YES

Problem:
 f(x,nil()) -> g(nil(),x)
 f(x,g(y,z)) -> g(f(x,y),z)
 ++(x,nil()) -> x
 ++(x,g(y,z)) -> g(++(x,y),z)
 null(nil()) -> true()
 null(g(x,y)) -> false()
 mem(nil(),y) -> false()
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(x,max(x)) -> not(null(x))
 max(g(g(nil(),x),y)) -> max'(x,y)
 max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())

Proof:
 DP Processor:
  DPs:
   f#(x,g(y,z)) -> f#(x,y)
   ++#(x,g(y,z)) -> ++#(x,y)
   mem#(g(x,y),z) -> mem#(x,z)
   mem#(x,max(x)) -> null#(x)
   max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
  TRS:
   f(x,nil()) -> g(nil(),x)
   f(x,g(y,z)) -> g(f(x,y),z)
   ++(x,nil()) -> x
   ++(x,g(y,z)) -> g(++(x,y),z)
   null(nil()) -> true()
   null(g(x,y)) -> false()
   mem(nil(),y) -> false()
   mem(g(x,y),z) -> or(=(y,z),mem(x,z))
   mem(x,max(x)) -> not(null(x))
   max(g(g(nil(),x),y)) -> max'(x,y)
   max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())
  Usable Rule Processor:
   DPs:
    f#(x,g(y,z)) -> f#(x,y)
    ++#(x,g(y,z)) -> ++#(x,y)
    mem#(g(x,y),z) -> mem#(x,z)
    mem#(x,max(x)) -> null#(x)
    max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
   TRS:
    
   CDG Processor:
    DPs:
     f#(x,g(y,z)) -> f#(x,y)
     ++#(x,g(y,z)) -> ++#(x,y)
     mem#(g(x,y),z) -> mem#(x,z)
     mem#(x,max(x)) -> null#(x)
     max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
    TRS:
     
    graph:
     
    Qed