YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 f(0()) -> s(0())
 f(s(x)) -> minus(s(x),g(f(x)))
 g(0()) -> 0()
 g(s(x)) -> minus(s(x),f(g(x)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 3x0,
   
   [f](x0) = 3x0 + 2,
   
   [s](x0) = 6x0 + 2,
   
   [minus](x0, x1) = x0 + x1,
   
   [0] = 0
  orientation:
   minus(x,0()) = x >= x = x
   
   minus(s(x),s(y)) = 6x + 6y + 4 >= x + y = minus(x,y)
   
   f(0()) = 2 >= 2 = s(0())
   
   f(s(x)) = 18x + 8 >= 15x + 8 = minus(s(x),g(f(x)))
   
   g(0()) = 0 >= 0 = 0()
   
   g(s(x)) = 18x + 6 >= 15x + 4 = minus(s(x),f(g(x)))
  problem:
   minus(x,0()) -> x
   f(0()) -> s(0())
   f(s(x)) -> minus(s(x),g(f(x)))
   g(0()) -> 0()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = 3x0,
    
    [f](x0) = 4x0 + 1,
    
    [s](x0) = 4x0 + 1,
    
    [minus](x0, x1) = x0 + x1 + 1,
    
    [0] = 0
   orientation:
    minus(x,0()) = x + 1 >= x = x
    
    f(0()) = 1 >= 1 = s(0())
    
    f(s(x)) = 16x + 5 >= 16x + 5 = minus(s(x),g(f(x)))
    
    g(0()) = 0 >= 0 = 0()
   problem:
    f(0()) -> s(0())
    f(s(x)) -> minus(s(x),g(f(x)))
    g(0()) -> 0()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = x0,
     
     [f](x0) = 5x0 + 3,
     
     [s](x0) = 3x0,
     
     [minus](x0, x1) = x0 + x1,
     
     [0] = 5
    orientation:
     f(0()) = 28 >= 15 = s(0())
     
     f(s(x)) = 15x + 3 >= 8x + 3 = minus(s(x),g(f(x)))
     
     g(0()) = 5 >= 5 = 0()
    problem:
     f(s(x)) -> minus(s(x),g(f(x)))
     g(0()) -> 0()
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [g](x0) = 2x0,
      
      [f](x0) = 4x0,
      
      [s](x0) = 3x0 + 7,
      
      [minus](x0, x1) = x0 + x1 + 5,
      
      [0] = 0
     orientation:
      f(s(x)) = 12x + 28 >= 11x + 12 = minus(s(x),g(f(x)))
      
      g(0()) = 0 >= 0 = 0()
     problem:
      g(0()) -> 0()
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 0 0]     [1]
       [g](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
       
             [0]
       [0] = [0]
             [0]
      orientation:
                [1]    [0]      
       g(0()) = [0] >= [0] = 0()
                [0]    [0]      
      problem:
       
      Qed