YES

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

Proof:
 Uncurry Processor:
  a1(x) -> b1(c1(x))
  a1(b1(x)) -> b1(a1(x))
  d1(c1(x)) -> d1(a1(x))
  a1(c1(x)) -> c1(a1(x))
  f(a(),x1) -> a1(x1)
  f(b(),x1) -> b1(x1)
  f(c(),x1) -> c1(x1)
  f(d(),x1) -> d1(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [d1](x0) = 4x0,
    
    [c1](x0) = 4x0,
    
    [b1](x0) = x0,
    
    [a1](x0) = 4x0,
    
    [d] = 2,
    
    [c] = 7,
    
    [b] = 0,
    
    [f](x0, x1) = x0 + 4x1,
    
    [a] = 0
   orientation:
    a1(x) = 4x >= 4x = b1(c1(x))
    
    a1(b1(x)) = 4x >= 4x = b1(a1(x))
    
    d1(c1(x)) = 16x >= 16x = d1(a1(x))
    
    a1(c1(x)) = 16x >= 16x = c1(a1(x))
    
    f(a(),x1) = 4x1 >= 4x1 = a1(x1)
    
    f(b(),x1) = 4x1 >= x1 = b1(x1)
    
    f(c(),x1) = 4x1 + 7 >= 4x1 = c1(x1)
    
    f(d(),x1) = 4x1 + 2 >= 4x1 = d1(x1)
   problem:
    a1(x) -> b1(c1(x))
    a1(b1(x)) -> b1(a1(x))
    d1(c1(x)) -> d1(a1(x))
    a1(c1(x)) -> c1(a1(x))
    f(a(),x1) -> a1(x1)
    f(b(),x1) -> b1(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [d1](x0) = x0 + 4,
     
     [c1](x0) = x0 + 4,
     
     [b1](x0) = x0,
     
     [a1](x0) = x0 + 4,
     
     [b] = 3,
     
     [f](x0, x1) = x0 + x1 + 4,
     
     [a] = 0
    orientation:
     a1(x) = x + 4 >= x + 4 = b1(c1(x))
     
     a1(b1(x)) = x + 4 >= x + 4 = b1(a1(x))
     
     d1(c1(x)) = x + 8 >= x + 8 = d1(a1(x))
     
     a1(c1(x)) = x + 8 >= x + 8 = c1(a1(x))
     
     f(a(),x1) = x1 + 4 >= x1 + 4 = a1(x1)
     
     f(b(),x1) = x1 + 7 >= x1 = b1(x1)
    problem:
     a1(x) -> b1(c1(x))
     a1(b1(x)) -> b1(a1(x))
     d1(c1(x)) -> d1(a1(x))
     a1(c1(x)) -> c1(a1(x))
     f(a(),x1) -> a1(x1)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [d1](x0) = x0 + 2,
      
      [c1](x0) = x0,
      
      [b1](x0) = x0,
      
      [a1](x0) = x0,
      
      [f](x0, x1) = x0 + x1 + 1,
      
      [a] = 0
     orientation:
      a1(x) = x >= x = b1(c1(x))
      
      a1(b1(x)) = x >= x = b1(a1(x))
      
      d1(c1(x)) = x + 2 >= x + 2 = d1(a1(x))
      
      a1(c1(x)) = x >= x = c1(a1(x))
      
      f(a(),x1) = x1 + 1 >= x1 = a1(x1)
     problem:
      a1(x) -> b1(c1(x))
      a1(b1(x)) -> b1(a1(x))
      d1(c1(x)) -> d1(a1(x))
      a1(c1(x)) -> c1(a1(x))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                  [1 1 0]  
       [d1](x0) = [0 0 0]x0
                  [0 1 0]  ,
       
                  [1 0 0]     [0]
       [c1](x0) = [0 1 0]x0 + [1]
                  [0 1 0]     [0],
       
                  [1 0 0]  
       [b1](x0) = [0 0 1]x0
                  [0 0 0]  ,
       
                       [1]
       [a1](x0) = x0 + [0]
                       [0]
      orientation:
                   [1]    [1 0 0]             
       a1(x) = x + [0] >= [0 1 0]x = b1(c1(x))
                   [0]    [0 0 0]             
       
                   [1 0 0]    [1]    [1 0 0]    [1]            
       a1(b1(x)) = [0 0 1]x + [0] >= [0 0 1]x + [0] = b1(a1(x))
                   [0 0 0]    [0]    [0 0 0]    [0]            
       
                   [1 1 0]    [1]    [1 1 0]    [1]            
       d1(c1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = d1(a1(x))
                   [0 1 0]    [1]    [0 1 0]    [0]            
       
                   [1 0 0]    [1]    [1 0 0]    [1]            
       a1(c1(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = c1(a1(x))
                   [0 1 0]    [0]    [0 1 0]    [0]            
      problem:
       a1(b1(x)) -> b1(a1(x))
       d1(c1(x)) -> d1(a1(x))
       a1(c1(x)) -> c1(a1(x))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [d1](x0) = 2x0,
        
        [c1](x0) = x0 + 4,
        
        [b1](x0) = 4x0 + 1,
        
        [a1](x0) = x0
       orientation:
        a1(b1(x)) = 4x + 1 >= 4x + 1 = b1(a1(x))
        
        d1(c1(x)) = 2x + 8 >= 2x = d1(a1(x))
        
        a1(c1(x)) = x + 4 >= x + 4 = c1(a1(x))
       problem:
        a1(b1(x)) -> b1(a1(x))
        a1(c1(x)) -> c1(a1(x))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [c1](x0) = 4x0 + 4,
         
         [b1](x0) = x0,
         
         [a1](x0) = 5x0 + 5
        orientation:
         a1(b1(x)) = 5x + 5 >= 5x + 5 = b1(a1(x))
         
         a1(c1(x)) = 20x + 25 >= 20x + 24 = c1(a1(x))
        problem:
         a1(b1(x)) -> b1(a1(x))
        Matrix Interpretation Processor: dim=3
         
         interpretation:
                     [1 0 0]     [0]
          [b1](x0) = [0 1 0]x0 + [1]
                     [0 0 0]     [1],
          
                     [1 1 0]  
          [a1](x0) = [0 1 0]x0
                     [0 0 1]  
         orientation:
                      [1 1 0]    [1]    [1 1 0]    [0]            
          a1(b1(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = b1(a1(x))
                      [0 0 0]    [1]    [0 0 0]    [1]            
         problem:
          
         Qed