/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: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1)))))))))
    2: i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
    3: j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
    4: j(s(x1)) -> s(s(s(s(p(p(s(s(i(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(s(s(s(s(x1)))))))))
Number of strict rules: 7
Direct poly ... removes: 1 3
  s(x1)		w: (x1)
  p(x1)		w: (x1)
  0(x1)		w: (29534 + x1)
  j(x1)		w: (868 + x1)
  i(x1)		w: (868 + x1)
Number of strict rules: 5
Direct poly ... failed.
Freezing p
2: i(s(x1)) -> p❆1_s(p❆1_s(s(j(p❆1_s(p❆1_s(p(p(p(p❆1_s(s(s(s(x1)))))))))))))
4: j(s(x1)) -> s(s(s(s(p(p❆1_s(s(i(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(s(s(s(s(x1)))))))))
8: p(0(_1)) ->= p❆1_0(_1)
9: p(s(_1)) ->= p❆1_s(_1)
Number of strict rules: 5
Direct poly ... failed.
Dependency Pairs:
   #1: #i(s(x1)) -> #p❆1_s(p❆1_s(s(j(p❆1_s(p❆1_s(p(p(p(p❆1_s(s(s(s(x1)))))))))))))
   #2: #i(s(x1)) -> #p❆1_s(s(j(p❆1_s(p❆1_s(p(p(p(p❆1_s(s(s(s(x1))))))))))))
   #3: #i(s(x1)) -> #j(p❆1_s(p❆1_s(p(p(p(p❆1_s(s(s(s(x1))))))))))
   #4: #i(s(x1)) -> #p❆1_s(p❆1_s(p(p(p(p❆1_s(s(s(s(x1)))))))))
   #5: #i(s(x1)) -> #p❆1_s(p(p(p(p❆1_s(s(s(s(x1))))))))
   #6: #i(s(x1)) -> #p(p(p(p❆1_s(s(s(s(x1)))))))
   #7: #i(s(x1)) -> #p(p(p❆1_s(s(s(s(x1))))))
   #8: #i(s(x1)) -> #p(p❆1_s(s(s(s(x1)))))
   #9: #i(s(x1)) -> #p❆1_s(s(s(s(x1))))
   #10: #p(s(_1)) ->? #p❆1_s(_1)
   #11: #p(p❆1_s(x1)) -> #p(x1)
   #12: #p(0(_1)) ->? #p❆1_0(_1)
   #13: #j(s(x1)) -> #p(p❆1_s(s(i(p❆1_s(p❆1_s(x1))))))
   #14: #j(s(x1)) -> #p❆1_s(s(i(p❆1_s(p❆1_s(x1)))))
   #15: #j(s(x1)) -> #i(p❆1_s(p❆1_s(x1)))
   #16: #j(s(x1)) -> #p❆1_s(p❆1_s(x1))
   #17: #j(s(x1)) -> #p❆1_s(x1)
Number of SCCs: 2, DPs: 3
	SCC { #11 }
Sum... succeeded.
  s(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)
  #j(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  j(x1)		w: (0)
  i(x1)		w: (0)
  #i(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 2
	SCC { #3 #15 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 10 + x1})
  p❆1_s(x1)		w: (max{0, 1 + x1})
  #p❆1_0(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (max{0, -9 + x1})
  0(x1)		w: (0)
  #j(x1)		w: (max{0, -12 + x1})
  p❆1_0(x1)		w: (0)
  j(x1)		w: (0)
  i(x1)		w: (0)
  #i(x1)		w: (max{0, -5 + x1})
    USABLE RULES: { 5..9 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0