Input TRS:
    1: +(0(),y) -> y
    2: +(s(x),y) -> s(+(x,y))
    3: ++(nil(),ys) -> ys
    4: ++(:(x,xs),ys) -> :(x,++(xs,ys))
    5: sum(:(x,nil())) -> :(x,nil())
    6: sum(:(x,:(y,xs))) -> sum(:(+(x,y),xs))
    7: sum(++(xs,:(x,:(y,ys)))) -> sum(++(xs,sum(:(x,:(y,ys)))))
    8: -(x,0()) -> x
    9: -(0(),s(y)) -> 0()
    10: -(s(x),s(y)) -> -(x,y)
    11: quot(0(),s(y)) -> 0()
    12: quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
    13: length(nil()) -> 0()
    14: length(:(x,xs)) -> s(length(xs))
    15: hd(:(x,xs)) -> x
    16: avg(xs) -> quot(hd(sum(xs)),length(xs))
Number of strict rules: 16
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(s(x),y) -> #+(x,y)
   #2: #sum(:(x,:(y,xs))) -> #sum(:(+(x,y),xs))
   #3: #sum(:(x,:(y,xs))) -> #+(x,y)
   #4: #quot(s(x),s(y)) -> #quot(-(x,y),s(y))
   #5: #quot(s(x),s(y)) -> #-(x,y)
   #6: #length(:(x,xs)) -> #length(xs)
   #7: #sum(++(xs,:(x,:(y,ys)))) -> #sum(++(xs,sum(:(x,:(y,ys)))))
   #8: #sum(++(xs,:(x,:(y,ys)))) -> #++(xs,sum(:(x,:(y,ys))))
   #9: #sum(++(xs,:(x,:(y,ys)))) -> #sum(:(x,:(y,ys)))
   #10: #-(s(x),s(y)) -> #-(x,y)
   #11: #avg(xs) -> #quot(hd(sum(xs)),length(xs))
   #12: #avg(xs) -> #hd(sum(xs))
   #13: #avg(xs) -> #sum(xs)
   #14: #avg(xs) -> #length(xs)
   #15: #++(:(x,xs),ys) -> #++(xs,ys)
Number of SCCs: 7, DPs: 7, edges: 7
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: 0
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 2) + x2
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: 0
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: x1
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 6, DPs: 6, edges: 6
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 2)
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: 0
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 5, DPs: 5, edges: 5
	SCC { #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 2)
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 2) + x2
  #++(x1,x2)	weight: x1
   nil()	weight: 0
     -(x1,x2)	weight: 0
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #15
Number of SCCs: 4, DPs: 4, edges: 4
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 2)
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: 0
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: x2
#quot(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 4)
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: (/ 1 4) + x1
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: x1
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { 8..10 }
    Removed DPs: #4
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
    ++(x1,x2)	weight: 0
   sum(x1)	weight: 0
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 4) + x2
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: (/ 1 4) + x1
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: x1
     +(x1,x2)	weight: (/ 1 4)
 #sum(x1)	weight: x1
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    hd(x1)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
    ++(x1,x2)	weight: (/ 1 4) + x1 + x2
   sum(x1)	weight: (/ 1 4)
 #avg(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: 0
     :(x1,x2)	weight: (/ 1 4) + x2
  #++(x1,x2)	weight: 0
   nil()	weight: 0
     -(x1,x2)	weight: (/ 1 4) + x1
   avg(x1)	weight: 0
  #hd(x1)	weight: 0
   #-(x1,x2)	weight: 0
#quot(x1,x2)	weight: x1
     +(x1,x2)	weight: (/ 1 4)
 #sum(x1)	weight: x1
length(x1)	weight: 0
#length(x1)	weight: 0
   #+(x1,x2)	weight: 0
    Usable rules: { 3..6 }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0, edges: 0
YES