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))
Number of strict rules: 17
Direct Order(PosReal,>,Poly) ... failed.
Freezing minus ge plus
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❆1_0(0()) -> 0()
11: plus❆1_0(s(x)) -> s(plus❆1_0(x))
12: plus❆1_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: plus(0(),_1) ->= plus❆1_0(_1)
19: plus(s(_1),_2) ->= plus❆1_s(_1,_2)
20: ge(0(),_1) ->= ge❆1_0(_1)
21: ge(s(_1),_2) ->= ge❆1_s(_1,_2)
22: minus(0(),_1) ->= minus❆1_0(_1)
23: minus(s(_1),_2) ->= minus❆1_s(_1,_2)
Number of strict rules: 17
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❆1_0(s(x)) -> #plus❆1_0(x)
   #6: #minus(s(_1),_2) ->? #minus❆1_s(_1,_2)
   #7: #plus❆1_s(x,y) -> #plus(x,y)
   #8: #ge(0(),_1) ->? #ge❆1_0(_1)
   #9: #minus❆1_0(s(x)) -> #minus❆1_0(x)
   #10: #ge❆1_s(x,s(y)) -> #ge(x,y)
   #11: #minus(0(),_1) ->? #minus❆1_0(_1)
   #12: #if(true(),x,y) -> #div(minus(x,y),y)
   #13: #if(true(),x,y) -> #minus(x,y)
   #14: #plus(s(_1),_2) ->? #plus❆1_s(_1,_2)
   #15: #ge(s(_1),_2) ->? #ge❆1_s(_1,_2)
   #16: #minus❆1_s(x,0()) -> #minus(x,0())
   #17: #ify(true(),x,y) -> #if(ge(x,y),x,y)
   #18: #ify(true(),x,y) -> #ge(x,y)
   #19: #ge❆1_0(s(s(x))) -> #ge❆1_0(s(x))
   #20: #plus(0(),_1) ->? #plus❆1_0(_1)
Number of SCCs: 7, DPs: 14, edges: 16
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: x1
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#plus❆1_s(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 6, DPs: 13, edges: 15
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: x1
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#plus❆1_s(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 5, DPs: 12, edges: 14
	SCC { #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: x1
#ge❆1_s(x1,x2)	weight: 0
#plus❆1_s(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #19
Number of SCCs: 4, DPs: 11, edges: 13
	SCC { #7 #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: 0
#plus❆1_s(x1,x2)	weight: (/ 1 4) + x1
    Usable rules: { }
    Removed DPs: #7 #14
Number of SCCs: 3, DPs: 9, edges: 11
	SCC { #1 #10 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: x2
#minus❆1_s(x1,x2)	weight: 0
  true()	weight: 0
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: x2
#plus❆1_s(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 8, edges: 9
	SCC { #1 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: 0
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: (/ 1 4) + x1
#plus❆1_s(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #1 #15
Number of SCCs: 2, DPs: 6, edges: 7
	SCC { #4 #6 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
minus❆1_s(x1,x2)	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
plus❆1_0(x1)	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
ge❆1_0(x1)	weight: 0
     0()	weight: 0
    if(x1,x2,x3)	weight: 0
    ge(x1,x2)	weight: 0
minus❆1_0(x1)	weight: 0
#plus❆1_0(x1)	weight: 0
ge❆1_s(x1,x2)	weight: 0
   ify(x1,x2,x3)	weight: 0
#minus(x1,x2)	weight: x1
#minus❆1_0(x1)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
plus❆1_s(x1,x2)	weight: 0
#ge❆1_0(x1)	weight: 0
#ge❆1_s(x1,x2)	weight: (/ 1 4)
#plus❆1_s(x1,x2)	weight: (/ 1 4)
    Usable rules: { }
    Removed DPs: #4 #6 #16
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #2 #12 #17 }
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