Input TRS:
    1: ge(|0|(),|0|()) -> true()
    2: ge(s(x),|0|()) -> ge(x,|0|())
    3: ge(|0|(),s(|0|())) -> false()
    4: ge(|0|(),s(s(x))) -> ge(|0|(),s(x))
    5: ge(s(x),s(y)) -> ge(x,y)
    6: minus(|0|(),|0|()) -> |0|()
    7: minus(|0|(),s(x)) -> minus(|0|(),x)
    8: minus(s(x),|0|()) -> s(minus(x,|0|()))
    9: minus(s(x),s(y)) -> minus(x,y)
    10: plus(|0|(),|0|()) -> |0|()
    11: plus(|0|(),s(x)) -> s(plus(|0|(),x))
    12: plus(s(x),y) -> s(plus(x,y))
    13: div(x,y) -> ify(ge(y,s(|0|())),x,y)
    14: ify(false(),x,y) -> divByZeroError()
    15: ify(true(),x,y) -> if(ge(x,y),x,y)
    16: if(false(),x,y) -> |0|()
    17: if(true(),x,y) -> s(div(minus(x,y),y))
    18: div(plus(x,y),z) -> plus(div(x,z),div(y,z))
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Freezing minus ge
1: ge❆1_|0|(|0|()) -> true()
2: ge❆1_s(x,|0|()) -> ge(x,|0|())
3: ge❆1_|0|(s(|0|())) -> false()
4: ge❆1_|0|(s(s(x))) -> ge❆1_|0|(s(x))
5: ge❆1_s(x,s(y)) -> ge(x,y)
6: minus❆1_|0|(|0|()) -> |0|()
7: minus❆1_|0|(s(x)) -> minus❆1_|0|(x)
8: minus❆1_s(x,|0|()) -> s(minus(x,|0|()))
9: minus❆1_s(x,s(y)) -> minus(x,y)
10: plus(|0|(),|0|()) -> |0|()
11: plus(|0|(),s(x)) -> s(plus(|0|(),x))
12: plus(s(x),y) -> s(plus(x,y))
13: div(x,y) -> ify(ge(y,s(|0|())),x,y)
14: ify(false(),x,y) -> divByZeroError()
15: ify(true(),x,y) -> if(ge(x,y),x,y)
16: if(false(),x,y) -> |0|()
17: if(true(),x,y) -> s(div(minus(x,y),y))
18: div(plus(x,y),z) -> plus(div(x,z),div(y,z))
19: ge(|0|(),_1) ->= ge❆1_|0|(_1)
20: ge(s(_1),_2) ->= ge❆1_s(_1,_2)
21: minus(|0|(),_1) ->= minus❆1_|0|(_1)
22: minus(s(_1),_2) ->= minus❆1_s(_1,_2)
Number of strict rules: 18
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #ge❆1_s(x,|0|()) -> #ge(x,|0|())
   #2: #div(x,y) -> #ify(ge(y,s(|0|())),x,y)
   #3: #div(x,y) -> #ge(y,s(|0|()))
   #4: #minus❆1_s(x,s(y)) -> #minus(x,y)
   #5: #plus(|0|(),s(x)) -> #plus(|0|(),x)
   #6: #plus(s(x),y) -> #plus(x,y)
   #7: #ge(s(_1),_2) ->? #ge❆1_s(_1,_2)
   #8: #minus❆1_|0|(s(x)) -> #minus❆1_|0|(x)
   #9: #ge❆1_s(x,s(y)) -> #ge(x,y)
   #10: #minus(s(_1),_2) ->? #minus❆1_s(_1,_2)
   #11: #if(true(),x,y) -> #div(minus(x,y),y)
   #12: #if(true(),x,y) -> #minus(x,y)
   #13: #ge(|0|(),_1) ->? #ge❆1_|0|(_1)
   #14: #minus(|0|(),_1) ->? #minus❆1_|0|(_1)
   #15: #minus❆1_s(x,|0|()) -> #minus(x,|0|())
   #16: #ify(true(),x,y) -> #if(ge(x,y),x,y)
   #17: #ify(true(),x,y) -> #ge(x,y)
   #18: #ge❆1_|0|(s(s(x))) -> #ge❆1_|0|(s(x))
   #19: #div(plus(x,y),z) -> #plus(div(x,z),div(y,z))
   #20: #div(plus(x,y),z) -> #div(x,z)
   #21: #div(plus(x,y),z) -> #div(y,z)
Number of SCCs: 8, DPs: 15, edges: 19
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#minus❆1_|0|(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #8
Number of SCCs: 7, DPs: 14, edges: 18
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: x2
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 6, DPs: 13, edges: 17
	SCC { #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: x1
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6
Number of SCCs: 5, DPs: 12, edges: 16
	SCC { #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: x1
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #18
Number of SCCs: 4, DPs: 11, edges: 15
	SCC { #20 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: x1
     s(x1)	weight: (/ 1 2)
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: (/ 1 2) + x1 + x2
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #20 #21
Number of SCCs: 3, DPs: 9, edges: 11
	SCC { #1 #7 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: x1
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: (/ 1 4)
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: (/ 1 4) + x1
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #7 #9
Number of SCCs: 2, DPs: 6, edges: 7
	SCC { #4 #10 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
minus❆1_s(x1,x2)	weight: 0
ge❆1_|0|(x1)	weight: 0
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
divByZeroError()	weight: 0
 minus(x1,x2)	weight: 0
 #ify(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
#minus❆1_s(x1,x2)	weight: (/ 1 4) + x1
  true()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
ge❆1_s(x1,x2)	weight: 0
minus❆1_|0|(x1)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: x1
#ge❆1_|0|(x1)	weight: 0
  plus(x1,x2)	weight: (/ 1 4)
  #if(x1,x2,x3)	weight: 0
#ge❆1_s(x1,x2)	weight: (/ 1 4)
#minus❆1_|0|(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #10 #15
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #2 #11 #16 }
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