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)))
  TDG 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)))
   graph:
    g#(s(x)) -> g#(x) -> g#(s(x)) -> -#(s(x),f(g(x)))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> f#(g(x))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> -#(s(x),g(f(x)))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> g#(f(x))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> f#(x)
    g#(s(x)) -> -#(s(x),f(g(x))) -> -#(s(x),s(y)) -> -#(x,y)
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> -#(s(x),f(g(x)))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> f#(g(x))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x)
    f#(s(x)) -> f#(x) -> f#(s(x)) -> -#(s(x),g(f(x)))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> g#(f(x))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> f#(x)
    f#(s(x)) -> -#(s(x),g(f(x))) -> -#(s(x),s(y)) -> -#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 15/49
    DPs:
     g#(s(x)) -> g#(x)
     g#(s(x)) -> f#(g(x))
     f#(s(x)) -> f#(x)
     f#(s(x)) -> g#(f(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)))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = 1x0 + 0,
      
      [f#](x0) = 1x0 + 0,
      
      [g](x0) = 2x0 + 0,
      
      [f](x0) = 2x0 + 0,
      
      [s](x0) = 2x0 + 0,
      
      [-](x0, x1) = x0 + x1 + 0,
      
      [0] = 2
     orientation:
      g#(s(x)) = 3x + 1 >= 1x + 0 = g#(x)
      
      g#(s(x)) = 3x + 1 >= 3x + 1 = f#(g(x))
      
      f#(s(x)) = 3x + 1 >= 1x + 0 = f#(x)
      
      f#(s(x)) = 3x + 1 >= 3x + 1 = g#(f(x))
      
      -(x,0()) = x + 2 >= x = x
      
      -(0(),s(y)) = 2y + 2 >= 2 = 0()
      
      -(s(x),s(y)) = 2x + 2y + 0 >= x + y + 0 = -(x,y)
      
      f(0()) = 4 >= 2 = 0()
      
      f(s(x)) = 4x + 2 >= 4x + 2 = -(s(x),g(f(x)))
      
      g(0()) = 4 >= 4 = s(0())
      
      g(s(x)) = 4x + 2 >= 4x + 2 = -(s(x),f(g(x)))
     problem:
      DPs:
       g#(s(x)) -> f#(g(x))
       f#(s(x)) -> g#(f(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)))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [g#](x0) = x0,
       
       [f#](x0) = x0,
       
       [g](x0) = 1x0,
       
       [f](x0) = x0,
       
       [s](x0) = 1x0,
       
       [-](x0, x1) = x0 + x1,
       
       [0] = 4
      orientation:
       g#(s(x)) = 1x >= 1x = f#(g(x))
       
       f#(s(x)) = 1x >= x = g#(f(x))
       
       -(x,0()) = x + 4 >= x = x
       
       -(0(),s(y)) = 1y + 4 >= 4 = 0()
       
       -(s(x),s(y)) = 1x + 1y >= x + y = -(x,y)
       
       f(0()) = 4 >= 4 = 0()
       
       f(s(x)) = 1x >= 1x = -(s(x),g(f(x)))
       
       g(0()) = 5 >= 5 = s(0())
       
       g(s(x)) = 2x >= 1x = -(s(x),f(g(x)))
      problem:
       DPs:
        g#(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)))
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 8/1
       
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    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)))
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 1
     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