YES

Problem:
 f(0()) -> 1()
 f(s(x)) -> g(f(x))
 g(x) -> +(x,s(x))
 f(s(x)) -> +(f(x),s(f(x)))

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> f#(x)
   f#(s(x)) -> g#(f(x))
  TRS:
   f(0()) -> 1()
   f(s(x)) -> g(f(x))
   g(x) -> +(x,s(x))
   f(s(x)) -> +(f(x),s(f(x)))
  CDG Processor:
   DPs:
    f#(s(x)) -> f#(x)
    f#(s(x)) -> g#(f(x))
   TRS:
    f(0()) -> 1()
    f(s(x)) -> g(f(x))
    g(x) -> +(x,s(x))
    f(s(x)) -> +(f(x),s(f(x)))
   graph:
    f#(s(x)) -> f#(x) -> f#(s(x)) -> f#(x)
    f#(s(x)) -> f#(x) -> f#(s(x)) -> g#(f(x))
   Restore Modifier:
    DPs:
     f#(s(x)) -> f#(x)
     f#(s(x)) -> g#(f(x))
    TRS:
     f(0()) -> 1()
     f(s(x)) -> g(f(x))
     g(x) -> +(x,s(x))
     f(s(x)) -> +(f(x),s(f(x)))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 2/4
     DPs:
      f#(s(x)) -> f#(x)
     TRS:
      f(0()) -> 1()
      f(s(x)) -> g(f(x))
      g(x) -> +(x,s(x))
      f(s(x)) -> +(f(x),s(f(x)))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0) = x0 + 1,
       
       [+](x0, x1) = 0,
       
       [g](x0) = 0,
       
       [s](x0) = x0 + 1,
       
       [1] = 0,
       
       [f](x0) = 0,
       
       [0] = 0
      orientation:
       f#(s(x)) = x + 2 >= x + 1 = f#(x)
       
       f(0()) = 0 >= 0 = 1()
       
       f(s(x)) = 0 >= 0 = g(f(x))
       
       g(x) = 0 >= 0 = +(x,s(x))
       
       f(s(x)) = 0 >= 0 = +(f(x),s(f(x)))
      problem:
       DPs:
        
       TRS:
        f(0()) -> 1()
        f(s(x)) -> g(f(x))
        g(x) -> +(x,s(x))
        f(s(x)) -> +(f(x),s(f(x)))
      Qed