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