YES

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

Proof:
 Uncurry Processor:
  a1(a1(x)) -> c1(b1(x))
  b1(b1(x)) -> a1(c1(x))
  c1(c1(x)) -> b1(a1(x))
  f(a(),x1) -> a1(x1)
  f(c(),x1) -> c1(x1)
  f(b(),x1) -> b1(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [b1](x0) = x0,
    
    [c1](x0) = x0,
    
    [a1](x0) = x0,
    
    [b] = 1,
    
    [c] = 0,
    
    [f](x0, x1) = x0 + x1,
    
    [a] = 0
   orientation:
    a1(a1(x)) = x >= x = c1(b1(x))
    
    b1(b1(x)) = x >= x = a1(c1(x))
    
    c1(c1(x)) = x >= x = b1(a1(x))
    
    f(a(),x1) = x1 >= x1 = a1(x1)
    
    f(c(),x1) = x1 >= x1 = c1(x1)
    
    f(b(),x1) = x1 + 1 >= x1 = b1(x1)
   problem:
    a1(a1(x)) -> c1(b1(x))
    b1(b1(x)) -> a1(c1(x))
    c1(c1(x)) -> b1(a1(x))
    f(a(),x1) -> a1(x1)
    f(c(),x1) -> c1(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [b1](x0) = 4x0 + 2,
     
     [c1](x0) = 4x0 + 2,
     
     [a1](x0) = 4x0 + 2,
     
     [c] = 1,
     
     [f](x0, x1) = x0 + 4x1 + 2,
     
     [a] = 0
    orientation:
     a1(a1(x)) = 16x + 10 >= 16x + 10 = c1(b1(x))
     
     b1(b1(x)) = 16x + 10 >= 16x + 10 = a1(c1(x))
     
     c1(c1(x)) = 16x + 10 >= 16x + 10 = b1(a1(x))
     
     f(a(),x1) = 4x1 + 2 >= 4x1 + 2 = a1(x1)
     
     f(c(),x1) = 4x1 + 3 >= 4x1 + 2 = c1(x1)
    problem:
     a1(a1(x)) -> c1(b1(x))
     b1(b1(x)) -> a1(c1(x))
     c1(c1(x)) -> b1(a1(x))
     f(a(),x1) -> a1(x1)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [b1](x0) = x0,
      
      [c1](x0) = x0,
      
      [a1](x0) = x0,
      
      [f](x0, x1) = x0 + x1 + 3,
      
      [a] = 2
     orientation:
      a1(a1(x)) = x >= x = c1(b1(x))
      
      b1(b1(x)) = x >= x = a1(c1(x))
      
      c1(c1(x)) = x >= x = b1(a1(x))
      
      f(a(),x1) = x1 + 5 >= x1 = a1(x1)
     problem:
      a1(a1(x)) -> c1(b1(x))
      b1(b1(x)) -> a1(c1(x))
      c1(c1(x)) -> b1(a1(x))
     Bounds Processor:
      bound: 0
      enrichment: match
      automaton:
       final states: {6,4,1}
       transitions:
        f70() -> 2*
        c{1,0}(2) -> 5*
        c{1,0}(3) -> 1*
        b{1,0}(7) -> 6*
        b{1,0}(2) -> 3*
        a{1,0}(5) -> 4*
        a{1,0}(2) -> 7*
        1 -> 7*
        4 -> 3*
        6 -> 5*
      problem:
       
      Qed