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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [rem#](x0, x1) = 4x0 + 4,
    
    [f#](x0, x1) = 2x1,
    
    [norm#](x0) = 5x0,
    
    [rem](x0, x1) = 2x0 + 3x1 + 1,
    
    [f](x0, x1) = 6x1,
    
    [s](x0) = 7x0,
    
    [g](x0, x1) = 4x0 + 4,
    
    [0] = 0,
    
    [norm](x0) = 0,
    
    [nil] = 2
   orientation:
    norm#(g(x,y)) = 20x + 20 >= 5x = norm#(x)
    
    f#(x,g(y,z)) = 8y + 8 >= 2y = f#(x,y)
    
    rem#(g(x,y),s(z)) = 16x + 20 >= 4x + 4 = rem#(x,z)
    
    norm(nil()) = 0 >= 0 = 0()
    
    norm(g(x,y)) = 0 >= 0 = s(norm(x))
    
    f(x,nil()) = 12 >= 12 = g(nil(),x)
    
    f(x,g(y,z)) = 24y + 24 >= 24y + 4 = g(f(x,y),z)
    
    rem(nil(),y) = 3y + 5 >= 2 = nil()
    
    rem(g(x,y),0()) = 8x + 9 >= 4x + 4 = g(x,y)
    
    rem(g(x,y),s(z)) = 8x + 21z + 9 >= 2x + 3z + 1 = rem(x,z)
   problem:
    DPs:
     
    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)
   Qed