YES
TRS:
 {             f(x, g(y, z)) -> g(f(x, y), z),
                 f(x, nil()) -> g(nil(), x),
              ++(x, g(y, z)) -> g(++(x, y), z),
                ++(x, nil()) -> x,
               null(g(x, y)) -> false(),
                 null(nil()) -> true(),
              mem(x, max(x)) -> not(null(x)),
             mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
               mem(nil(), y) -> false(),
  max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
      max(g(g(nil(), x), y)) -> max'(x, y)}
 DP:
  Strict:
   {             f#(x, g(y, z)) -> f#(x, y),
                ++#(x, g(y, z)) -> ++#(x, y),
                mem#(x, max(x)) -> null#(x),
               mem#(g(x, y), z) -> mem#(x, z),
    max#(g(g(g(x, y), z), u())) -> max#(g(g(x, y), z))}
  Weak:
  {             f(x, g(y, z)) -> g(f(x, y), z),
                  f(x, nil()) -> g(nil(), x),
               ++(x, g(y, z)) -> g(++(x, y), z),
                 ++(x, nil()) -> x,
                null(g(x, y)) -> false(),
                  null(nil()) -> true(),
               mem(x, max(x)) -> not(null(x)),
              mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
                mem(nil(), y) -> false(),
   max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
       max(g(g(nil(), x), y)) -> max'(x, y)}
  EDG:
   {(mem#(g(x, y), z) -> mem#(x, z), mem#(g(x, y), z) -> mem#(x, z))
    (mem#(g(x, y), z) -> mem#(x, z), mem#(x, max(x)) -> null#(x))
    (++#(x, g(y, z)) -> ++#(x, y), ++#(x, g(y, z)) -> ++#(x, y))
    (max#(g(g(g(x, y), z), u())) -> max#(g(g(x, y), z)), max#(g(g(g(x, y), z), u())) -> max#(g(g(x, y), z)))
    (f#(x, g(y, z)) -> f#(x, y), f#(x, g(y, z)) -> f#(x, y))}
   SCCS:
    Scc:
     {max#(g(g(g(x, y), z), u())) -> max#(g(g(x, y), z))}
    Scc:
     {mem#(g(x, y), z) -> mem#(x, z)}
    Scc:
     {++#(x, g(y, z)) -> ++#(x, y)}
    Scc:
     {f#(x, g(y, z)) -> f#(x, y)}
    SCC:
     Strict:
      {max#(g(g(g(x, y), z), u())) -> max#(g(g(x, y), z))}
     Weak:
     {             f(x, g(y, z)) -> g(f(x, y), z),
                     f(x, nil()) -> g(nil(), x),
                  ++(x, g(y, z)) -> g(++(x, y), z),
                    ++(x, nil()) -> x,
                   null(g(x, y)) -> false(),
                     null(nil()) -> true(),
                  mem(x, max(x)) -> not(null(x)),
                 mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
                   mem(nil(), y) -> false(),
      max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
          max(g(g(nil(), x), y)) -> max'(x, y)}
     SPSC:
      Simple Projection:
       pi(max#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {mem#(g(x, y), z) -> mem#(x, z)}
     Weak:
     {             f(x, g(y, z)) -> g(f(x, y), z),
                     f(x, nil()) -> g(nil(), x),
                  ++(x, g(y, z)) -> g(++(x, y), z),
                    ++(x, nil()) -> x,
                   null(g(x, y)) -> false(),
                     null(nil()) -> true(),
                  mem(x, max(x)) -> not(null(x)),
                 mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
                   mem(nil(), y) -> false(),
      max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
          max(g(g(nil(), x), y)) -> max'(x, y)}
     SPSC:
      Simple Projection:
       pi(mem#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {++#(x, g(y, z)) -> ++#(x, y)}
     Weak:
     {             f(x, g(y, z)) -> g(f(x, y), z),
                     f(x, nil()) -> g(nil(), x),
                  ++(x, g(y, z)) -> g(++(x, y), z),
                    ++(x, nil()) -> x,
                   null(g(x, y)) -> false(),
                     null(nil()) -> true(),
                  mem(x, max(x)) -> not(null(x)),
                 mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
                   mem(nil(), y) -> false(),
      max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
          max(g(g(nil(), x), y)) -> max'(x, y)}
     SPSC:
      Simple Projection:
       pi(++#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(x, g(y, z)) -> f#(x, y)}
     Weak:
     {             f(x, g(y, z)) -> g(f(x, y), z),
                     f(x, nil()) -> g(nil(), x),
                  ++(x, g(y, z)) -> g(++(x, y), z),
                    ++(x, nil()) -> x,
                   null(g(x, y)) -> false(),
                     null(nil()) -> true(),
                  mem(x, max(x)) -> not(null(x)),
                 mem(g(x, y), z) -> or(=(y, z), mem(x, z)),
                   mem(nil(), y) -> false(),
      max(g(g(g(x, y), z), u())) -> max'(max(g(g(x, y), z)), u()),
          max(g(g(nil(), x), y)) -> max'(x, y)}
     SPSC:
      Simple Projection:
       pi(f#) = 1
      Strict:
       {}
      Qed