Input TRS:
    1: minus(s(x),y) -> if(gt(s(x),y),x,y)
    2: if(true(),x,y) -> s(minus(x,y))
    3: if(false(),x,y) -> 0()
    4: ge(x,0()) -> true()
    5: ge(0(),s(x)) -> false()
    6: ge(s(x),s(y)) -> ge(x,y)
    7: gt(0(),y) -> false()
    8: gt(s(x),0()) -> true()
    9: gt(s(x),s(y)) -> gt(x,y)
    10: div(x,y) -> if1(ge(x,y),x,y)
    11: if1(true(),x,y) -> if2(gt(y,0()),x,y)
    12: if1(false(),x,y) -> 0()
    13: if2(true(),x,y) -> s(div(minus(x,y),y))
    14: if2(false(),x,y) -> 0()
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Freezing gt
1: minus(s(x),y) -> if(gt❆1_s(x,y),x,y)
2: if(true(),x,y) -> s(minus(x,y))
3: if(false(),x,y) -> 0()
4: ge(x,0()) -> true()
5: ge(0(),s(x)) -> false()
6: ge(s(x),s(y)) -> ge(x,y)
7: gt❆1_0(y) -> false()
8: gt❆1_s(x,0()) -> true()
9: gt❆1_s(x,s(y)) -> gt(x,y)
10: div(x,y) -> if1(ge(x,y),x,y)
11: if1(true(),x,y) -> if2(gt(y,0()),x,y)
12: if1(false(),x,y) -> 0()
13: if2(true(),x,y) -> s(div(minus(x,y),y))
14: if2(false(),x,y) -> 0()
15: gt(0(),_1) ->= gt❆1_0(_1)
16: gt(s(_1),_2) ->= gt❆1_s(_1,_2)
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #if(true(),x,y) -> #minus(x,y)
   #2: #ge(s(x),s(y)) -> #ge(x,y)
   #3: #if2(true(),x,y) -> #div(minus(x,y),y)
   #4: #if2(true(),x,y) -> #minus(x,y)
   #5: #gt❆1_s(x,s(y)) -> #gt(x,y)
   #6: #if1(true(),x,y) -> #if2(gt(y,0()),x,y)
   #7: #if1(true(),x,y) -> #gt(y,0())
   #8: #div(x,y) -> #if1(ge(x,y),x,y)
   #9: #div(x,y) -> #ge(x,y)
   #10: #gt(s(_1),_2) ->? #gt❆1_s(_1,_2)
   #11: #minus(s(x),y) -> #if(gt❆1_s(x,y),x,y)
   #12: #minus(s(x),y) -> #gt❆1_s(x,y)
   #13: #gt(0(),_1) ->? #gt❆1_0(_1)
Number of SCCs: 4, DPs: 8, edges: 8
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
gt❆1_0(x1)	weight: 0
    gt(x1,x2)	weight: 0
 minus(x1,x2)	weight: 0
   if1(x1,x2,x3)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: x2
  true()	weight: 0
 #if1(x1,x2,x3)	weight: 0
   if2(x1,x2,x3)	weight: 0
    if(x1,x2,x3)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#gt❆1_0(x1)	weight: 0
  #gt(x1,x2)	weight: 0
#gt❆1_s(x1,x2)	weight: 0
#minus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
gt❆1_s(x1,x2)	weight: 0
 #if2(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 3, DPs: 7, edges: 7
	SCC { #5 #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
gt❆1_0(x1)	weight: 0
    gt(x1,x2)	weight: 0
 minus(x1,x2)	weight: 0
   if1(x1,x2,x3)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
  true()	weight: 0
 #if1(x1,x2,x3)	weight: 0
   if2(x1,x2,x3)	weight: 0
    if(x1,x2,x3)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#gt❆1_0(x1)	weight: 0
  #gt(x1,x2)	weight: x1
#gt❆1_s(x1,x2)	weight: (/ 1 4) + x1
#minus(x1,x2)	weight: 0
  #if(x1,x2,x3)	weight: 0
gt❆1_s(x1,x2)	weight: 0
 #if2(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #10
Number of SCCs: 2, DPs: 5, edges: 5
	SCC { #1 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 #div(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
gt❆1_0(x1)	weight: (/ 1 4)
    gt(x1,x2)	weight: x1 + x2
 minus(x1,x2)	weight: 0
   if1(x1,x2,x3)	weight: 0
 false()	weight: 0
   div(x1,x2)	weight: 0
  #ge(x1,x2)	weight: 0
  true()	weight: 0
 #if1(x1,x2,x3)	weight: 0
   if2(x1,x2,x3)	weight: 0
    if(x1,x2,x3)	weight: 0
     0()	weight: 0
    ge(x1,x2)	weight: 0
#gt❆1_0(x1)	weight: 0
  #gt(x1,x2)	weight: 0
#gt❆1_s(x1,x2)	weight: (/ 1 4)
#minus(x1,x2)	weight: x1
  #if(x1,x2,x3)	weight: (/ 1 4) + x2
gt❆1_s(x1,x2)	weight: (/ 3 4)
 #if2(x1,x2,x3)	weight: 0
    Usable rules: { }
    Removed DPs: #1 #11
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #3 #6 #8 }
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