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