Input TRS:
    1: plus(x,0()) -> x
    2: plus(0(),y) -> y
    3: plus(s(x),y) -> s(plus(x,y))
    4: times(0(),y) -> 0()
    5: times(s(0()),y) -> y
    6: times(s(x),y) -> plus(y,times(x,y))
    7: div(0(),y) -> 0()
    8: div(x,y) -> quot(x,y,y)
    9: quot(0(),s(y),z) -> 0()
    10: quot(s(x),s(y),z) -> quot(x,y,z)
    11: quot(x,0(),s(z)) -> s(div(x,s(z)))
    12: div(div(x,y),z) -> div(x,times(y,z))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #times(s(x),y) -> #plus(y,times(x,y))
   #2: #times(s(x),y) -> #times(x,y)
   #3: #quot(x,0(),s(z)) -> #div(x,s(z))
   #4: #div(div(x,y),z) -> #div(x,times(y,z))
   #5: #div(div(x,y),z) -> #times(y,z)
   #6: #quot(s(x),s(y),z) -> #quot(x,y,z)
   #7: #plus(s(x),y) -> #plus(x,y)
   #8: #div(x,y) -> #quot(x,y,y)
Number of SCCs: 3, DPs: 6, edges: 10
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: x1
   div(x1,x2)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
  quot(x1,x2,x3)	weight: 0
 times(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#quot(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 2, DPs: 5, edges: 9
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
#plus(x1,x2)	weight: 0
   div(x1,x2)	weight: 0
#times(x1,x2)	weight: x1
     0()	weight: 0
  quot(x1,x2,x3)	weight: 0
 times(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#quot(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 4, edges: 8
	SCC { #3 #4 #6 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 4) + x1
#plus(x1,x2)	weight: 0
   div(x1,x2)	weight: (/ 1 4) + x1 + x2
#times(x1,x2)	weight: 0
     0()	weight: 0
  quot(x1,x2,x3)	weight: 0
 times(x1,x2)	weight: (/ 1 4) + x1 + x2
  plus(x1,x2)	weight: (/ 1 2) + x2
#quot(x1,x2,x3)	weight: x1
    Usable rules: { }
    Removed DPs: #4 #6
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #3 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
 #div(x1,x2)	weight: max{0, x2}
     s(x1)	weight: 0
#plus(x1,x2)	weight: 0
   div(x1,x2)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: (/ 1 2)
  quot(x1,x2,x3)	weight: 0
 times(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
#quot(x1,x2,x3)	weight: max{0, x2}
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0, edges: 0
YES