YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 4x0 + 1,
   
   [-](x0, x1) = x0 + x1,
   
   [f](x0) = 4x0,
   
   [0] = 0,
   
   [s](x0) = 6x0 + 1
  orientation:
   -(x,0()) = x >= x = x
   
   -(0(),s(y)) = 6y + 1 >= 0 = 0()
   
   -(s(x),s(y)) = 6x + 6y + 2 >= x + y = -(x,y)
   
   f(0()) = 0 >= 0 = 0()
   
   f(s(x)) = 24x + 4 >= 22x + 2 = -(s(x),g(f(x)))
   
   g(0()) = 1 >= 1 = s(0())
   
   g(s(x)) = 24x + 5 >= 22x + 5 = -(s(x),f(g(x)))
  problem:
   -(x,0()) -> x
   f(0()) -> 0()
   g(0()) -> s(0())
   g(s(x)) -> -(s(x),f(g(x)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = 2x0 + 5,
    
    [-](x0, x1) = x0 + x1 + 5,
    
    [f](x0) = x0,
    
    [0] = 0,
    
    [s](x0) = 2x0 + 5
   orientation:
    -(x,0()) = x + 5 >= x = x
    
    f(0()) = 0 >= 0 = 0()
    
    g(0()) = 5 >= 5 = s(0())
    
    g(s(x)) = 4x + 15 >= 4x + 15 = -(s(x),f(g(x)))
   problem:
    f(0()) -> 0()
    g(0()) -> s(0())
    g(s(x)) -> -(s(x),f(g(x)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = 2x0 + 5,
     
     [-](x0, x1) = x0 + x1 + 4,
     
     [f](x0) = x0,
     
     [0] = 0,
     
     [s](x0) = 2x0 + 5
    orientation:
     f(0()) = 0 >= 0 = 0()
     
     g(0()) = 5 >= 5 = s(0())
     
     g(s(x)) = 4x + 15 >= 4x + 14 = -(s(x),f(g(x)))
    problem:
     f(0()) -> 0()
     g(0()) -> s(0())
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]     [1]
      [g](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [0],
      
                [1 0 0]     [1]
      [f](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [0],
      
            [0]
      [0] = [0]
            [0],
      
                [1 0 0]  
      [s](x0) = [0 0 0]x0
                [0 0 0]  
     orientation:
               [1]    [0]      
      f(0()) = [0] >= [0] = 0()
               [0]    [0]      
      
               [1]    [0]         
      g(0()) = [0] >= [0] = s(0())
               [0]    [0]         
     problem:
      
     Qed