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


--------------------------------------------------------------------------------


YES
Input TRS:
    1: thrice(0(x1)) -> p(s(p(p(p(s(s(s(0(p(s(p(s(x1)))))))))))))
    2: thrice(s(x1)) -> p(p(s(s(half(p(p(s(s(p(s(sixtimes(p(s(p(p(s(s(x1))))))))))))))))))
    3: half(0(x1)) -> p(p(s(s(p(s(0(p(s(s(s(s(x1))))))))))))
    4: half(s(x1)) -> p(s(p(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1)))))))))))))))))
    5: half(s(s(x1))) -> p(s(p(s(s(p(p(s(s(half(p(p(s(s(p(s(x1))))))))))))))))
    6: sixtimes(0(x1)) -> p(s(p(s(0(s(s(s(s(s(p(s(p(s(x1))))))))))))))
    7: sixtimes(s(x1)) -> p(p(s(s(s(s(s(s(s(p(p(s(p(s(s(s(sixtimes(p(s(p(p(p(s(s(s(x1)))))))))))))))))))))))))
    8: p(p(s(x1))) -> p(x1)
    9: p(s(x1)) -> x1
    10: p(0(x1)) -> 0(s(s(s(s(x1)))))
    11: 0(x1) -> x1
Number of strict rules: 11
Direct poly ... removes: 1 3 11 6 2
  s(x1)		w: (x1)
  half(x1)		w: (2655 + x1)
  p(x1)		w: (x1)
  0(x1)		w: (1 + x1)
  sixtimes(x1)		w: (24066 + x1)
  thrice(x1)		w: (26722 + x1)
Number of strict rules: 6
Direct poly ... failed.
Freezing p
4: half(s(x1)) -> p❆1_s(p(p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))))))
5: half(s(s(x1))) -> p❆1_s(p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1)))))))))))
7: sixtimes(s(x1)) -> p(p❆1_s(s(s(s(s(s(s(p(p❆1_s(p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1))))))))))))))))))))
8: p(p❆1_s(x1)) -> p(x1)
9: p❆1_s(x1) -> x1
10: p❆1_0(x1) -> 0(s(s(s(s(x1)))))
12: p(0(_1)) ->= p❆1_0(_1)
13: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 6
Direct poly ... failed.
Dependency Pairs:
   #1: #p(s(_1)) ->? #p❆1_s(_1)
   #2: #p(0(_1)) ->? #p❆1_0(_1)
   #3: #sixtimes(s(x1)) -> #p(p❆1_s(s(s(s(s(s(s(p(p❆1_s(p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1))))))))))))))))))))
   #4: #sixtimes(s(x1)) -> #p❆1_s(s(s(s(s(s(s(p(p❆1_s(p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1)))))))))))))))))))
   #5: #sixtimes(s(x1)) -> #p(p❆1_s(p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1))))))))))))
   #6: #sixtimes(s(x1)) -> #p❆1_s(p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1)))))))))))
   #7: #sixtimes(s(x1)) -> #p❆1_s(s(s(sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1))))))))))
   #8: #sixtimes(s(x1)) -> #sixtimes(p❆1_s(p(p(p❆1_s(s(s(x1)))))))
   #9: #sixtimes(s(x1)) -> #p❆1_s(p(p(p❆1_s(s(s(x1))))))
   #10: #sixtimes(s(x1)) -> #p(p(p❆1_s(s(s(x1)))))
   #11: #sixtimes(s(x1)) -> #p(p❆1_s(s(s(x1))))
   #12: #sixtimes(s(x1)) -> #p❆1_s(s(s(x1)))
   #13: #half(s(s(x1))) -> #p❆1_s(p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1)))))))))))
   #14: #half(s(s(x1))) -> #p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))))
   #15: #half(s(s(x1))) -> #p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))
   #16: #half(s(s(x1))) -> #p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1)))))))
   #17: #half(s(s(x1))) -> #half(p(p❆1_s(s(p❆1_s(x1)))))
   #18: #half(s(s(x1))) -> #p(p❆1_s(s(p❆1_s(x1))))
   #19: #half(s(s(x1))) -> #p❆1_s(s(p❆1_s(x1)))
   #20: #half(s(s(x1))) -> #p❆1_s(x1)
   #21: #p(p❆1_s(x1)) -> #p(x1)
   #22: #half(s(x1)) -> #p❆1_s(p(p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))))))
   #23: #half(s(x1)) -> #p(p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1)))))))))))
   #24: #half(s(x1)) -> #p❆1_s(s(p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))))
   #25: #half(s(x1)) -> #p(p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1))))))))
   #26: #half(s(x1)) -> #p❆1_s(s(half(p(p❆1_s(s(p❆1_s(x1)))))))
   #27: #half(s(x1)) -> #half(p(p❆1_s(s(p❆1_s(x1)))))
   #28: #half(s(x1)) -> #p(p❆1_s(s(p❆1_s(x1))))
   #29: #half(s(x1)) -> #p❆1_s(s(p❆1_s(x1)))
   #30: #half(s(x1)) -> #p❆1_s(x1)
Number of SCCs: 3, DPs: 4
	SCC { #21 }
Sum... succeeded.
  s(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  #sixtimes(x1)		w: (0)
  #half(x1)		w: (0)
  #p(x1)		w: (x1)
  #p❆1_s(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  sixtimes(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  thrice(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #21
Number of SCCs: 2, DPs: 3
	SCC { #8 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 96250 + x1})
  p❆1_s(x1)		w: (max{0, 21239 + x1})
  #p❆1_0(x1)		w: (0)
  #sixtimes(x1)		w: (max{0, -84957 + x1})
  #half(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (max{0, -75011 + x1})
  0(x1)		w: (0)
  sixtimes(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  thrice(x1)		w: (0)
    USABLE RULES: { 8..10 12 13 }
    Removed DPs: #8
Number of SCCs: 1, DPs: 2
	SCC { #17 #27 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (x1)
  #p❆1_0(x1)		w: (0)
  #sixtimes(x1)		w: (0)
  #half(x1)		w: (2437 + x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (x1)
  0(x1)		w: (21242)
  sixtimes(x1)		w: (0)
  p❆1_0(x1)		w: (21242)
  thrice(x1)		w: (0)
    USABLE RULES: { 8..10 12 13 }
    Removed DPs: #17
Number of SCCs: 1, DPs: 1
	SCC { #27 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 40657 + x1})
  p❆1_s(x1)		w: (max{0, 2 + x1})
  #p❆1_0(x1)		w: (0)
  #sixtimes(x1)		w: (max{0, x1})
  #half(x1)		w: (max{0, -8370 + x1})
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (max{0, -32290 + x1})
  0(x1)		w: (0)
  sixtimes(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  thrice(x1)		w: (0)
    USABLE RULES: { 8..10 12 13 }
    Removed DPs: #27
Number of SCCs: 0, DPs: 0