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))
  TDG 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) -> g#(x,y)
    g#(h(x),y) -> g#(x,y) -> g#(h(x),y) -> f#(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) -> g#(x,y)
    f#(x,y) -> g#(x,y) -> g#(h(x),y) -> f#(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))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 5/1