YES

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

Proof:
 DP Processor:
  DPs:
   g#(f(x),y) -> h#(x,y)
   h#(x,y) -> g#(x,f(y))
  TRS:
   g(f(x),y) -> f(h(x,y))
   h(x,y) -> g(x,f(y))
  EDG Processor:
   DPs:
    g#(f(x),y) -> h#(x,y)
    h#(x,y) -> g#(x,f(y))
   TRS:
    g(f(x),y) -> f(h(x,y))
    h(x,y) -> g(x,f(y))
   graph:
    h#(x,y) -> g#(x,f(y)) -> g#(f(x),y) -> h#(x,y)
    g#(f(x),y) -> h#(x,y) -> h#(x,y) -> g#(x,f(y))
   Subterm Criterion Processor:
    simple projection:
     pi(g#) = 0
     pi(h#) = 0
    problem:
     DPs:
      h#(x,y) -> g#(x,f(y))
     TRS:
      g(f(x),y) -> f(h(x,y))
      h(x,y) -> g(x,f(y))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [h#](x0, x1) = 1,
      
      [g#](x0, x1) = 0,
      
      [h](x0, x1) = 0,
      
      [g](x0, x1) = 0,
      
      [f](x0) = 0
     orientation:
      h#(x,y) = 1 >= 0 = g#(x,f(y))
      
      g(f(x),y) = 0 >= 0 = f(h(x,y))
      
      h(x,y) = 0 >= 0 = g(x,f(y))
     problem:
      DPs:
       
      TRS:
       g(f(x),y) -> f(h(x,y))
       h(x,y) -> g(x,f(y))
     Qed