Input TRS:
    1: lt(x,0()) -> false()
    2: lt(0(),s(y)) -> true()
    3: lt(s(x),s(y)) -> lt(x,y)
    4: plus(x,0()) -> x
    5: plus(x,s(y)) -> s(plus(x,y))
    6: quot(x,s(y)) -> help(x,s(y),0())
    7: help(x,s(y),c) -> if(lt(c,x),x,s(y),c)
    8: if(true(),x,s(y),c) -> s(help(x,s(y),plus(c,s(y))))
    9: if(false(),x,s(y),c) -> 0()
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #quot(x,s(y)) -> #help(x,s(y),0())
   #2: #help(x,s(y),c) -> #if(lt(c,x),x,s(y),c)
   #3: #help(x,s(y),c) -> #lt(c,x)
   #4: #plus(x,s(y)) -> #plus(x,y)
   #5: #lt(s(x),s(y)) -> #lt(x,y)
   #6: #if(true(),x,s(y),c) -> #help(x,s(y),plus(c,s(y)))
   #7: #if(true(),x,s(y),c) -> #plus(c,s(y))
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: 0
#help(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: x2
 false()	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
#quot(x1,x2)	weight: 0
  help(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: x2
#help(x1,x2,x3)	weight: 0
#plus(x1,x2)	weight: 0
 false()	weight: 0
  true()	weight: 0
     0()	weight: 0
    if(x1,x2,x3,x4)	weight: 0
  quot(x1,x2)	weight: 0
  plus(x1,x2)	weight: 0
  #if(x1,x2,x3,x4)	weight: 0
#quot(x1,x2)	weight: 0
  help(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #2 #6 }
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