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
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [h#](x0, x1) = 4x0 + x1 + -14,
    
    [f#](x0, x1) = 5x0 + 5x1 + 0,
    
    [h](x0, x1) = 8x0 + -9x1 + 8,
    
    [f](x0, x1) = 9x0 + 9x1 + 12
   orientation:
    f#(x,y) = 5x + 5y + 0 >= 4x + y + -14 = h#(x,y)
    
    f#(x,y) = 5x + 5y + 0 >= x + 4y + -14 = h#(y,x)
    
    f(x,y) = 9x + 9y + 12 >= 8x + -9y + 8 = h(x,y)
    
    f(x,y) = 9x + 9y + 12 >= -9x + 8y + 8 = h(y,x)
    
    h(x,x) = 8x + 8 >= x = x
   problem:
    DPs:
     
    TRS:
     f(x,y) -> h(x,y)
     f(x,y) -> h(y,x)
     h(x,x) -> x
   Qed