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.
 #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
     0()	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.
 #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
     0()	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.
 #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
     0()	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