YES

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

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> g#(s(s(x)))
   g#(s(s(x))) -> f#(x)
  TRS:
   f(0()) -> s(0())
   f(s(x)) -> g(s(s(x)))
   g(0()) -> s(0())
   g(s(0())) -> s(0())
   g(s(s(x))) -> f(x)
  EDG Processor:
   DPs:
    f#(s(x)) -> g#(s(s(x)))
    g#(s(s(x))) -> f#(x)
   TRS:
    f(0()) -> s(0())
    f(s(x)) -> g(s(s(x)))
    g(0()) -> s(0())
    g(s(0())) -> s(0())
    g(s(s(x))) -> f(x)
   graph:
    g#(s(s(x))) -> f#(x) -> f#(s(x)) -> g#(s(s(x)))
    f#(s(x)) -> g#(s(s(x))) -> g#(s(s(x))) -> f#(x)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [g#](x0) = x0,
     
     [f#](x0) = x0 + 1,
     
     [g](x0) = 1,
     
     [s](x0) = x0 + 1,
     
     [f](x0) = 1,
     
     [0] = 0
    orientation:
     f#(s(x)) = x + 2 >= x + 2 = g#(s(s(x)))
     
     g#(s(s(x))) = x + 2 >= x + 1 = f#(x)
     
     f(0()) = 1 >= 1 = s(0())
     
     f(s(x)) = 1 >= 1 = g(s(s(x)))
     
     g(0()) = 1 >= 1 = s(0())
     
     g(s(0())) = 1 >= 1 = s(0())
     
     g(s(s(x))) = 1 >= 1 = f(x)
    problem:
     DPs:
      f#(s(x)) -> g#(s(s(x)))
     TRS:
      f(0()) -> s(0())
      f(s(x)) -> g(s(s(x)))
      g(0()) -> s(0())
      g(s(0())) -> s(0())
      g(s(s(x))) -> f(x)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = 0,
      
      [f#](x0) = 1,
      
      [g](x0) = 0,
      
      [s](x0) = 0,
      
      [f](x0) = 0,
      
      [0] = 0
     orientation:
      f#(s(x)) = 1 >= 0 = g#(s(s(x)))
      
      f(0()) = 0 >= 0 = s(0())
      
      f(s(x)) = 0 >= 0 = g(s(s(x)))
      
      g(0()) = 0 >= 0 = s(0())
      
      g(s(0())) = 0 >= 0 = s(0())
      
      g(s(s(x))) = 0 >= 0 = f(x)
     problem:
      DPs:
       
      TRS:
       f(0()) -> s(0())
       f(s(x)) -> g(s(s(x)))
       g(0()) -> s(0())
       g(s(0())) -> s(0())
       g(s(s(x))) -> f(x)
     Qed