/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: q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1)))))))))
    2: q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))))
    3: r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1)))))))))))
    4: r(s(x1)) -> p(s(p(s(s(q(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(x1))))
Number of strict rules: 7
Direct poly ... removes: 1 3
  q(x1)		w: (23612 + 2 * x1)
  s(x1)		w: (x1)
  r(x1)		w: (23612 + 2 * x1)
  p(x1)		w: (x1)
  0(x1)		w: (12618 + x1)
Number of strict rules: 5
Direct poly ... failed.
Freezing p
2: q(s(x1)) -> p(p❆1_s(s(s(s(s(s(r(p(p❆1_s(s(x1)))))))))))
4: r(s(x1)) -> p❆1_s(p❆1_s(s(q(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(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: #q(s(x1)) -> #p(p❆1_s(s(s(s(s(s(r(p(p❆1_s(s(x1)))))))))))
   #2: #q(s(x1)) -> #p❆1_s(s(s(s(s(s(r(p(p❆1_s(s(x1))))))))))
   #3: #q(s(x1)) -> #r(p(p❆1_s(s(x1))))
   #4: #q(s(x1)) -> #p(p❆1_s(s(x1)))
   #5: #q(s(x1)) -> #p❆1_s(s(x1))
   #6: #p(s(_1)) ->? #p❆1_s(_1)
   #7: #p(p❆1_s(x1)) -> #p(x1)
   #8: #p(0(_1)) ->? #p❆1_0(_1)
   #9: #r(s(x1)) -> #p❆1_s(p❆1_s(s(q(p❆1_s(p❆1_s(x1))))))
   #10: #r(s(x1)) -> #p❆1_s(s(q(p❆1_s(p❆1_s(x1)))))
   #11: #r(s(x1)) -> #q(p❆1_s(p❆1_s(x1)))
   #12: #r(s(x1)) -> #p❆1_s(p❆1_s(x1))
   #13: #r(s(x1)) -> #p❆1_s(x1)
Number of SCCs: 2, DPs: 3
	SCC { #7 }
Sum... succeeded.
  q(x1)		w: (0)
  s(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  r(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)
  #r(x1)		w: (0)
  #q(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 2
	SCC { #3 #11 }
Sum... succeeded.
  q(x1)		w: (0)
  s(x1)		w: (7316 + x1)
  p❆1_s(x1)		w: (2438 + x1)
  #p❆1_0(x1)		w: (0)
  r(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  p(x1)		w: (x1)
  0(x1)		w: (21239)
  p❆1_0(x1)		w: (21239)
  #r(x1)		w: (x1)
  #q(x1)		w: (2439 + x1)
    USABLE RULES: { 5..9 }
    Removed DPs: #3 #11
Number of SCCs: 0, DPs: 0