Input TRS:
    1: fib(N) -> sel(N,fib1(s(0()),s(0())))
    2: fib1(X,Y) -> cons(X,fib1(Y,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,XS)
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #fib1(X,Y) -> #fib1(Y,add(X,Y))
   #2: #fib1(X,Y) -> #add(X,Y)
   #3: #sel(s(N),cons(X,XS)) -> #sel(N,XS)
   #4: #fib(N) -> #sel(N,fib1(s(0()),s(0())))
   #5: #fib(N) -> #fib1(s(0()),s(0()))
   #6: #add(s(X),Y) -> #add(X,Y)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#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: #6
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  found.
  #fib1(X,X_{1})	-#1->
  #fib1(X_{1},add(X,X_{1}))	--->*
  #fib1(X_{1},add(X,X_{1}))
  Looping with: [ X := X_{1}; X_{1} := add(X,X_{1}); ]
NO