Input TRS:
    1: from(X) -> cons(X,n__from(s(X)))
    2: head(cons(X,XS)) -> X
    3: 2nd(cons(X,XS)) -> head(activate(XS))
    4: take(0(),XS) -> nil()
    5: take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
    6: sel(0(),cons(X,XS)) -> X
    7: sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    8: from(X) -> n__from(X)
    9: take(X1,X2) -> n__take(X1,X2)
    10: activate(n__from(X)) -> from(X)
    11: activate(n__take(X1,X2)) -> take(X1,X2)
    12: activate(X) -> X
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #activate(n__take(X1,X2)) -> #take(X1,X2)
   #2: #sel(s(N),cons(X,XS)) -> #sel(N,activate(XS))
   #3: #sel(s(N),cons(X,XS)) -> #activate(XS)
   #4: #activate(n__from(X)) -> #from(X)
   #5: #take(s(N),cons(X,XS)) -> #activate(XS)
   #6: #2nd(cons(X,XS)) -> #head(activate(XS))
   #7: #2nd(cons(X,XS)) -> #activate(XS)
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#take(x1,x2)	weight: 0
activate(x1)	weight: (/ 1 2) + x1
  take(x1,x2)	weight: (/ 1 2) + x2
n__from(x1)	weight: (/ 1 2)
#activate(x1)	weight: 0
   2nd(x1)	weight: 0
#head(x1)	weight: 0
     0()	weight: 0
n__take(x1,x2)	weight: (/ 1 2) + x1
 #sel(x1,x2)	weight: x1
  from(x1)	weight: (/ 1 2)
   sel(x1,x2)	weight: 0
   nil()	weight: 0
 #2nd(x1)	weight: 0
#from(x1)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x1
    Usable rules: { 4 5 8 12 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
#take(x1,x2)	weight: x1 + x2
activate(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: (/ 3 4)
n__from(x1)	weight: 0
#activate(x1)	weight: (/ 1 4) + x1
   2nd(x1)	weight: 0
#head(x1)	weight: 0
     0()	weight: 0
n__take(x1,x2)	weight: (/ 1 4) + x1 + x2
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 1 4)
   sel(x1,x2)	weight: 0
   nil()	weight: 0
 #2nd(x1)	weight: 0
#from(x1)	weight: 0
  head(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
    Usable rules: { }
    Removed DPs: #1 #5
Number of SCCs: 0, DPs: 0, edges: 0
YES