/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: twoto(0(x1)) -> p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1))))))))))))))))
    2: twoto(s(x1)) -> p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
    3: twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
    4: twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
    5: p(p(s(x1))) -> p(x1)
    6: p(s(x1)) -> x1
    7: p(0(x1)) -> 0(s(s(s(s(p(s(x1)))))))
    8: 0(x1) -> x1
Number of strict rules: 8
Direct poly ... removes: 8 1
  s(x1)		w: (x1)
  twice(x1)		w: (x1)
  p(x1)		w: (x1)
  0(x1)		w: (12457 + x1)
  twoto(x1)		w: (868 + x1)
Number of strict rules: 6
Direct poly ... failed.
Freezing p
2: twoto(s(x1)) -> p(p❆1_s(s(p(p(p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))))))))))))))
3: twice(0(x1)) -> p❆1_s(p❆1_s(0(s(p❆1_s(s(s(s(p❆1_s(x1)))))))))
4: twice(s(x1)) -> s(p(p(p(p❆1_s(s(s(s(s(twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))))))
5: p(p❆1_s(x1)) -> p(x1)
6: p❆1_s(x1) -> x1
7: p❆1_0(x1) -> 0(s(s(s(s(p❆1_s(x1))))))
9: p(0(_1)) ->= p❆1_0(_1)
10: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 6
Direct poly ... failed.
Dependency Pairs:
   #1: #twoto(s(x1)) -> #p(p❆1_s(s(p(p(p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))))))))))))))
   #2: #twoto(s(x1)) -> #p❆1_s(s(p(p(p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))))))))))))))
   #3: #twoto(s(x1)) -> #p(p(p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))))))))))))
   #4: #twoto(s(x1)) -> #p(p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))))))))))
   #5: #twoto(s(x1)) -> #p❆1_s(s(s(twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))))))))))
   #6: #twoto(s(x1)) -> #twice(p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))))))
   #7: #twoto(s(x1)) -> #p(p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))))))
   #8: #twoto(s(x1)) -> #p❆1_s(s(p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))))
   #9: #twoto(s(x1)) -> #p(p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))))
   #10: #twoto(s(x1)) -> #p(p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1)))))))
   #11: #twoto(s(x1)) -> #p❆1_s(s(s(twoto(p❆1_s(p❆1_s(x1))))))
   #12: #twoto(s(x1)) -> #twoto(p❆1_s(p❆1_s(x1)))
   #13: #twoto(s(x1)) -> #p❆1_s(p❆1_s(x1))
   #14: #twoto(s(x1)) -> #p❆1_s(x1)
   #15: #p(0(_1)) ->? #p❆1_0(_1)
   #16: #p❆1_0(x1) -> #p❆1_s(x1)
   #17: #p(s(_1)) ->? #p❆1_s(_1)
   #18: #p(p❆1_s(x1)) -> #p(x1)
   #19: #twice(0(x1)) -> #p❆1_s(p❆1_s(0(s(p❆1_s(s(s(s(p❆1_s(x1)))))))))
   #20: #twice(0(x1)) -> #p❆1_s(0(s(p❆1_s(s(s(s(p❆1_s(x1))))))))
   #21: #twice(0(x1)) -> #p❆1_s(s(s(s(p❆1_s(x1)))))
   #22: #twice(0(x1)) -> #p❆1_s(x1)
   #23: #twice(s(x1)) -> #p(p(p(p❆1_s(s(s(s(s(twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))))))
   #24: #twice(s(x1)) -> #p(p(p❆1_s(s(s(s(s(twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))))
   #25: #twice(s(x1)) -> #p(p❆1_s(s(s(s(s(twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1)))))))))))
   #26: #twice(s(x1)) -> #p❆1_s(s(s(s(s(twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1))))))))))
   #27: #twice(s(x1)) -> #twice(p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1)))))
   #28: #twice(s(x1)) -> #p❆1_s(p❆1_s(p❆1_s(p❆1_s(x1))))
   #29: #twice(s(x1)) -> #p❆1_s(p❆1_s(p❆1_s(x1)))
   #30: #twice(s(x1)) -> #p❆1_s(p❆1_s(x1))
   #31: #twice(s(x1)) -> #p❆1_s(x1)
Number of SCCs: 3, DPs: 3
	SCC { #18 }
Sum... succeeded.
  s(x1)		w: (0)
  twice(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  #p(x1)		w: (x1)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  twoto(x1)		w: (0)
  #twice(x1)		w: (0)
  #twoto(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #18
Number of SCCs: 2, DPs: 2
	SCC { #12 }
Sum... succeeded.
  s(x1)		w: (3 + x1)
  twice(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  twoto(x1)		w: (0)
  #twice(x1)		w: (0)
  #twoto(x1)		w: (x1)
    USABLE RULES: { 6 }
    Removed DPs: #12
Number of SCCs: 1, DPs: 1
	SCC { #27 }
Sum... succeeded.
  s(x1)		w: (5 + x1)
  twice(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  twoto(x1)		w: (0)
  #twice(x1)		w: (x1)
  #twoto(x1)		w: (x1)
    USABLE RULES: { 6 }
    Removed DPs: #27
Number of SCCs: 0, DPs: 0