Input TRS:
    1: fib(0()) -> 0()
    2: fib(s(0())) -> s(0())
    3: fib(s(s(0()))) -> s(0())
    4: fib(s(s(x))) -> sp(g(x))
    5: g(0()) -> pair(s(0()),0())
    6: g(s(0())) -> pair(s(0()),s(0()))
    7: g(s(x)) -> np(g(x))
    8: sp(pair(x,y)) -> +(x,y)
    9: np(pair(x,y)) -> pair(+(x,y),x)
    10: +(x,0()) -> x
    11: +(x,s(y)) -> s(+(x,y))
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #np(pair(x,y)) -> #+(x,y)
   #2: #+(x,s(y)) -> #+(x,y)
   #3: #g(s(x)) -> #np(g(x))
   #4: #g(s(x)) -> #g(x)
   #5: #sp(pair(x,y)) -> #+(x,y)
   #6: #fib(s(s(x))) -> #sp(g(x))
   #7: #fib(s(s(x))) -> #g(x)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
  pair(x1,x2)	weight: 0
    sp(x1)	weight: 0
   fib(x1)	weight: 0
     0()	weight: 0
   #g(x1)	weight: x1
    np(x1)	weight: 0
  #sp(x1)	weight: 0
     +(x1,x2)	weight: 0
 #fib(x1)	weight: 0
  #np(x1)	weight: 0
     g(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
  pair(x1,x2)	weight: 0
    sp(x1)	weight: 0
   fib(x1)	weight: 0
     0()	weight: 0
   #g(x1)	weight: 0
    np(x1)	weight: 0
  #sp(x1)	weight: 0
     +(x1,x2)	weight: 0
 #fib(x1)	weight: 0
  #np(x1)	weight: 0
     g(x1)	weight: 0
   #+(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0, edges: 0
YES