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:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   c ==> c0/0 c1/1
   b ==> b0/0 b1/1
   a ==> a0/0 a1/1
   
  uncurry-rules:
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
   f(c0(),x5) -> c1(x5)
  eta-rules:
   
  problem:
   a1(b1(x)) -> b1(a1(x))
   b1(c1(x)) -> c1(b1(x))
   c1(a1(x)) -> a1(c1(x))
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
   f(c0(),x5) -> c1(x5)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a0] = 1,
    
    [c0] = 2,
    
    [a1](x0) = 2x0 + 2,
    
    [b1](x0) = 2x0 + 2,
    
    [c1](x0) = 2x0 + 2,
    
    [b0] = 1,
    
    [f](x0, x1) = x0 + 2x1 + 1
   orientation:
    a1(b1(x)) = 4x + 6 >= 4x + 6 = b1(a1(x))
    
    b1(c1(x)) = 4x + 6 >= 4x + 6 = c1(b1(x))
    
    c1(a1(x)) = 4x + 6 >= 4x + 6 = a1(c1(x))
    
    f(a0(),x1) = 2x1 + 2 >= 2x1 + 2 = a1(x1)
    
    f(b0(),x3) = 2x3 + 2 >= 2x3 + 2 = b1(x3)
    
    f(c0(),x5) = 2x5 + 3 >= 2x5 + 2 = c1(x5)
   problem:
    a1(b1(x)) -> b1(a1(x))
    b1(c1(x)) -> c1(b1(x))
    c1(a1(x)) -> a1(c1(x))
    f(a0(),x1) -> a1(x1)
    f(b0(),x3) -> b1(x3)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
            [0]
     [a0] = [0]
            [1],
     
                [1 0 1]     [0]
     [a1](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0],
     
                [1 0 1]     [0]
     [b1](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0],
     
                [1 1 1]     [0]
     [c1](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1],
     
            [0]
     [b0] = [0]
            [0],
     
                   [1 0 1]     [1 0 1]     [0]
     [f](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1]
                   [0 0 0]     [1 1 0]     [0]
    orientation:
                 [1 1 1]    [0]    [1 1 1]    [0]            
     a1(b1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = b1(a1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]            
     
                 [1 1 1]    [1]    [1 1 1]    [1]            
     b1(c1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = c1(b1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]            
     
                 [1 1 1]    [1]    [1 1 1]    [1]            
     c1(a1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a1(c1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]            
     
                  [1 0 1]     [1]    [1 0 1]     [0]         
     f(a0(),x1) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a1(x1)
                  [1 1 0]     [0]    [0 1 0]     [0]         
     
                  [1 0 1]     [0]    [1 0 1]     [0]         
     f(b0(),x3) = [1 0 0]x3 + [1] >= [0 0 0]x3 + [1] = b1(x3)
                  [1 1 0]     [0]    [0 1 0]     [0]         
    problem:
     a1(b1(x)) -> b1(a1(x))
     b1(c1(x)) -> c1(b1(x))
     c1(a1(x)) -> a1(c1(x))
     f(b0(),x3) -> b1(x3)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a1](x0) = x0 + 1,
      
      [b1](x0) = x0,
      
      [c1](x0) = x0 + 3,
      
      [b0] = 0,
      
      [f](x0, x1) = x0 + x1 + 1
     orientation:
      a1(b1(x)) = x + 1 >= x + 1 = b1(a1(x))
      
      b1(c1(x)) = x + 3 >= x + 3 = c1(b1(x))
      
      c1(a1(x)) = x + 4 >= x + 4 = a1(c1(x))
      
      f(b0(),x3) = x3 + 1 >= x3 = b1(x3)
     problem:
      a1(b1(x)) -> b1(a1(x))
      b1(c1(x)) -> c1(b1(x))
      c1(a1(x)) -> a1(c1(x))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                  [1 0 1]     [0]
       [a1](x0) = [0 1 0]x0 + [1]
                  [0 0 1]     [0],
       
                  [1 0 0]     [0]
       [b1](x0) = [0 1 1]x0 + [0]
                  [0 0 1]     [1],
       
                    
       [c1](x0) = x0
                    
      orientation:
                   [1 0 1]    [1]    [1 0 1]    [0]            
       a1(b1(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = b1(a1(x))
                   [0 0 1]    [1]    [0 0 1]    [1]            
       
                   [1 0 0]    [0]    [1 0 0]    [0]            
       b1(c1(x)) = [0 1 1]x + [0] >= [0 1 1]x + [0] = c1(b1(x))
                   [0 0 1]    [1]    [0 0 1]    [1]            
       
                   [1 0 1]    [0]    [1 0 1]    [0]            
       c1(a1(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = a1(c1(x))
                   [0 0 1]    [0]    [0 0 1]    [0]            
      problem:
       b1(c1(x)) -> c1(b1(x))
       c1(a1(x)) -> a1(c1(x))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [a1](x0) = 4x0 + 4,
        
        [b1](x0) = 4x0 + 2,
        
        [c1](x0) = 4x0 + 4
       orientation:
        b1(c1(x)) = 16x + 18 >= 16x + 12 = c1(b1(x))
        
        c1(a1(x)) = 16x + 20 >= 16x + 20 = a1(c1(x))
       problem:
        c1(a1(x)) -> a1(c1(x))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                    [1 0 0]     [0]
         [a1](x0) = [0 1 0]x0 + [1]
                    [0 0 0]     [0],
         
                    [1 1 0]  
         [c1](x0) = [0 1 0]x0
                    [0 0 0]  
        orientation:
                     [1 1 0]    [1]    [1 1 0]    [0]            
         c1(a1(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = a1(c1(x))
                     [0 0 0]    [0]    [0 0 0]    [0]            
        problem:
         
        Qed