YES

Problem:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(x))) -> +(fib(s(x)),fib(x))

Proof:
 DP Processor:
  DPs:
   fib#(s(s(x))) -> fib#(x)
   fib#(s(s(x))) -> fib#(s(x))
  TRS:
   fib(0()) -> 0()
   fib(s(0())) -> s(0())
   fib(s(s(x))) -> +(fib(s(x)),fib(x))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [fib#](x0) = x0 + 0,
    
    [+](x0, x1) = 0,
    
    [s](x0) = 2x0 + 0,
    
    [fib](x0) = 2x0 + 0,
    
    [0] = 0
   orientation:
    fib#(s(s(x))) = 4x + 2 >= x + 0 = fib#(x)
    
    fib#(s(s(x))) = 4x + 2 >= 2x + 0 = fib#(s(x))
    
    fib(0()) = 2 >= 0 = 0()
    
    fib(s(0())) = 4 >= 2 = s(0())
    
    fib(s(s(x))) = 6x + 4 >= 0 = +(fib(s(x)),fib(x))
   problem:
    DPs:
     
    TRS:
     fib(0()) -> 0()
     fib(s(0())) -> s(0())
     fib(s(s(x))) -> +(fib(s(x)),fib(x))
   Qed