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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [rem](x0, x1) = 2x0 + x1 + 4,
   
   [f](x0, x1) = x0 + 5x1,
   
   [s](x0) = x0,
   
   [g](x0, x1) = x0 + x1,
   
   [0] = 0,
   
   [norm](x0) = x0,
   
   [nil] = 4
  orientation:
   norm(nil()) = 4 >= 0 = 0()
   
   norm(g(x,y)) = x + y >= x = s(norm(x))
   
   f(x,nil()) = x + 20 >= x + 4 = g(nil(),x)
   
   f(x,g(y,z)) = x + 5y + 5z >= x + 5y + z = g(f(x,y),z)
   
   rem(nil(),y) = y + 12 >= 4 = nil()
   
   rem(g(x,y),0()) = 2x + 2y + 4 >= x + y = g(x,y)
   
   rem(g(x,y),s(z)) = 2x + 2y + z + 4 >= 2x + z + 4 = rem(x,z)
  problem:
   norm(g(x,y)) -> s(norm(x))
   f(x,g(y,z)) -> g(f(x,y),z)
   rem(g(x,y),s(z)) -> rem(x,z)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [rem](x0, x1) = 7x0 + 3x1 + 2,
    
    [f](x0, x1) = x0 + x1 + 1,
    
    [s](x0) = x0 + 2,
    
    [g](x0, x1) = x0 + x1 + 2,
    
    [norm](x0) = x0 + 4
   orientation:
    norm(g(x,y)) = x + y + 6 >= x + 6 = s(norm(x))
    
    f(x,g(y,z)) = x + y + z + 3 >= x + y + z + 3 = g(f(x,y),z)
    
    rem(g(x,y),s(z)) = 7x + 7y + 3z + 22 >= 7x + 3z + 2 = rem(x,z)
   problem:
    norm(g(x,y)) -> s(norm(x))
    f(x,g(y,z)) -> g(f(x,y),z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [f](x0, x1) = x0 + 2x1 + 5,
     
     [s](x0) = x0 + 1,
     
     [g](x0, x1) = x0 + 5x1 + 1,
     
     [norm](x0) = x0 + 5
    orientation:
     norm(g(x,y)) = x + 5y + 6 >= x + 6 = s(norm(x))
     
     f(x,g(y,z)) = x + 2y + 10z + 7 >= x + 2y + 5z + 6 = g(f(x,y),z)
    problem:
     norm(g(x,y)) -> s(norm(x))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [s](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                    [1 0 0]     [1 0 0]     [1]
      [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [0],
      
                   [1 0 0]  
      [norm](x0) = [0 0 0]x0
                   [0 0 0]  
     orientation:
                     [1 0 0]    [1 0 0]    [1]    [1 0 0]              
      norm(g(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x = s(norm(x))
                     [0 0 0]    [0 0 0]    [0]    [0 0 0]              
     problem:
      
     Qed