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:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   f#(s(x)) -> f#(x)
   f#(s(x)) -> g#(f(x))
   f#(s(x)) -> minus#(s(x),g(f(x)))
   g#(s(x)) -> g#(x)
   g#(s(x)) -> f#(g(x))
   g#(s(x)) -> minus#(s(x),f(g(x)))
  TRS:
   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)))
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    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)))
   interpretation:
    [g#](x0) = 2x0 + 4,
    
    [f#](x0) = 5x0 + 4,
    
    [minus#](x0, x1) = x1 + 5,
    
    [g](x0) = 2x0,
    
    [f](x0) = 4x0 + 2,
    
    [s](x0) = 5x0 + 2,
    
    [minus](x0, x1) = x0,
    
    [0] = 0
   orientation:
    minus#(s(x),s(y)) = 5y + 7 >= y + 5 = minus#(x,y)
    
    f#(s(x)) = 25x + 14 >= 5x + 4 = f#(x)
    
    f#(s(x)) = 25x + 14 >= 8x + 8 = g#(f(x))
    
    f#(s(x)) = 25x + 14 >= 8x + 9 = minus#(s(x),g(f(x)))
    
    g#(s(x)) = 10x + 8 >= 2x + 4 = g#(x)
    
    g#(s(x)) = 10x + 8 >= 10x + 4 = f#(g(x))
    
    g#(s(x)) = 10x + 8 >= 8x + 7 = minus#(s(x),f(g(x)))
    
    minus(x,0()) = x >= x = x
    
    minus(s(x),s(y)) = 5x + 2 >= x = minus(x,y)
    
    f(0()) = 2 >= 2 = s(0())
    
    f(s(x)) = 20x + 10 >= 5x + 2 = minus(s(x),g(f(x)))
    
    g(0()) = 0 >= 0 = 0()
    
    g(s(x)) = 10x + 4 >= 5x + 2 = minus(s(x),f(g(x)))
   problem:
    DPs:
     
    TRS:
     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)))
   Qed