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)
  Usable Rule Processor:
   DPs:
    f#(x,h(y)) -> f#(h(x),y)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0, x1) = x1,
     
     [h](x0) = 1x0 + -2
    orientation:
     f#(x,h(y)) = 1y + -2 >= y = f#(h(x),y)
    problem:
     DPs:
      
     TRS:
      
    Qed