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


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YES
Input TRS:
    1: half(0()) -> 0()
    2: half(s(0())) -> 0()
    3: half(s(s(x))) -> s(half(x))
    4: le(0(),y) -> true()
    5: le(s(x),0()) -> false()
    6: le(s(x),s(y)) -> le(x,y)
    7: inc(0()) -> 0()
    8: inc(s(x)) -> s(inc(x))
    9: log(x) -> log2(x,0())
    10: log2(x,y) -> if(le(x,s(0())),x,inc(y))
    11: if(true(),x,s(y)) -> y
    12: if(false(),x,y) -> log2(half(x),y)
Number of strict rules: 12
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #le(s(x),s(y)) -> #le(x,y)
   #2: #log(x) -> #log2(x,0())
   #3: #if(false(),x,y) -> #log2(half(x),y)
   #4: #if(false(),x,y) -> #half(x)
   #5: #log2(x,y) -> #if(le(x,s(0())),x,inc(y))
   #6: #log2(x,y) -> #le(x,s(0()))
   #7: #log2(x,y) -> #inc(y)
   #8: #half(s(s(x))) -> #half(x)
   #9: #inc(s(x)) -> #inc(x)
Number of SCCs: 4, DPs: 5
	SCC { #9 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  #log2(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (0)
  false()		w: (0)
  #log(x1)		w: (0)
  #half(x1)		w: (0)
  #inc(x1)		w: (x1)
  inc(x1)		w: (0)
  true()		w: (0)
  half(x1)		w: (0)
  log(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #if(x1,x2,x3)		w: (0)
  log2(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #9
Number of SCCs: 3, DPs: 4
	SCC { #8 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  #log2(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (0)
  false()		w: (0)
  #log(x1)		w: (0)
  #half(x1)		w: (x1)
  #inc(x1)		w: (0)
  inc(x1)		w: (0)
  true()		w: (0)
  half(x1)		w: (0)
  log(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #if(x1,x2,x3)		w: (0)
  log2(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 2, DPs: 3
	SCC { #1 }
Sum... succeeded.
  le(x1,x2)		w: (0)
  #log2(x1,x2)		w: (0)
  s(x1)		w: (1 + x1)
  #le(x1,x2)		w: (x2)
  false()		w: (0)
  #log(x1)		w: (0)
  #half(x1)		w: (0)
  #inc(x1)		w: (0)
  inc(x1)		w: (0)
  true()		w: (0)
  half(x1)		w: (0)
  log(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #if(x1,x2,x3)		w: (0)
  log2(x1,x2)		w: (0)
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 2
	SCC { #3 #5 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  le(x1,x2)		w: (max{0, 36741 + x1})
  #log2(x1,x2)		w: (max{0, 16204 + x1})
  s(x1)		w: (max{0, 1144 + x1})
  #le(x1,x2)		w: (0)
  false()		w: (37885)
  #log(x1)		w: (0)
  #half(x1)		w: (0)
  #inc(x1)		w: (0)
  inc(x1)		w: (0)
  true()		w: (1)
  half(x1)		w: (max{0, -282 + x1})
  log(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (0)
  #if(x1,x2,x3)		w: (max{0, 15922 + x2, -20538 + x1})
  log2(x1,x2)		w: (0)
    USABLE RULES: { 1..6 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0