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