YES
Time: 0.001331
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)}
 DP:
  DP:
   {     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)}
  EDG:
   {(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)}
   SCCS (3):
    Scc:
     {rem#(g(x, y), s z) -> rem#(x, z)}
    Scc:
     {f#(x, g(y, z)) -> f#(x, y)}
    Scc:
     {norm# g(x, y) -> norm# x}
    SCC (1):
     Strict:
      {rem#(g(x, y), s z) -> rem#(x, z)}
     Weak:
     {       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)}
     SPSC:
      Simple Projection:
       pi(rem#) = 1
      Strict:
       {}
      Qed
    SCC (1):
     Strict:
      {f#(x, g(y, z)) -> f#(x, y)}
     Weak:
     {       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)}
     SPSC:
      Simple Projection:
       pi(f#) = 1
      Strict:
       {}
      Qed
    SCC (1):
     Strict:
      {norm# g(x, y) -> norm# x}
     Weak:
     {       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)}
     SPSC:
      Simple Projection:
       pi(norm#) = 0
      Strict:
       {}
      Qed