YES

Problem:
 h(X,Z) -> f(X,s(X),Z)
 f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
 g(0(),Y) -> 0()
 g(X,s(Y)) -> g(X,Y)

Proof:
 DP Processor:
  DPs:
   h#(X,Z) -> f#(X,s(X),Z)
   f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
   g#(X,s(Y)) -> g#(X,Y)
  TRS:
   h(X,Z) -> f(X,s(X),Z)
   f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
   g(0(),Y) -> 0()
   g(X,s(Y)) -> g(X,Y)
  Usable Rule Processor:
   DPs:
    h#(X,Z) -> f#(X,s(X),Z)
    f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
    g#(X,s(Y)) -> g#(X,Y)
   TRS:
    g(0(),Y) -> 0()
    g(X,s(Y)) -> g(X,Y)
   CDG Processor:
    DPs:
     h#(X,Z) -> f#(X,s(X),Z)
     f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
     g#(X,s(Y)) -> g#(X,Y)
    TRS:
     g(0(),Y) -> 0()
     g(X,s(Y)) -> g(X,Y)
    graph:
     g#(X,s(Y)) -> g#(X,Y) -> g#(X,s(Y)) -> g#(X,Y)
     f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y)) -> h#(X,Z) -> f#(X,s(X),Z)
    Restore Modifier:
     DPs:
      h#(X,Z) -> f#(X,s(X),Z)
      f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
      g#(X,s(Y)) -> g#(X,Y)
     TRS:
      h(X,Z) -> f(X,s(X),Z)
      f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
      g(0(),Y) -> 0()
      g(X,s(Y)) -> g(X,Y)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/9
      DPs:
       g#(X,s(Y)) -> g#(X,Y)
      TRS:
       h(X,Z) -> f(X,s(X),Z)
       f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
       g(0(),Y) -> 0()
       g(X,s(Y)) -> g(X,Y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0, x1) = x1 + 1,
        
        [0] = 0,
        
        [g](x0, x1) = 0,
        
        [f](x0, x1, x2) = 0,
        
        [s](x0) = x0 + 1,
        
        [h](x0, x1) = 0
       orientation:
        g#(X,s(Y)) = Y + 2 >= Y + 1 = g#(X,Y)
        
        h(X,Z) = 0 >= 0 = f(X,s(X),Z)
        
        f(X,Y,g(X,Y)) = 0 >= 0 = h(0(),g(X,Y))
        
        g(0(),Y) = 0 >= 0 = 0()
        
        g(X,s(Y)) = 0 >= 0 = g(X,Y)
       problem:
        DPs:
         
        TRS:
         h(X,Z) -> f(X,s(X),Z)
         f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
         g(0(),Y) -> 0()
         g(X,s(Y)) -> g(X,Y)
       Qed