Input TRS:
    1: fib(N) -> sel(N,fib1(s(0()),s(0())))
    2: fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
    3: add(0(),X) -> X
    4: add(s(X),Y) -> s(add(X,Y))
    5: sel(0(),cons(X,XS)) -> X
    6: sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    7: fib1(X1,X2) -> n__fib1(X1,X2)
    8: add(X1,X2) -> n__add(X1,X2)
    9: activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
    10: activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
    11: activate(X) -> X
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #sel(s(N),cons(X,XS)) -> #sel(N,activate(XS))
   #2: #sel(s(N),cons(X,XS)) -> #activate(XS)
   #3: #activate(n__fib1(X1,X2)) -> #fib1(activate(X1),activate(X2))
   #4: #activate(n__fib1(X1,X2)) -> #activate(X1)
   #5: #activate(n__fib1(X1,X2)) -> #activate(X2)
   #6: #activate(n__add(X1,X2)) -> #add(activate(X1),activate(X2))
   #7: #activate(n__add(X1,X2)) -> #activate(X1)
   #8: #activate(n__add(X1,X2)) -> #activate(X2)
   #9: #fib(N) -> #sel(N,fib1(s(0()),s(0())))
   #10: #fib(N) -> #fib1(s(0()),s(0()))
   #11: #add(s(X),Y) -> #add(X,Y)
Number of SCCs: 3, DPs: 6, edges: 18
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
activate(x1)	weight: 0
#activate(x1)	weight: 0
n__add(x1,x2)	weight: 0
#fib1(x1,x2)	weight: 0
n__fib1(x1,x2)	weight: 0
  fib1(x1,x2)	weight: 0
   fib(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
 #add(x1,x2)	weight: x1
   add(x1,x2)	weight: 0
 #fib(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 2, DPs: 5, edges: 17
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
activate(x1)	weight: (/ 1 4)
#activate(x1)	weight: 0
n__add(x1,x2)	weight: (/ 3 4)
#fib1(x1,x2)	weight: 0
n__fib1(x1,x2)	weight: (/ 3 4)
  fib1(x1,x2)	weight: (/ 1 2)
   fib(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x1
   sel(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 3 4)
 #add(x1,x2)	weight: 0
   add(x1,x2)	weight: (/ 1 2)
 #fib(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 4, edges: 16
	SCC { #4 #5 #7 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
activate(x1)	weight: (/ 1 4)
#activate(x1)	weight: x1
n__add(x1,x2)	weight: (/ 1 2) + x1 + x2
#fib1(x1,x2)	weight: 0
n__fib1(x1,x2)	weight: (/ 3 4) + x1 + x2
  fib1(x1,x2)	weight: (/ 1 2)
   fib(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
  cons(x1,x2)	weight: x2
 #add(x1,x2)	weight: 0
   add(x1,x2)	weight: (/ 1 4) + x2
 #fib(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #5 #7 #8
Number of SCCs: 0, DPs: 0, edges: 0
YES