YES

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

Proof:
 DP Processor:
  DPs:
   g#(s(x)) -> f#(x)
   f#(s(x)) -> g#(x)
  TRS:
   g(s(x)) -> f(x)
   f(0()) -> s(0())
   f(s(x)) -> s(s(g(x)))
   g(0()) -> 0()
  Usable Rule Processor:
   DPs:
    g#(s(x)) -> f#(x)
    f#(s(x)) -> g#(x)
   TRS:
    
   EDG Processor:
    DPs:
     g#(s(x)) -> f#(x)
     f#(s(x)) -> g#(x)
    TRS:
     
    graph:
     f#(s(x)) -> g#(x) -> g#(s(x)) -> f#(x)
     g#(s(x)) -> f#(x) -> f#(s(x)) -> g#(x)
    Restore Modifier:
     DPs:
      g#(s(x)) -> f#(x)
      f#(s(x)) -> g#(x)
     TRS:
      g(s(x)) -> f(x)
      f(0()) -> s(0())
      f(s(x)) -> s(s(g(x)))
      g(0()) -> 0()
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 2/4
      DPs:
       f#(s(x)) -> g#(x)
       g#(s(x)) -> f#(x)
      TRS:
       g(s(x)) -> f(x)
       f(0()) -> s(0())
       f(s(x)) -> s(s(g(x)))
       g(0()) -> 0()
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0 + 1,
        
        [g#](x0) = x0,
        
        [0] = 0,
        
        [f](x0) = x0 + 1,
        
        [g](x0) = x0,
        
        [s](x0) = x0 + 1
       orientation:
        f#(s(x)) = x + 2 >= x = g#(x)
        
        g#(s(x)) = x + 1 >= x + 1 = f#(x)
        
        g(s(x)) = x + 1 >= x + 1 = f(x)
        
        f(0()) = 1 >= 1 = s(0())
        
        f(s(x)) = x + 2 >= x + 2 = s(s(g(x)))
        
        g(0()) = 0 >= 0 = 0()
       problem:
        DPs:
         g#(s(x)) -> f#(x)
        TRS:
         g(s(x)) -> f(x)
         f(0()) -> s(0())
         f(s(x)) -> s(s(g(x)))
         g(0()) -> 0()
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [f#](x0) = 0,
         
         [g#](x0) = x0 + 1,
         
         [0] = 0,
         
         [f](x0) = 1,
         
         [g](x0) = x0,
         
         [s](x0) = 1
        orientation:
         g#(s(x)) = 2 >= 0 = f#(x)
         
         g(s(x)) = 1 >= 1 = f(x)
         
         f(0()) = 1 >= 1 = s(0())
         
         f(s(x)) = 1 >= 1 = s(s(g(x)))
         
         g(0()) = 0 >= 0 = 0()
        problem:
         DPs:
          
         TRS:
          g(s(x)) -> f(x)
          f(0()) -> s(0())
          f(s(x)) -> s(s(g(x)))
          g(0()) -> 0()
        Qed