Input TRS:
    1: lt(0(),s(x)) -> true()
    2: lt(x,0()) -> false()
    3: lt(s(x),s(y)) -> lt(x,y)
    4: logarithm(x) -> ifa(lt(0(),x),x)
    5: ifa(true(),x) -> help(x,1())
    6: ifa(false(),x) -> logZeroError()
    7: help(x,y) -> ifb(lt(y,x),x,y)
    8: ifb(true(),x,y) -> help(half(x),s(y))
    9: ifb(false(),x,y) -> y
    10: half(0()) -> 0()
    11: half(s(0())) -> 0()
    12: half(s(s(x))) -> s(half(x))
Number of strict rules: 12
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #half(s(s(x))) -> #half(x)
   #2: #help(x,y) -> #ifb(lt(y,x),x,y)
   #3: #help(x,y) -> #lt(y,x)
   #4: #ifa(true(),x) -> #help(x,1())
   #5: #lt(s(x),s(y)) -> #lt(x,y)
   #6: #ifb(true(),x,y) -> #help(half(x),s(y))
   #7: #ifb(true(),x,y) -> #half(x)
   #8: #logarithm(x) -> #ifa(lt(0(),x),x)
   #9: #logarithm(x) -> #lt(0(),x)
Number of SCCs: 3, DPs: 4, edges: 4
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   ifa(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
  #lt(x1,x2)	weight: 0
#help(x1,x2)	weight: 0
 #ifb(x1,x2,x3)	weight: 0
 false()	weight: 0
logZeroError()	weight: 0
#half(x1)	weight: x1
  true()	weight: 0
  half(x1)	weight: 0
     0()	weight: 0
 #ifa(x1,x2)	weight: 0
logarithm(x1)	weight: 0
#logarithm(x1)	weight: 0
  help(x1,x2)	weight: 0
   ifb(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3, edges: 3
	SCC { #5 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     1()	weight: 0
   ifa(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 2) + x1
  #lt(x1,x2)	weight: x2
#help(x1,x2)	weight: 0
 #ifb(x1,x2,x3)	weight: 0
 false()	weight: 0
logZeroError()	weight: 0
#half(x1)	weight: 0
  true()	weight: 0
  half(x1)	weight: 0
     0()	weight: 0
 #ifa(x1,x2)	weight: 0
logarithm(x1)	weight: 0
#logarithm(x1)	weight: 0
  help(x1,x2)	weight: 0
   ifb(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)... succeeded.
     1()	weight: 0
   ifa(x1,x2)	weight: 0
     s(x1)	weight: max{0, (/ 1 4) + x1}
  #lt(x1,x2)	weight: 0
#help(x1,x2)	weight: max{0, (- (/ 1 8)) + x1}
 #ifb(x1,x2,x3)	weight: max{0, (- (/ 1 16)) + x1, (- (/ 3 16)) + x2}
 false()	weight: 0
logZeroError()	weight: 0
#half(x1)	weight: 0
  true()	weight: (/ 1 8)
  half(x1)	weight: max{0, (- (/ 1 8)) + x1}
     0()	weight: 0
 #ifa(x1,x2)	weight: 0
logarithm(x1)	weight: 0
#logarithm(x1)	weight: 0
  help(x1,x2)	weight: 0
   ifb(x1,x2,x3)	weight: 0
    lt(x1,x2)	weight: max{0, (- (/ 1 8)) + x2}
    Usable rules: { 1..3 10..12 }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0, edges: 0
YES