YES

Problem:
 norm(nil()) -> 0()
 norm(g(x,y)) -> s(norm(x))
 f(x,nil()) -> g(nil(),x)
 f(x,g(y,z)) -> g(f(x,y),z)
 rem(nil(),y) -> nil()
 rem(g(x,y),0()) -> g(x,y)
 rem(g(x,y),s(z)) -> rem(x,z)

Proof:
 DP Processor:
  DPs:
   norm#(g(x,y)) -> norm#(x)
   f#(x,g(y,z)) -> f#(x,y)
   rem#(g(x,y),s(z)) -> rem#(x,z)
  TRS:
   norm(nil()) -> 0()
   norm(g(x,y)) -> s(norm(x))
   f(x,nil()) -> g(nil(),x)
   f(x,g(y,z)) -> g(f(x,y),z)
   rem(nil(),y) -> nil()
   rem(g(x,y),0()) -> g(x,y)
   rem(g(x,y),s(z)) -> rem(x,z)
  TDG Processor:
   DPs:
    norm#(g(x,y)) -> norm#(x)
    f#(x,g(y,z)) -> f#(x,y)
    rem#(g(x,y),s(z)) -> rem#(x,z)
   TRS:
    norm(nil()) -> 0()
    norm(g(x,y)) -> s(norm(x))
    f(x,nil()) -> g(nil(),x)
    f(x,g(y,z)) -> g(f(x,y),z)
    rem(nil(),y) -> nil()
    rem(g(x,y),0()) -> g(x,y)
    rem(g(x,y),s(z)) -> rem(x,z)
   graph:
    rem#(g(x,y),s(z)) -> rem#(x,z) -> rem#(g(x,y),s(z)) -> rem#(x,z)
    f#(x,g(y,z)) -> f#(x,y) -> f#(x,g(y,z)) -> f#(x,y)
    norm#(g(x,y)) -> norm#(x) -> norm#(g(x,y)) -> norm#(x)
   CDG Processor:
    DPs:
     norm#(g(x,y)) -> norm#(x)
     f#(x,g(y,z)) -> f#(x,y)
     rem#(g(x,y),s(z)) -> rem#(x,z)
    TRS:
     norm(nil()) -> 0()
     norm(g(x,y)) -> s(norm(x))
     f(x,nil()) -> g(nil(),x)
     f(x,g(y,z)) -> g(f(x,y),z)
     rem(nil(),y) -> nil()
     rem(g(x,y),0()) -> g(x,y)
     rem(g(x,y),s(z)) -> rem(x,z)
    graph:
     
    Qed