YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,y) -> g#(x,y)
   g#(h(x),y) -> f#(x,y)
   g#(h(x),y) -> g#(x,y)
  TRS:
   f(x,y) -> g(x,y)
   g(h(x),y) -> h(f(x,y))
   g(h(x),y) -> h(g(x,y))
  Usable Rule Processor:
   DPs:
    f#(x,y) -> g#(x,y)
    g#(h(x),y) -> f#(x,y)
    g#(h(x),y) -> g#(x,y)
   TRS:
    
   EDG Processor:
    DPs:
     f#(x,y) -> g#(x,y)
     g#(h(x),y) -> f#(x,y)
     g#(h(x),y) -> g#(x,y)
    TRS:
     
    graph:
     g#(h(x),y) -> g#(x,y) -> g#(h(x),y) -> f#(x,y)
     g#(h(x),y) -> g#(x,y) -> g#(h(x),y) -> g#(x,y)
     g#(h(x),y) -> f#(x,y) -> f#(x,y) -> g#(x,y)
     f#(x,y) -> g#(x,y) -> g#(h(x),y) -> f#(x,y)
     f#(x,y) -> g#(x,y) -> g#(h(x),y) -> g#(x,y)
    Restore Modifier:
     DPs:
      f#(x,y) -> g#(x,y)
      g#(h(x),y) -> f#(x,y)
      g#(h(x),y) -> g#(x,y)
     TRS:
      f(x,y) -> g(x,y)
      g(h(x),y) -> h(f(x,y))
      g(h(x),y) -> h(g(x,y))
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 5/9
      DPs:
       g#(h(x),y) -> g#(x,y)
       g#(h(x),y) -> f#(x,y)
       f#(x,y) -> g#(x,y)
      TRS:
       f(x,y) -> g(x,y)
       g(h(x),y) -> h(f(x,y))
       g(h(x),y) -> h(g(x,y))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0, x1) = x0,
        
        [f#](x0, x1) = x0 + 1,
        
        [h](x0) = x0 + 1,
        
        [g](x0, x1) = x0,
        
        [f](x0, x1) = x0
       orientation:
        g#(h(x),y) = x + 1 >= x = g#(x,y)
        
        g#(h(x),y) = x + 1 >= x + 1 = f#(x,y)
        
        f#(x,y) = x + 1 >= x = g#(x,y)
        
        f(x,y) = x >= x = g(x,y)
        
        g(h(x),y) = x + 1 >= x + 1 = h(f(x,y))
        
        g(h(x),y) = x + 1 >= x + 1 = h(g(x,y))
       problem:
        DPs:
         g#(h(x),y) -> f#(x,y)
        TRS:
         f(x,y) -> g(x,y)
         g(h(x),y) -> h(f(x,y))
         g(h(x),y) -> h(g(x,y))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [g#](x0, x1) = 1,
         
         [f#](x0, x1) = 0,
         
         [h](x0) = 0,
         
         [g](x0, x1) = 0,
         
         [f](x0, x1) = 0
        orientation:
         g#(h(x),y) = 1 >= 0 = f#(x,y)
         
         f(x,y) = 0 >= 0 = g(x,y)
         
         g(h(x),y) = 0 >= 0 = h(f(x,y))
         
         g(h(x),y) = 0 >= 0 = h(g(x,y))
        problem:
         DPs:
          
         TRS:
          f(x,y) -> g(x,y)
          g(h(x),y) -> h(f(x,y))
          g(h(x),y) -> h(g(x,y))
        Qed