YES

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

Proof:
 DP Processor:
  DPs:
   f#(s(X)) -> f#(X)
   g#(cons(0(),Y)) -> g#(Y)
   h#(cons(X,Y)) -> g#(cons(X,Y))
   h#(cons(X,Y)) -> h#(g(cons(X,Y)))
  TRS:
   f(s(X)) -> f(X)
   g(cons(0(),Y)) -> g(Y)
   g(cons(s(X),Y)) -> s(X)
   h(cons(X,Y)) -> h(g(cons(X,Y)))
  EDG Processor:
   DPs:
    f#(s(X)) -> f#(X)
    g#(cons(0(),Y)) -> g#(Y)
    h#(cons(X,Y)) -> g#(cons(X,Y))
    h#(cons(X,Y)) -> h#(g(cons(X,Y)))
   TRS:
    f(s(X)) -> f(X)
    g(cons(0(),Y)) -> g(Y)
    g(cons(s(X),Y)) -> s(X)
    h(cons(X,Y)) -> h(g(cons(X,Y)))
   graph:
    h#(cons(X,Y)) -> g#(cons(X,Y)) -> g#(cons(0(),Y)) -> g#(Y)
    g#(cons(0(),Y)) -> g#(Y) -> g#(cons(0(),Y)) -> g#(Y)
    f#(s(X)) -> f#(X) -> f#(s(X)) -> f#(X)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 3/16
    DPs:
     f#(s(X)) -> f#(X)
    TRS:
     f(s(X)) -> f(X)
     g(cons(0(),Y)) -> g(Y)
     g(cons(s(X),Y)) -> s(X)
     h(cons(X,Y)) -> h(g(cons(X,Y)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0 + 1,
      
      [h](x0) = 0,
      
      [g](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [0] = 0,
      
      [f](x0) = 0,
      
      [s](x0) = x0 + 1
     orientation:
      f#(s(X)) = X + 2 >= X + 1 = f#(X)
      
      f(s(X)) = 0 >= 0 = f(X)
      
      g(cons(0(),Y)) = Y >= Y = g(Y)
      
      g(cons(s(X),Y)) = X + Y + 1 >= X + 1 = s(X)
      
      h(cons(X,Y)) = 0 >= 0 = h(g(cons(X,Y)))
     problem:
      DPs:
       
      TRS:
       f(s(X)) -> f(X)
       g(cons(0(),Y)) -> g(Y)
       g(cons(s(X),Y)) -> s(X)
       h(cons(X,Y)) -> h(g(cons(X,Y)))
     Qed
    
    DPs:
     g#(cons(0(),Y)) -> g#(Y)
    TRS:
     f(s(X)) -> f(X)
     g(cons(0(),Y)) -> g(Y)
     g(cons(s(X),Y)) -> s(X)
     h(cons(X,Y)) -> h(g(cons(X,Y)))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [h](x0) = x0,
      
      [g](x0) = 0,
      
      [cons](x0, x1) = x0 + x1 + 1,
      
      [0] = 1,
      
      [f](x0) = 0,
      
      [s](x0) = 0
     orientation:
      g#(cons(0(),Y)) = Y + 2 >= Y = g#(Y)
      
      f(s(X)) = 0 >= 0 = f(X)
      
      g(cons(0(),Y)) = 0 >= 0 = g(Y)
      
      g(cons(s(X),Y)) = 0 >= 0 = s(X)
      
      h(cons(X,Y)) = X + Y + 1 >= 0 = h(g(cons(X,Y)))
     problem:
      DPs:
       
      TRS:
       f(s(X)) -> f(X)
       g(cons(0(),Y)) -> g(Y)
       g(cons(s(X),Y)) -> s(X)
       h(cons(X,Y)) -> h(g(cons(X,Y)))
     Qed