Input TRS:
    1: min(0(),y) -> 0()
    2: min(s(x),0()) -> 0()
    3: min(s(x),s(y)) -> min(x,y)
    4: len(nil()) -> 0()
    5: len(cons(x,xs)) -> s(len(xs))
    6: sum(x,0()) -> x
    7: sum(x,s(y)) -> s(sum(x,y))
    8: le(0(),x) -> true()
    9: le(s(x),0()) -> false()
    10: le(s(x),s(y)) -> le(x,y)
    11: take(0(),cons(y,ys)) -> y
    12: take(s(x),cons(y,ys)) -> take(x,ys)
    13: addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
    14: if(false(),c,x,y,z) -> z
    15: if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing le
1: min(0(),y) -> 0()
2: min(s(x),0()) -> 0()
3: min(s(x),s(y)) -> min(x,y)
4: len(nil()) -> 0()
5: len(cons(x,xs)) -> s(len(xs))
6: sum(x,0()) -> x
7: sum(x,s(y)) -> s(sum(x,y))
8: le❆1_0(x) -> true()
9: le❆1_s(x,0()) -> false()
10: le❆1_s(x,s(y)) -> le(x,y)
11: take(0(),cons(y,ys)) -> y
12: take(s(x),cons(y,ys)) -> take(x,ys)
13: addList(x,y) -> if(le❆1_0(min(len(x),len(y))),0(),x,y,nil())
14: if(false(),c,x,y,z) -> z
15: if(true(),c,xs,ys,z) -> if(le❆1_s(c,min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
16: le(0(),_1) ->= le❆1_0(_1)
17: le(s(_1),_2) ->= le❆1_s(_1,_2)
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #addList(x,y) -> #if(le❆1_0(min(len(x),len(y))),0(),x,y,nil())
   #2: #addList(x,y) -> #le❆1_0(min(len(x),len(y)))
   #3: #addList(x,y) -> #min(len(x),len(y))
   #4: #addList(x,y) -> #len(x)
   #5: #addList(x,y) -> #len(y)
   #6: #take(s(x),cons(y,ys)) -> #take(x,ys)
   #7: #sum(x,s(y)) -> #sum(x,y)
   #8: #le❆1_s(x,s(y)) -> #le(x,y)
   #9: #len(cons(x,xs)) -> #len(xs)
   #10: #le(s(_1),_2) ->? #le❆1_s(_1,_2)
   #11: #le(0(),_1) ->? #le❆1_0(_1)
   #12: #min(s(x),s(y)) -> #min(x,y)
   #13: #if(true(),c,xs,ys,z) -> #if(le❆1_s(c,min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
   #14: #if(true(),c,xs,ys,z) -> #le❆1_s(c,min(len(xs),len(ys)))
   #15: #if(true(),c,xs,ys,z) -> #min(len(xs),len(ys))
   #16: #if(true(),c,xs,ys,z) -> #len(xs)
   #17: #if(true(),c,xs,ys,z) -> #len(ys)
   #18: #if(true(),c,xs,ys,z) -> #sum(take(c,xs),take(c,ys))
   #19: #if(true(),c,xs,ys,z) -> #take(c,xs)
   #20: #if(true(),c,xs,ys,z) -> #take(c,ys)
Number of SCCs: 5, DPs: 6, edges: 6
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
 #len(x1)	weight: x1
     s(x1)	weight: 0
  #le(x1,x2)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
 false()	weight: 0
 #min(x1,x2)	weight: 0
addList(x1,x2)	weight: 0
  true()	weight: 0
#le❆1_0(x1)	weight: 0
le❆1_s(x1,x2)	weight: 0
   sum(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
   nil()	weight: 0
#le❆1_s(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
  #if(x1,x2,x3,x4,x5)	weight: 0
le❆1_0(x1)	weight: 0
 #sum(x1,x2)	weight: 0
#addList(x1,x2)	weight: 0
   len(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 4, DPs: 5, edges: 5
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
 #len(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
 false()	weight: 0
 #min(x1,x2)	weight: 0
addList(x1,x2)	weight: 0
  true()	weight: 0
#le❆1_0(x1)	weight: 0
le❆1_s(x1,x2)	weight: 0
   sum(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
   nil()	weight: 0
#le❆1_s(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
  #if(x1,x2,x3,x4,x5)	weight: 0
le❆1_0(x1)	weight: 0
 #sum(x1,x2)	weight: x2
#addList(x1,x2)	weight: 0
   len(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #12 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
 #len(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
 false()	weight: 0
 #min(x1,x2)	weight: x2
addList(x1,x2)	weight: 0
  true()	weight: 0
#le❆1_0(x1)	weight: 0
le❆1_s(x1,x2)	weight: 0
   sum(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
   nil()	weight: 0
#le❆1_s(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
  #if(x1,x2,x3,x4,x5)	weight: 0
le❆1_0(x1)	weight: 0
 #sum(x1,x2)	weight: 0
#addList(x1,x2)	weight: 0
   len(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
 #len(x1)	weight: 0
     s(x1)	weight: (/ 1 2)
  #le(x1,x2)	weight: 0
#take(x1,x2)	weight: x2
  take(x1,x2)	weight: 0
 false()	weight: 0
 #min(x1,x2)	weight: 0
addList(x1,x2)	weight: 0
  true()	weight: 0
#le❆1_0(x1)	weight: 0
le❆1_s(x1,x2)	weight: 0
   sum(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
   nil()	weight: 0
#le❆1_s(x1,x2)	weight: 0
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
  #if(x1,x2,x3,x4,x5)	weight: 0
le❆1_0(x1)	weight: 0
 #sum(x1,x2)	weight: 0
#addList(x1,x2)	weight: 0
   len(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #8 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
    le(x1,x2)	weight: 0
 #len(x1)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #le(x1,x2)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
 false()	weight: 0
 #min(x1,x2)	weight: 0
addList(x1,x2)	weight: 0
  true()	weight: 0
#le❆1_0(x1)	weight: 0
le❆1_s(x1,x2)	weight: 0
   sum(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4,x5)	weight: 0
   nil()	weight: 0
#le❆1_s(x1,x2)	weight: (/ 1 4) + x1
   min(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 4)
  #if(x1,x2,x3,x4,x5)	weight: 0
le❆1_0(x1)	weight: 0
 #sum(x1,x2)	weight: 0
#addList(x1,x2)	weight: 0
   len(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8 #10
Number of SCCs: 0, DPs: 0, edges: 0
YES