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:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   f#(s(x)) -> f#(x)
   f#(s(x)) -> g#(f(x))
   f#(s(x)) -> -#(s(x),g(f(x)))
   g#(s(x)) -> g#(x)
   g#(s(x)) -> f#(g(x))
   g#(s(x)) -> -#(s(x),f(g(x)))
  TRS:
   -(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)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g#](x0) = 4x0 + 3,
    
    [f#](x0) = 6x0,
    
    [-#](x0, x1) = x0,
    
    [g](x0) = 2x0 + 1,
    
    [f](x0) = 3x0,
    
    [s](x0) = 3x0 + 1,
    
    [-](x0, x1) = 2x0 + 1,
    
    [0] = 0
   orientation:
    -#(s(x),s(y)) = 3x + 1 >= x = -#(x,y)
    
    f#(s(x)) = 18x + 6 >= 6x = f#(x)
    
    f#(s(x)) = 18x + 6 >= 12x + 3 = g#(f(x))
    
    f#(s(x)) = 18x + 6 >= 3x + 1 = -#(s(x),g(f(x)))
    
    g#(s(x)) = 12x + 7 >= 4x + 3 = g#(x)
    
    g#(s(x)) = 12x + 7 >= 12x + 6 = f#(g(x))
    
    g#(s(x)) = 12x + 7 >= 3x + 1 = -#(s(x),f(g(x)))
    
    -(x,0()) = 2x + 1 >= x = x
    
    -(0(),s(y)) = 1 >= 0 = 0()
    
    -(s(x),s(y)) = 6x + 3 >= 2x + 1 = -(x,y)
    
    f(0()) = 0 >= 0 = 0()
    
    f(s(x)) = 9x + 3 >= 6x + 3 = -(s(x),g(f(x)))
    
    g(0()) = 1 >= 1 = s(0())
    
    g(s(x)) = 6x + 3 >= 6x + 3 = -(s(x),f(g(x)))
   problem:
    DPs:
     
    TRS:
     -(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)))
   Qed