problem:
     f(a2(x4,x3),x5) -> a3(x4,x3,x5)
     f(a(),x5) -> a1(x5)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 0 0]     [1 0 0]     [1 0 0]  
      [a3](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                         [0 0 0]     [0 0 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]  
      [a1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                    [1 0 0]     [1 0 0]     [1]
      [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [0],
      
            [0]
      [a] = [0]
            [0]
     orientation:
                        [1 0 0]     [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]     [1 0 0]                 
      f(a2(x4,x3),x5) = [0 0 0]x3 + [0 0 0]x4 + [0 0 0]x5 + [0] >= [0 0 0]x3 + [0 0 0]x4 + [0 0 0]x5 = a3(x4,x3,x5)
                        [0 0 0]     [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0 0 0]                 
      
                  [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