YES

Problem:
 f(x,y,w,w,a()) -> g1(x,x,y,w)
 f(x,y,w,a(),a()) -> g1(y,x,x,w)
 f(x,y,a(),a(),w) -> g2(x,y,y,w)
 f(x,y,a(),w,w) -> g2(y,y,x,w)
 g1(x,x,y,a()) -> h(x,y)
 g1(y,x,x,a()) -> h(x,y)
 g2(x,y,y,a()) -> h(x,y)
 g2(y,y,x,a()) -> h(x,y)
 h(x,x) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h](x0, x1) = x0 + x1,
   
   [g2](x0, x1, x2, x3) = 2x0 + x1 + x2 + x3 + 1,
   
   [g1](x0, x1, x2, x3) = x0 + x1 + x2 + x3,
   
   [f](x0, x1, x2, x3, x4) = 3x0 + 3x1 + x2 + 2x3 + x4 + 2,
   
   [a] = 0
  orientation:
   f(x,y,w,w,a()) = 3w + 3x + 3y + 2 >= w + 2x + y = g1(x,x,y,w)
   
   f(x,y,w,a(),a()) = w + 3x + 3y + 2 >= w + 2x + y = g1(y,x,x,w)
   
   f(x,y,a(),a(),w) = w + 3x + 3y + 2 >= w + 2x + 2y + 1 = g2(x,y,y,w)
   
   f(x,y,a(),w,w) = 3w + 3x + 3y + 2 >= w + x + 3y + 1 = g2(y,y,x,w)
   
   g1(x,x,y,a()) = 2x + y >= x + y = h(x,y)
   
   g1(y,x,x,a()) = 2x + y >= x + y = h(x,y)
   
   g2(x,y,y,a()) = 2x + 2y + 1 >= x + y = h(x,y)
   
   g2(y,y,x,a()) = x + 3y + 1 >= x + y = h(x,y)
   
   h(x,x) = 2x >= x = x
  problem:
   g1(x,x,y,a()) -> h(x,y)
   g1(y,x,x,a()) -> h(x,y)
   h(x,x) -> x
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h](x0, x1) = 5x0 + x1 + 2,
    
    [g1](x0, x1, x2, x3) = x0 + 4x1 + x2 + 2x3,
    
    [a] = 1
   orientation:
    g1(x,x,y,a()) = 5x + y + 2 >= 5x + y + 2 = h(x,y)
    
    g1(y,x,x,a()) = 5x + y + 2 >= 5x + y + 2 = h(x,y)
    
    h(x,x) = 6x + 2 >= x = x
   problem:
    g1(x,x,y,a()) -> h(x,y)
    g1(y,x,x,a()) -> h(x,y)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 0 0]  
     [h](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
     
                            [1 0 0]     [1 0 0]     [1 0 0]     [1 0 1]  
     [g1](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3
                            [0 0 0]     [0 0 0]     [0 0 0]     [0 0 0]  ,
     
           [1]
     [a] = [0]
           [1]
    orientation:
                     [2 0 0]    [1 0 0]    [2]    [1 0 0]    [1 0 0]          
     g1(x,x,y,a()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = h(x,y)
                     [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
     
                     [2 0 0]    [1 0 0]    [2]    [1 0 0]    [1 0 0]          
     g1(y,x,x,a()) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = h(x,y)
                     [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]          
    problem:
     
    Qed