Input TRS:
    1: times(x,y) -> sum(generate(x,y))
    2: generate(x,y) -> gen(x,y,0())
    3: gen(x,y,z) -> if(ge(z,x),x,y,z)
    4: if(true(),x,y,z) -> nil()
    5: if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
    6: sum(nil()) -> 0()
    7: sum(cons(0(),xs)) -> sum(xs)
    8: sum(cons(s(x),xs)) -> s(sum(cons(x,xs)))
    9: ge(x,0()) -> true()
    10: ge(0(),s(y)) -> false()
    11: ge(s(x),s(y)) -> ge(x,y)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing sum
1: times(x,y) -> sum(generate(x,y))
2: generate(x,y) -> gen(x,y,0())
3: gen(x,y,z) -> if(ge(z,x),x,y,z)
4: if(true(),x,y,z) -> nil()
5: if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
6: sum❆1_nil() -> 0()
7: sum❆1_cons(0(),xs) -> sum(xs)
8: sum❆1_cons(s(x),xs) -> s(sum❆1_cons(x,xs))
9: ge(x,0()) -> true()
10: ge(0(),s(y)) -> false()
11: ge(s(x),s(y)) -> ge(x,y)
12: sum(cons(_1,_2)) ->= sum❆1_cons(_1,_2)
13: sum(nil()) ->= sum❆1_nil()
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #generate(x,y) -> #gen(x,y,0())
   #2: #sum(nil()) ->? #sum❆1_nil()
   #3: #ge(s(x),s(y)) -> #ge(x,y)
   #4: #sum(cons(_1,_2)) ->? #sum❆1_cons(_1,_2)
   #5: #sum❆1_cons(0(),xs) -> #sum(xs)
   #6: #if(false(),x,y,z) -> #gen(x,y,s(z))
   #7: #gen(x,y,z) -> #if(ge(z,x),x,y,z)
   #8: #gen(x,y,z) -> #ge(z,x)
   #9: #times(x,y) -> #sum(generate(x,y))
   #10: #times(x,y) -> #generate(x,y)
   #11: #sum❆1_cons(s(x),xs) -> #sum❆1_cons(x,xs)
Number of SCCs: 3, DPs: 6, edges: 8
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
#generate(x1,x2)	weight: 0
sum❆1_cons(x1,x2)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: x2
#sum❆1_cons(x1,x2)	weight: 0
  true()	weight: 0
   sum(x1)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
    ge(x1,x2)	weight: 0
 times(x1,x2)	weight: 0
   nil()	weight: 0
 #gen(x1,x2,x3)	weight: 0
   gen(x1,x2,x3)	weight: 0
generate(x1,x2)	weight: 0
  cons(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
 #sum(x1)	weight: 0
sum❆1_nil()	weight: 0
#sum❆1_nil()	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 5, edges: 7
	SCC { #4 #5 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4)
#generate(x1,x2)	weight: 0
sum❆1_cons(x1,x2)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: 0
#sum❆1_cons(x1,x2)	weight: (/ 1 4) + x2
  true()	weight: 0
   sum(x1)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
    ge(x1,x2)	weight: 0
 times(x1,x2)	weight: 0
   nil()	weight: 0
 #gen(x1,x2,x3)	weight: 0
   gen(x1,x2,x3)	weight: 0
generate(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2) + x2
  #if(x1,x2,x3,x4)	weight: 0
 #sum(x1)	weight: x1
sum❆1_nil()	weight: 0
#sum❆1_nil()	weight: 0
    Usable rules: { }
    Removed DPs: #4 #5
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 4) + x1
#generate(x1,x2)	weight: 0
sum❆1_cons(x1,x2)	weight: 0
 false()	weight: 0
  #ge(x1,x2)	weight: 0
#sum❆1_cons(x1,x2)	weight: (/ 1 4) + x1
  true()	weight: 0
   sum(x1)	weight: 0
#times(x1,x2)	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
    ge(x1,x2)	weight: 0
 times(x1,x2)	weight: 0
   nil()	weight: 0
 #gen(x1,x2,x3)	weight: 0
   gen(x1,x2,x3)	weight: 0
generate(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 2)
  #if(x1,x2,x3,x4)	weight: 0
 #sum(x1)	weight: 0
sum❆1_nil()	weight: 0
#sum❆1_nil()	weight: 0
    Usable rules: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #6 #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)... failed.
Removing edges: failed.
Finding a loop...  failed.
MAYBE