Input TRS:
    1: f(X) -> cons(X,f(g(X)))
    2: g(0()) -> s(0())
    3: g(s(X)) -> s(s(g(X)))
    4: sel(0(),cons(X,Y)) -> X
    5: sel(s(X),cons(Y,Z)) -> sel(X,Z)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #sel(s(X),cons(Y,Z)) -> #sel(X,Z)
   #2: #g(s(X)) -> #g(X)
   #3: #f(X) -> #f(g(X))
   #4: #f(X) -> #g(X)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
     f(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: x1
  cons(x1,x2)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
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.
  #f(X)	-#3->
  #f(g(X))	--->*
  #f(g(X))
  Looping with: [ X := g(X); ]
NO