YES

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

Proof:
 DP Processor:
  DPs:
   g#(f(x,y),z) -> g#(y,z)
   g#(h(x,y),z) -> g#(x,f(y,z))
   g#(x,h(y,z)) -> g#(x,y)
  TRS:
   g(f(x,y),z) -> f(x,g(y,z))
   g(h(x,y),z) -> g(x,f(y,z))
   g(x,h(y,z)) -> h(g(x,y),z)
  EDG Processor:
   DPs:
    g#(f(x,y),z) -> g#(y,z)
    g#(h(x,y),z) -> g#(x,f(y,z))
    g#(x,h(y,z)) -> g#(x,y)
   TRS:
    g(f(x,y),z) -> f(x,g(y,z))
    g(h(x,y),z) -> g(x,f(y,z))
    g(x,h(y,z)) -> h(g(x,y),z)
   graph:
    g#(h(x,y),z) -> g#(x,f(y,z)) -> g#(f(x,y),z) -> g#(y,z)
    g#(h(x,y),z) -> g#(x,f(y,z)) -> g#(h(x,y),z) -> g#(x,f(y,z))
    g#(f(x,y),z) -> g#(y,z) -> g#(f(x,y),z) -> g#(y,z)
    g#(f(x,y),z) -> g#(y,z) -> g#(h(x,y),z) -> g#(x,f(y,z))
    g#(f(x,y),z) -> g#(y,z) -> g#(x,h(y,z)) -> g#(x,y)
    g#(x,h(y,z)) -> g#(x,y) -> g#(f(x,y),z) -> g#(y,z)
    g#(x,h(y,z)) -> g#(x,y) -> g#(h(x,y),z) -> g#(x,f(y,z))
    g#(x,h(y,z)) -> g#(x,y) -> g#(x,h(y,z)) -> g#(x,y)
   CDG Processor:
    DPs:
     g#(f(x,y),z) -> g#(y,z)
     g#(h(x,y),z) -> g#(x,f(y,z))
     g#(x,h(y,z)) -> g#(x,y)
    TRS:
     g(f(x,y),z) -> f(x,g(y,z))
     g(h(x,y),z) -> g(x,f(y,z))
     g(x,h(y,z)) -> h(g(x,y),z)
    graph:
     
    Qed