YES

Problem:
 f(x,y) -> h(x,y)
 f(x,y) -> h(y,x)
 h(x,x) -> x

Proof:
 DP Processor:
  DPs:
   f#(x,y) -> h#(x,y)
   f#(x,y) -> h#(y,x)
  TRS:
   f(x,y) -> h(x,y)
   f(x,y) -> h(y,x)
   h(x,x) -> x
  Usable Rule Processor:
   DPs:
    f#(x,y) -> h#(x,y)
    f#(x,y) -> h#(y,x)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [h#](x0, x1) = 8,
     
     [f#](x0, x1) = -8x0 + x1 + 9
    orientation:
     f#(x,y) = -8x + y + 9 >= 8 = h#(x,y)
     
     f#(x,y) = -8x + y + 9 >= 8 = h#(y,x)
    problem:
     DPs:
      
     TRS:
      
    Qed