Input TRS:
    1: +(x,0()) -> x
    2: +(x,s(y)) -> s(+(x,y))
    3: *(x,0()) -> 0()
    4: *(x,s(y)) -> +(*(x,y),x)
    5: ge(x,0()) -> true()
    6: ge(0(),s(y)) -> false()
    7: ge(s(x),s(y)) -> ge(x,y)
    8: -(x,0()) -> x
    9: -(s(x),s(y)) -> -(x,y)
    10: fact(x) -> iffact(x,ge(x,s(s(0()))))
    11: iffact(x,true()) -> *(x,fact(-(x,s(0()))))
    12: iffact(x,false()) -> s(0())
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #+(x,s(y)) -> #+(x,y)
   #2: #-(s(x),s(y)) -> #-(x,y)
   #3: #iffact(x,true()) -> #*(x,fact(-(x,s(0()))))
   #4: #iffact(x,true()) -> #fact(-(x,s(0())))
   #5: #iffact(x,true()) -> #-(x,s(0()))
   #6: #ge(s(x),s(y)) -> #ge(x,y)
   #7: #fact(x) -> #iffact(x,ge(x,s(s(0()))))
   #8: #fact(x) -> #ge(x,s(s(0())))
   #9: #*(x,s(y)) -> #+(*(x,y),x)
   #10: #*(x,s(y)) -> #*(x,y)
Number of SCCs: 5, DPs: 6, edges: 6
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
iffact(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
#fact(x1)	weight: 0
  true()	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#iffact(x1,x2)	weight: 0
  fact(x1)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: x2
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 4, DPs: 5, edges: 5
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
iffact(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
   #*(x1,x2)	weight: x2
#fact(x1)	weight: 0
  true()	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#iffact(x1,x2)	weight: 0
  fact(x1)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
iffact(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
   #*(x1,x2)	weight: 0
#fact(x1)	weight: 0
  true()	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#iffact(x1,x2)	weight: 0
  fact(x1)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: x2
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
 false()	weight: 0
iffact(x1,x2)	weight: 0
  #ge(x1,x2)	weight: x2
   #*(x1,x2)	weight: 0
#fact(x1)	weight: 0
  true()	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#iffact(x1,x2)	weight: 0
  fact(x1)	weight: 0
     -(x1,x2)	weight: 0
   #-(x1,x2)	weight: 0
     +(x1,x2)	weight: 0
   #+(x1,x2)	weight: 0
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #4 #7 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... succeeded.
     s(x1)	weight: max{0, (/ 3 8) + x1_1}; (- (/ 3 8))
 false()	weight: (/ 1 8); (- (/ 1 8))
iffact(x1,x2)	weight: 0; 0
  #ge(x1,x2)	weight: 0; 0
   #*(x1,x2)	weight: 0; 0
#fact(x1)	weight: max{0, (/ 3 8) + x1_1}; 0
  true()	weight: (/ 3 8); (- (/ 3 8))
     0()	weight: (/ 1 8); (- (/ 1 8))
    ge(x1,x2)	weight: max{0, (/ 1 2) + x2_2 + x1_1}; (- (/ 1 8))
#iffact(x1,x2)	weight: max{0, (/ 1 8) + x1_2, (/ 1 4) + x1_1, (/ 1 8) + x2_1}; 0
  fact(x1)	weight: 0; 0
     -(x1,x2)	weight: max{0, (/ 1 4) + x2_2 + x1_1}; 0
   #-(x1,x2)	weight: 0; 0
     +(x1,x2)	weight: 0; 0
   #+(x1,x2)	weight: 0; 0
     *(x1,x2)	weight: 0; 0
    Usable rules: { 5..9 }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0, edges: 0
YES