Input TRS:
    1: -(x,|0|()) -> x
    2: -(|0|(),s(y)) -> |0|()
    3: -(s(x),s(y)) -> -(x,y)
    4: lt(x,|0|()) -> false()
    5: lt(|0|(),s(y)) -> true()
    6: lt(s(x),s(y)) -> lt(x,y)
    7: if(true(),x,y) -> x
    8: if(false(),x,y) -> y
    9: div(x,|0|()) -> |0|()
    10: div(|0|(),y) -> |0|()
    11: div(s(x),s(y)) -> if(lt(x,y),|0|(),s(div(-(x,y),s(y))))
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #lt(s(x),s(y)) -> #lt(x,y)
   #2: #div(s(x),s(y)) -> #if(lt(x,y),|0|(),s(div(-(x,y),s(y))))
   #3: #div(s(x),s(y)) -> #lt(x,y)
   #4: #div(s(x),s(y)) -> #div(-(x,y),s(y))
   #5: #div(s(x),s(y)) -> #-(x,y)
   #6: #-(s(x),s(y)) -> #-(x,y)
Number of SCCs: 3, DPs: 3, edges: 3
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: x2
  #if(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: x2
 false()	weight: 0
   div(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
     -(x1,x2)	weight: (/ 1 4) + x1
   #-(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { 1..3 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0, edges: 0
YES