YES

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

Proof:
 Uncurry Processor:
  a1(b1(x)) -> b1(a1(x))
  b1(c1(x)) -> c1(b1(x))
  c1(a1(x)) -> a1(c1(x))
  f(a(),x1) -> a1(x1)
  f(b(),x1) -> b1(x1)
  f(c(),x1) -> c1(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c1](x0) = 2x0,
    
    [b1](x0) = 5x0,
    
    [a1](x0) = 5x0,
    
    [c] = 1,
    
    [f](x0, x1) = x0 + 5x1,
    
    [b] = 0,
    
    [a] = 0
   orientation:
    a1(b1(x)) = 25x >= 25x = b1(a1(x))
    
    b1(c1(x)) = 10x >= 10x = c1(b1(x))
    
    c1(a1(x)) = 10x >= 10x = a1(c1(x))
    
    f(a(),x1) = 5x1 >= 5x1 = a1(x1)
    
    f(b(),x1) = 5x1 >= 5x1 = b1(x1)
    
    f(c(),x1) = 5x1 + 1 >= 2x1 = c1(x1)
   problem:
    a1(b1(x)) -> b1(a1(x))
    b1(c1(x)) -> c1(b1(x))
    c1(a1(x)) -> a1(c1(x))
    f(a(),x1) -> a1(x1)
    f(b(),x1) -> b1(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c1](x0) = x0 + 2,
     
     [b1](x0) = x0 + 6,
     
     [a1](x0) = x0 + 2,
     
     [f](x0, x1) = x0 + x1 + 2,
     
     [b] = 5,
     
     [a] = 0
    orientation:
     a1(b1(x)) = x + 8 >= x + 8 = b1(a1(x))
     
     b1(c1(x)) = x + 8 >= x + 8 = c1(b1(x))
     
     c1(a1(x)) = x + 4 >= x + 4 = a1(c1(x))
     
     f(a(),x1) = x1 + 2 >= x1 + 2 = a1(x1)
     
     f(b(),x1) = x1 + 7 >= x1 + 6 = b1(x1)
    problem:
     a1(b1(x)) -> b1(a1(x))
     b1(c1(x)) -> c1(b1(x))
     c1(a1(x)) -> a1(c1(x))
     f(a(),x1) -> a1(x1)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [c1](x0) = x0,
      
      [b1](x0) = x0 + 2,
      
      [a1](x0) = x0 + 6,
      
      [f](x0, x1) = x0 + x1 + 3,
      
      [a] = 4
     orientation:
      a1(b1(x)) = x + 8 >= x + 8 = b1(a1(x))
      
      b1(c1(x)) = x + 2 >= x + 2 = c1(b1(x))
      
      c1(a1(x)) = x + 6 >= x + 6 = a1(c1(x))
      
      f(a(),x1) = x1 + 7 >= x1 + 6 = a1(x1)
     problem:
      a1(b1(x)) -> b1(a1(x))
      b1(c1(x)) -> c1(b1(x))
      c1(a1(x)) -> a1(c1(x))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [c1](x0) = 4x0 + 3,
       
       [b1](x0) = x0,
       
       [a1](x0) = x0 + 7
      orientation:
       a1(b1(x)) = x + 7 >= x + 7 = b1(a1(x))
       
       b1(c1(x)) = 4x + 3 >= 4x + 3 = c1(b1(x))
       
       c1(a1(x)) = 4x + 31 >= 4x + 10 = a1(c1(x))
      problem:
       a1(b1(x)) -> b1(a1(x))
       b1(c1(x)) -> c1(b1(x))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                   [1 1 0]     [1]
        [c1](x0) = [0 1 0]x0 + [0]
                   [0 0 0]     [0],
        
                        [0]
        [b1](x0) = x0 + [0]
                        [1],
        
                   [1 1 1]  
        [a1](x0) = [1 0 0]x0
                   [0 0 1]  
       orientation:
                    [1 1 1]    [1]    [1 1 1]    [0]            
        a1(b1(x)) = [1 0 0]x + [0] >= [1 0 0]x + [0] = b1(a1(x))
                    [0 0 1]    [1]    [0 0 1]    [1]            
        
                    [1 1 0]    [1]    [1 1 0]    [1]            
        b1(c1(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = c1(b1(x))
                    [0 0 0]    [1]    [0 0 0]    [0]            
       problem:
        b1(c1(x)) -> c1(b1(x))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                    [1 0 0]     [0]
         [c1](x0) = [0 1 0]x0 + [1]
                    [0 0 0]     [1],
         
                    [1 1 0]  
         [b1](x0) = [0 1 0]x0
                    [0 0 1]  
        orientation:
                     [1 1 0]    [1]    [1 1 0]    [0]            
         b1(c1(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = c1(b1(x))
                     [0 0 0]    [1]    [0 0 0]    [1]            
        problem:
         
        Qed