Input TRS:
    1: minus(x,|0|()) -> x
    2: minus(s(x),s(y)) -> minus(x,y)
    3: div(|0|(),s(y)) -> |0|()
    4: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    5: half(s(s(x))) -> div(x,s(s(|0|())))
    6: gen(s(x),a()) ->= c(s(s(|0|())),gen(s(x),b()))
    7: gen(s(x),a()) ->= c(half(s(s(|0|()))),gen(x,a()))
    8: gen(|0|(),a()) ->= gen(|0|(),a())
    9: gen(s(x),b()) ->= gen(s(x),b())
    10: gen(s(x),b()) ->= gen(x,a())
Removing trivial weak rule 9.
Removing trivial weak rule 8.
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing half gen
1: minus(x,|0|()) -> x
2: minus(s(x),s(y)) -> minus(x,y)
3: div(|0|(),s(y)) -> |0|()
4: div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
5: half❆1_s(s(x)) -> div(x,s(s(|0|())))
6: gen❆1_s(x,a()) ->= c(s(s(|0|())),gen❆1_s(x,b()))
7: gen❆1_s(x,a()) ->= c(half❆1_s(s(|0|())),gen(x,a()))
10: gen❆1_s(x,b()) ->= gen(x,a())
11: gen(s(_1),_2) ->= gen❆1_s(_1,_2)
12: half(s(_1)) ->= half❆1_s(_1)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #minus(s(x),s(y)) -> #minus(x,y)
   #2: #gen❆1_s(x,a()) ->? #gen❆1_s(x,b())
   #3: #gen(s(_1),_2) ->? #gen❆1_s(_1,_2)
   #4: #half(s(_1)) ->? #half❆1_s(_1)
   #5: #gen❆1_s(x,a()) ->? #half❆1_s(s(|0|()))
   #6: #gen❆1_s(x,a()) ->? #gen(x,a())
   #7: #gen❆1_s(x,b()) ->? #gen(x,a())
   #8: #half❆1_s(s(x)) -> #div(x,s(s(|0|())))
   #9: #div(s(x),s(y)) -> #div(minus(x,y),s(y))
   #10: #div(s(x),s(y)) -> #minus(x,y)
Number of SCCs: 3, DPs: 6, edges: 8
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     a()	weight: 0
gen❆1_s(x1,x2)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
 minus(x1,x2)	weight: 0
#half❆1_s(x1)	weight: 0
   div(x1,x2)	weight: 0
#half(x1)	weight: 0
     c(x1,x2)	weight: 0
  half(x1)	weight: 0
half❆1_s(x1)	weight: 0
 #gen(x1,x2)	weight: 0
   gen(x1,x2)	weight: 0
#minus(x1,x2)	weight: x2
#gen❆1_s(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 5, edges: 7
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     a()	weight: 0
gen❆1_s(x1,x2)	weight: 0
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
 minus(x1,x2)	weight: (/ 1 4) + x1
#half❆1_s(x1)	weight: 0
   div(x1,x2)	weight: 0
#half(x1)	weight: 0
     c(x1,x2)	weight: 0
  half(x1)	weight: 0
half❆1_s(x1)	weight: 0
 #gen(x1,x2)	weight: 0
   gen(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#gen❆1_s(x1,x2)	weight: 0
    Usable rules: { 1 2 }
    Removed DPs: #9
Number of SCCs: 1, DPs: 4, edges: 6
	SCC { #2 #3 #6 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
     a()	weight: 0
gen❆1_s(x1,x2)	weight: 0
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2) + x1
     b()	weight: 0
 minus(x1,x2)	weight: (/ 1 4) + x1
#half❆1_s(x1)	weight: 0
   div(x1,x2)	weight: 0
#half(x1)	weight: 0
     c(x1,x2)	weight: 0
  half(x1)	weight: 0
half❆1_s(x1)	weight: 0
 #gen(x1,x2)	weight: x1
   gen(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
#gen❆1_s(x1,x2)	weight: (/ 1 4) + x1
    Usable rules: { }
    Removed DPs: #3 #6 #7
Number of SCCs: 0, DPs: 0, edges: 0
YES