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))
  EDG 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))
   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)
   Subterm Criterion Processor:
    simple projection:
     pi(f#) = 0
     pi(g#) = 0
    problem:
     DPs:
      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) = 0,
      
      [f#](x0, x1) = 1,
      
      [h](x0) = 0,
      
      [g](x0, x1) = 0,
      
      [f](x0, x1) = 0
     orientation:
      f#(x,y) = 1 >= 0 = g#(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