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:
 DP Processor:
  DPs:
   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)
  TRS:
   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
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [h#](x0, x1) = [0],
    
    [g2#](x0, x1, x2, x3) = [1 0 0]x0 + [1 0 0]x2 + [1],
    
    [g1#](x0, x1, x2, x3) = [1 0 0]x3,
    
    [f#](x0, x1, x2, x3, x4) = [1 1 0]x0 + [1 0 0]x1 + [1 0 0]x2 + [0 1 0]x3 + [0 1 1]x4 + [1],
    
                  [0 0 0]     [1 0 0]     [1]
    [h](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                  [1 0 1]     [1 0 0]     [0],
    
                           [1 0 0]     [1 0 0]     [1]
    [g2](x0, x1, x2, x3) = [0 1 0]x0 + [0 1 0]x2 + [0]
                           [1 0 1]     [1 0 1]     [1],
    
                           [1 0 0]     [1 0 0]     [0 1 0]     [1]
    [g1](x0, x1, x2, x3) = [0 1 0]x0 + [0 1 0]x2 + [0 0 0]x3 + [1]
                           [1 0 1]     [1 0 1]     [0 0 0]     [1],
    
                              [1 0 0]     [1 0 0]     [0 1 0]     [1]
    [f](x0, x1, x2, x3, x4) = [0 1 0]x0 + [0 1 0]x1 + [0 0 0]x2 + [1]
                              [1 0 1]     [1 0 1]     [0 0 0]     [1],
    
          [1]
    [a] = [0]
          [0]
   orientation:
    f#(x,y,w,w,a()) = [1 1 0]w + [1 1 0]x + [1 0 0]y + [1] >= [1 0 0]w = g1#(x,x,y,w)
    
    f#(x,y,w,a(),a()) = [1 0 0]w + [1 1 0]x + [1 0 0]y + [1] >= [1 0 0]w = g1#(y,x,x,w)
    
    f#(x,y,a(),a(),w) = [0 1 1]w + [1 1 0]x + [1 0 0]y + [2] >= [1 0 0]x + [1 0 0]y + [1] = g2#(x,y,y,w)
    
    f#(x,y,a(),w,w) = [0 2 1]w + [1 1 0]x + [1 0 0]y + [2] >= [1 0 0]x + [1 0 0]y + [1] = g2#(y,y,x,w)
    
    g1#(x,x,y,a()) = [1] >= [0] = h#(x,y)
    
    g1#(y,x,x,a()) = [1] >= [0] = h#(x,y)
    
    g2#(x,y,y,a()) = [1 0 0]x + [1 0 0]y + [1] >= [0] = h#(x,y)
    
    g2#(y,y,x,a()) = [1 0 0]x + [1 0 0]y + [1] >= [0] = h#(x,y)
    
                     [0 1 0]    [1 0 0]    [1 0 0]    [1]    [0 1 0]    [1 0 0]    [1 0 0]    [1]              
    f(x,y,w,w,a()) = [0 0 0]w + [0 1 0]x + [0 1 0]y + [1] >= [0 0 0]w + [0 1 0]x + [0 1 0]y + [1] = g1(x,x,y,w)
                     [0 0 0]    [1 0 1]    [1 0 1]    [1]    [0 0 0]    [1 0 1]    [1 0 1]    [1]              
    
                       [0 1 0]    [1 0 0]    [1 0 0]    [1]    [0 1 0]    [1 0 0]    [1 0 0]    [1]              
    f(x,y,w,a(),a()) = [0 0 0]w + [0 1 0]x + [0 1 0]y + [1] >= [0 0 0]w + [0 1 0]x + [0 1 0]y + [1] = g1(y,x,x,w)
                       [0 0 0]    [1 0 1]    [1 0 1]    [1]    [0 0 0]    [1 0 1]    [1 0 1]    [1]              
    
                       [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]              
    f(x,y,a(),a(),w) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 1 0]y + [0] = g2(x,y,y,w)
                       [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]    [1]              
    
                     [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]              
    f(x,y,a(),w,w) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 1 0]y + [0] = g2(y,y,x,w)
                     [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 1]    [1]              
    
                    [1 0 0]    [1 0 0]    [1]    [0 0 0]    [1 0 0]    [1]         
    g1(x,x,y,a()) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 0 0]y + [0] = h(x,y)
                    [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 0]    [0]         
    
                    [1 0 0]    [1 0 0]    [1]    [0 0 0]    [1 0 0]    [1]         
    g1(y,x,x,a()) = [0 1 0]x + [0 1 0]y + [1] >= [0 1 0]x + [0 0 0]y + [0] = h(x,y)
                    [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 0]    [0]         
    
                    [1 0 0]    [1 0 0]    [1]    [0 0 0]    [1 0 0]    [1]         
    g2(x,y,y,a()) = [0 1 0]x + [0 1 0]y + [0] >= [0 1 0]x + [0 0 0]y + [0] = h(x,y)
                    [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 0]    [0]         
    
                    [1 0 0]    [1 0 0]    [1]    [0 0 0]    [1 0 0]    [1]         
    g2(y,y,x,a()) = [0 1 0]x + [0 1 0]y + [0] >= [0 1 0]x + [0 0 0]y + [0] = h(x,y)
                    [1 0 1]    [1 0 1]    [1]    [1 0 1]    [1 0 0]    [0]         
    
             [1 0 0]    [1]         
    h(x,x) = [0 1 0]x + [0] >= x = x
             [2 0 1]    [0]         
   problem:
    DPs:
     
    TRS:
     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
   Qed