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)
  Usable Rule 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:
    
   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:
     
    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)
    Restore Modifier:
     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)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 8/9
      DPs:
       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)
      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:
       dimension: 1
       interpretation:
        [g#](x0, x1) = x1,
        
        [h](x0, x1) = x0 + 1,
        
        [g](x0, x1) = x1,
        
        [f](x0, x1) = x1
       orientation:
        g#(h(x,y),z) = z >= z = g#(x,f(y,z))
        
        g#(f(x,y),z) = z >= z = g#(y,z)
        
        g#(x,h(y,z)) = y + 1 >= y = g#(x,y)
        
        g(f(x,y),z) = z >= z = f(x,g(y,z))
        
        g(h(x,y),z) = z >= z = g(x,f(y,z))
        
        g(x,h(y,z)) = y + 1 >= y + 1 = h(g(x,y),z)
       problem:
        DPs:
         g#(h(x,y),z) -> g#(x,f(y,z))
         g#(f(x,y),z) -> g#(y,z)
        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:
        dimension: 1
        interpretation:
         [g#](x0, x1) = x0,
         
         [h](x0, x1) = x0,
         
         [g](x0, x1) = x0 + 1,
         
         [f](x0, x1) = x1 + 1
        orientation:
         g#(h(x,y),z) = x >= x = g#(x,f(y,z))
         
         g#(f(x,y),z) = y + 1 >= y = g#(y,z)
         
         g(f(x,y),z) = y + 2 >= y + 2 = f(x,g(y,z))
         
         g(h(x,y),z) = x + 1 >= x + 1 = g(x,f(y,z))
         
         g(x,h(y,z)) = x + 1 >= x + 1 = h(g(x,y),z)
        problem:
         DPs:
          g#(h(x,y),z) -> g#(x,f(y,z))
         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:
         dimension: 1
         interpretation:
          [g#](x0, x1) = x0,
          
          [h](x0, x1) = x0 + 1,
          
          [g](x0, x1) = x1,
          
          [f](x0, x1) = x1
         orientation:
          g#(h(x,y),z) = x + 1 >= x = g#(x,f(y,z))
          
          g(f(x,y),z) = z >= z = f(x,g(y,z))
          
          g(h(x,y),z) = z >= z = g(x,f(y,z))
          
          g(x,h(y,z)) = y + 1 >= y + 1 = 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