YES

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

Proof:
 Uncurry Processor:
  f1(g1(f1(x))) -> f1(g1(g1(f1(x))))
  g1(f1(g1(x))) -> g1(f1(f1(g1(x))))
  a(f(),x1) -> f1(x1)
  a(g(),x1) -> g1(x1)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]  
    [g1](x0) = [0 0 1]x0
               [0 1 0]  ,
    
               [1 1 0]     [0]
    [f1](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
    
                  [1 0 0]     [1 1 1]     [0]
    [a](x0, x1) = [0 1 0]x0 + [0 0 1]x1 + [0]
                  [0 0 0]     [1 1 1]     [1],
    
          [0]
    [g] = [1]
          [0],
    
          [0]
    [f] = [0]
          [0]
   orientation:
                    [1 1 0]    [1]    [1 1 0]    [0]                    
    f1(g1(f1(x))) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f1(g1(g1(f1(x))))
                    [0 0 0]    [1]    [0 0 0]    [1]                    
    
                    [1 0 1]    [0]    [1 0 1]    [0]                    
    g1(f1(g1(x))) = [0 0 0]x + [1] >= [0 0 0]x + [1] = g1(f1(f1(g1(x))))
                    [0 0 0]    [0]    [0 0 0]    [0]                    
    
                [1 1 1]     [0]    [1 1 0]     [0]         
    a(f(),x1) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = f1(x1)
                [1 1 1]     [1]    [0 0 0]     [1]         
    
                [1 1 1]     [0]    [1 0 0]           
    a(g(),x1) = [0 0 1]x1 + [1] >= [0 0 1]x1 = g1(x1)
                [1 1 1]     [1]    [0 1 0]           
   problem:
    g1(f1(g1(x))) -> g1(f1(f1(g1(x))))
    a(f(),x1) -> f1(x1)
    a(g(),x1) -> g1(x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 1 0]     [0]
     [g1](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1],
     
                [1 0 0]  
     [f1](x0) = [0 0 1]x0
                [0 1 0]  ,
     
                   [1 0 0]     [1 1 1]     [1]
     [a](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                   [0 0 0]     [0 1 0]     [1],
     
           [0]
     [g] = [0]
           [0],
     
           [0]
     [f] = [0]
           [0]
    orientation:
                     [1 1 0]    [1]    [1 1 0]    [0]                    
     g1(f1(g1(x))) = [0 0 0]x + [0] >= [0 0 0]x + [0] = g1(f1(f1(g1(x))))
                     [0 0 0]    [1]    [0 0 0]    [1]                    
     
                 [1 1 1]     [1]    [1 0 0]           
     a(f(),x1) = [0 0 1]x1 + [0] >= [0 0 1]x1 = f1(x1)
                 [0 1 0]     [1]    [0 1 0]           
     
                 [1 1 1]     [1]    [1 1 0]     [0]         
     a(g(),x1) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = g1(x1)
                 [0 1 0]     [1]    [0 0 0]     [1]         
    problem:
     
    Qed