NO
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 POLO(bPol) ... failed.
Uncurrying ... 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
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      #fib1	w: 0
      fib1	w: 0
      fib	w: 0
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      cons	w: 0
      #add	w: x1
      add	w: 0
      #fib	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 2
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... 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}); ]