YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,h(y)) -> f#(h(x),y)
  TRS:
   f(x,g(x)) -> x
   f(x,h(y)) -> f(h(x),y)
  CDG Processor:
   DPs:
    f#(x,h(y)) -> f#(h(x),y)
   TRS:
    f(x,g(x)) -> x
    f(x,h(y)) -> f(h(x),y)
   graph:
    
   Qed