YES

Problem:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(0()))) -> s(0())
 fib(s(s(x))) -> sp(g(x))
 g(0()) -> pair(s(0()),0())
 g(s(0())) -> pair(s(0()),s(0()))
 g(s(x)) -> np(g(x))
 sp(pair(x,y)) -> +(x,y)
 np(pair(x,y)) -> pair(+(x,y),x)
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))

Proof:
 DP Processor:
  DPs:
   fib#(s(s(x))) -> g#(x)
   fib#(s(s(x))) -> sp#(g(x))
   g#(s(x)) -> g#(x)
   g#(s(x)) -> np#(g(x))
   sp#(pair(x,y)) -> +#(x,y)
   np#(pair(x,y)) -> +#(x,y)
   +#(x,s(y)) -> +#(x,y)
  TRS:
   fib(0()) -> 0()
   fib(s(0())) -> s(0())
   fib(s(s(0()))) -> s(0())
   fib(s(s(x))) -> sp(g(x))
   g(0()) -> pair(s(0()),0())
   g(s(0())) -> pair(s(0()),s(0()))
   g(s(x)) -> np(g(x))
   sp(pair(x,y)) -> +(x,y)
   np(pair(x,y)) -> pair(+(x,y),x)
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
  TDG Processor:
   DPs:
    fib#(s(s(x))) -> g#(x)
    fib#(s(s(x))) -> sp#(g(x))
    g#(s(x)) -> g#(x)
    g#(s(x)) -> np#(g(x))
    sp#(pair(x,y)) -> +#(x,y)
    np#(pair(x,y)) -> +#(x,y)
    +#(x,s(y)) -> +#(x,y)
   TRS:
    fib(0()) -> 0()
    fib(s(0())) -> s(0())
    fib(s(s(0()))) -> s(0())
    fib(s(s(x))) -> sp(g(x))
    g(0()) -> pair(s(0()),0())
    g(s(0())) -> pair(s(0()),s(0()))
    g(s(x)) -> np(g(x))
    sp(pair(x,y)) -> +(x,y)
    np(pair(x,y)) -> pair(+(x,y),x)
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    np#(pair(x,y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    sp#(pair(x,y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x)) -> np#(g(x)) -> np#(pair(x,y)) -> +#(x,y)
    g#(s(x)) -> g#(x) -> g#(s(x)) -> np#(g(x))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
    fib#(s(s(x))) -> sp#(g(x)) -> sp#(pair(x,y)) -> +#(x,y)
    fib#(s(s(x))) -> g#(x) -> g#(s(x)) -> np#(g(x))
    fib#(s(s(x))) -> g#(x) -> g#(s(x)) -> g#(x)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 9/49
    DPs:
     g#(s(x)) -> g#(x)
    TRS:
     fib(0()) -> 0()
     fib(s(0())) -> s(0())
     fib(s(s(0()))) -> s(0())
     fib(s(s(x))) -> sp(g(x))
     g(0()) -> pair(s(0()),0())
     g(s(0())) -> pair(s(0()),s(0()))
     g(s(x)) -> np(g(x))
     sp(pair(x,y)) -> +(x,y)
     np(pair(x,y)) -> pair(+(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       fib(0()) -> 0()
       fib(s(0())) -> s(0())
       fib(s(s(0()))) -> s(0())
       fib(s(s(x))) -> sp(g(x))
       g(0()) -> pair(s(0()),0())
       g(s(0())) -> pair(s(0()),s(0()))
       g(s(x)) -> np(g(x))
       sp(pair(x,y)) -> +(x,y)
       np(pair(x,y)) -> pair(+(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     fib(0()) -> 0()
     fib(s(0())) -> s(0())
     fib(s(s(0()))) -> s(0())
     fib(s(s(x))) -> sp(g(x))
     g(0()) -> pair(s(0()),0())
     g(s(0())) -> pair(s(0()),s(0()))
     g(s(x)) -> np(g(x))
     sp(pair(x,y)) -> +(x,y)
     np(pair(x,y)) -> pair(+(x,y),x)
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       fib(0()) -> 0()
       fib(s(0())) -> s(0())
       fib(s(s(0()))) -> s(0())
       fib(s(s(x))) -> sp(g(x))
       g(0()) -> pair(s(0()),0())
       g(s(0())) -> pair(s(0()),s(0()))
       g(s(x)) -> np(g(x))
       sp(pair(x,y)) -> +(x,y)
       np(pair(x,y)) -> pair(+(x,y),x)
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed