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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g#](x0, x1) = x0 + 2x1,
    
    [h](x0, x1) = x0 + 7,
    
    [g](x0, x1) = x0 + 4x1,
    
    [f](x0, x1) = x1 + 1
   orientation:
    g#(f(x,y),z) = y + 2z + 1 >= y + 2z = g#(y,z)
    
    g#(h(x,y),z) = x + 2z + 7 >= x + 2z + 2 = g#(x,f(y,z))
    
    g#(x,h(y,z)) = x + 2y + 14 >= x + 2y = g#(x,y)
    
    g(f(x,y),z) = y + 4z + 1 >= y + 4z + 1 = f(x,g(y,z))
    
    g(h(x,y),z) = x + 4z + 7 >= x + 4z + 4 = g(x,f(y,z))
    
    g(x,h(y,z)) = x + 4y + 28 >= x + 4y + 7 = h(g(x,y),z)
   problem:
    DPs:
     
    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)
   Qed