/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
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 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
	SCC { #1 }
Sum... succeeded.
  1()		w: (0)
  ifa(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #lt(x1,x2)		w: (0)
  #help(x1,x2)		w: (0)
  #ifb(x1,x2,x3)		w: (0)
  false()		w: (0)
  logZeroError()		w: (0)
  #half(x1)		w: (x1)
  true()		w: (0)
  half(x1)		w: (0)
  0()		w: (0)
  #ifa(x1,x2)		w: (0)
  logarithm(x1)		w: (0)
  #logarithm(x1)		w: (0)
  help(x1,x2)		w: (0)
  ifb(x1,x2,x3)		w: (0)
  lt(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 2, DPs: 3
	SCC { #5 }
Sum... succeeded.
  1()		w: (0)
  ifa(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #lt(x1,x2)		w: (x2)
  #help(x1,x2)		w: (0)
  #ifb(x1,x2,x3)		w: (0)
  false()		w: (0)
  logZeroError()		w: (0)
  #half(x1)		w: (0)
  true()		w: (0)
  half(x1)		w: (0)
  0()		w: (0)
  #ifa(x1,x2)		w: (0)
  logarithm(x1)		w: (0)
  #logarithm(x1)		w: (0)
  help(x1,x2)		w: (0)
  ifb(x1,x2,x3)		w: (0)
  lt(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 1, DPs: 2
	SCC { #2 #6 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  1()		w: (0)
  ifa(x1,x2)		w: (0)
  s(x1)		w: (max{0, 3 + x1})
  #lt(x1,x2)		w: (0)
  #help(x1,x2)		w: (max{0, 3000 + x1})
  #ifb(x1,x2,x3)		w: (max{0, 2999 + x2, 2998 + x1})
  false()		w: (2)
  logZeroError()		w: (0)
  #half(x1)		w: (0)
  true()		w: (3)
  half(x1)		w: (max{0, -2 + x1})
  0()		w: (0)
  #ifa(x1,x2)		w: (0)
  logarithm(x1)		w: (0)
  #logarithm(x1)		w: (0)
  help(x1,x2)		w: (0)
  ifb(x1,x2,x3)		w: (0)
  lt(x1,x2)		w: (max{0, 2 + x2})
    USABLE RULES: { 1..3 10..12 }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0