/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: log(s(x1)) -> s(log(half(s(x1))))
    2: half(0(x1)) -> 0(s(s(half(x1))))
    3: half(s(0(x1))) -> 0(x1)
    4: half(s(s(x1))) -> s(half(p(s(s(x1)))))
    5: half(half(s(s(s(s(x1)))))) -> s(s(half(half(x1))))
    6: p(s(s(s(x1)))) -> s(p(s(s(x1))))
    7: s(s(p(s(x1)))) -> s(s(x1))
    8: 0(x1) -> x1
Number of strict rules: 8
Direct poly ... removes: 8
  s(x1)		w: (x1)
  half(x1)		w: (x1)
  p(x1)		w: (x1)
  log(x1)		w: (1 + x1)
  0(x1)		w: (1 + x1)
Number of strict rules: 7
Direct poly ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #half(0(x1)) -> #s(s(half(x1)))
   #2: #half(0(x1)) -> #s(half(x1))
   #3: #half(0(x1)) -> #half(x1)
   #4: #p(s(s(s(x1)))) -> #s(p(s(s(x1))))
   #5: #p(s(s(s(x1)))) -> #p(s(s(x1)))
   #6: #s(s(p(s(x1)))) -> #s(s(x1))
   #7: #half(half(s(s(s(s(x1)))))) -> #s(s(half(half(x1))))
   #8: #half(half(s(s(s(s(x1)))))) -> #s(half(half(x1)))
   #9: #half(half(s(s(s(s(x1)))))) -> #half(half(x1))
   #10: #half(half(s(s(s(s(x1)))))) -> #half(x1)
   #11: #log(s(x1)) -> #s(log(half(s(x1))))
   #12: #log(s(x1)) -> #log(half(s(x1)))
   #13: #log(s(x1)) -> #half(s(x1))
   #14: #half(s(s(x1))) -> #s(half(p(s(s(x1)))))
   #15: #half(s(s(x1))) -> #half(p(s(s(x1))))
   #16: #half(s(s(x1))) -> #p(s(s(x1)))
Number of SCCs: 5, DPs: 7
	SCC { #12 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 3 + x1})
  #log(x1)		w: (max{0, -1 + x1})
  #half(x1)		w: (0)
  #p(x1)		w: (0)
  half(x1)		w: (max{0, -1 + x1})
  p(x1)		w: (max{0, -3 + x1})
  log(x1)		w: (0)
  0(x1)		w: (0)
  #s(x1)		w: (0)
    USABLE RULES: { 3 4 6 7 }
    Removed DPs: #12
Number of SCCs: 4, DPs: 6
	SCC { #6 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #log(x1)		w: (0)
  #half(x1)		w: (0)
  #p(x1)		w: (0)
  half(x1)		w: (21238 + x1)
  p(x1)		w: (2437 + x1)
  log(x1)		w: (0)
  0(x1)		w: (1)
  #s(x1)		w: (x1)
    USABLE RULES: { 3 6 7 }
    Removed DPs: #6
Number of SCCs: 3, DPs: 5
	SCC { #15 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 11799 + x1})
  #log(x1)		w: (max{0, x1})
  #half(x1)		w: (max{0, -3433 + x1})
  #p(x1)		w: (0)
  half(x1)		w: (max{0, -11798 + x1})
  p(x1)		w: (max{0, -11799 + x1})
  log(x1)		w: (0)
  0(x1)		w: (0)
  #s(x1)		w: (0)
    USABLE RULES: { 3 4 6 7 }
    Removed DPs: #15
Number of SCCs: 2, DPs: 4
	SCC { #5 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  #log(x1)		w: (0)
  #half(x1)		w: (0)
  #p(x1)		w: (28100 + x1)
  half(x1)		w: (57700 + x1)
  p(x1)		w: (x1)
  log(x1)		w: (0)
  0(x1)		w: (1)
  #s(x1)		w: (x1)
    USABLE RULES: { 3 7 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 3
	SCC { #3 #9 #10 }
Sum... succeeded.
  s(x1)		w: (x1)
  #log(x1)		w: (0)
  #half(x1)		w: (x1)
  #p(x1)		w: (28100 + x1)
  half(x1)		w: (15922 + x1)
  p(x1)		w: (x1)
  log(x1)		w: (0)
  0(x1)		w: (1 + x1)
  #s(x1)		w: (x1)
    USABLE RULES: { 2..7 }
    Removed DPs: #3 #10
Number of SCCs: 1, DPs: 1
	SCC { #9 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 3 + x1})
  #log(x1)		w: (max{0, x1})
  #half(x1)		w: (max{0, 284 + x1})
  #p(x1)		w: (0)
  half(x1)		w: (max{0, -2 + x1})
  p(x1)		w: (max{0, -3 + x1})
  log(x1)		w: (0)
  0(x1)		w: (0)
  #s(x1)		w: (0)
    USABLE RULES: { 2..7 }
    Removed DPs: #9
Number of SCCs: 0, DPs: 0