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


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


YES
Input TRS:
    1: p(0(x1)) -> 0(s(s(p(x1))))
    2: p(s(x1)) -> x1
    3: p(p(s(x1))) -> p(x1)
    4: f(s(x1)) -> p(s(g(p(s(s(x1))))))
    5: g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
    6: j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
    7: half(0(x1)) -> 0(s(s(half(p(s(p(s(x1))))))))
    8: half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
    9: rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))
Number of strict rules: 9
Direct poly ... failed.
Freezing j p
1: p❆1_0(x1) -> 0(s(s(p(x1))))
2: p❆1_s(x1) -> x1
3: p(p❆1_s(x1)) -> p(x1)
4: f(s(x1)) -> p❆1_s(g(p❆1_s(s(x1))))
5: g(s(x1)) -> p(p❆1_s(s(s(j❆1_s(p❆1_s(p❆1_s(x1)))))))
6: j❆1_s(x1) -> p❆1_s(s(p❆1_s(f(p❆1_s(p(p❆1_s(x1)))))))
7: half(0(x1)) -> 0(s(s(half(p❆1_s(p❆1_s(x1))))))
8: half(s(s(x1))) -> s(half(p(p❆1_s(s(x1)))))
9: rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))
10: p(0(_1)) ->= p❆1_0(_1)
11: p(s(_1)) ->= p❆1_s(_1)
12: j(s(_1)) ->= j❆1_s(_1)
Number of strict rules: 9
Direct poly ... removes: 12
  s(x1)		w: (x1)
  p❆1_s(x1)		w: (x1)
  j❆1_s(x1)		w: (24773 + x1)
  rd(x1)		w: (14098 + x1)
  f(x1)		w: (24773 + x1)
  half(x1)		w: (1 + 2 * x1)
  p(x1)		w: (x1)
  0(x1)		w: (x1)
  p❆1_0(x1)		w: (x1)
  j(x1)		w: (24827 + x1)
  g(x1)		w: (24773 + x1)
Number of strict rules: 9
Direct poly ... failed.
Dependency Pairs:
   #1: #j❆1_s(x1) -> #p❆1_s(s(p❆1_s(f(p❆1_s(p(p❆1_s(x1)))))))
   #2: #j❆1_s(x1) -> #p❆1_s(f(p❆1_s(p(p❆1_s(x1)))))
   #3: #j❆1_s(x1) -> #f(p❆1_s(p(p❆1_s(x1))))
   #4: #j❆1_s(x1) -> #p❆1_s(p(p❆1_s(x1)))
   #5: #j❆1_s(x1) -> #p(p❆1_s(x1))
   #6: #j❆1_s(x1) -> #p❆1_s(x1)
   #7: #rd(0(x1)) -> #rd(x1)
   #8: #p(s(_1)) ->? #p❆1_s(_1)
   #9: #half(0(x1)) -> #half(p❆1_s(p❆1_s(x1)))
   #10: #half(0(x1)) -> #p❆1_s(p❆1_s(x1))
   #11: #half(0(x1)) -> #p❆1_s(x1)
   #12: #p(0(_1)) ->? #p❆1_0(_1)
   #13: #g(s(x1)) -> #p(p❆1_s(s(s(j❆1_s(p❆1_s(p❆1_s(x1)))))))
   #14: #g(s(x1)) -> #p❆1_s(s(s(j❆1_s(p❆1_s(p❆1_s(x1))))))
   #15: #g(s(x1)) -> #j❆1_s(p❆1_s(p❆1_s(x1)))
   #16: #g(s(x1)) -> #p❆1_s(p❆1_s(x1))
   #17: #g(s(x1)) -> #p❆1_s(x1)
   #18: #p(p❆1_s(x1)) -> #p(x1)
   #19: #p❆1_0(x1) -> #p(x1)
   #20: #half(s(s(x1))) -> #half(p(p❆1_s(s(x1))))
   #21: #half(s(s(x1))) -> #p(p❆1_s(s(x1)))
   #22: #half(s(s(x1))) -> #p❆1_s(s(x1))
   #23: #f(s(x1)) -> #p❆1_s(g(p❆1_s(s(x1))))
   #24: #f(s(x1)) -> #g(p❆1_s(s(x1)))
   #25: #f(s(x1)) -> #p❆1_s(s(x1))
Number of SCCs: 4, DPs: 9
	SCC { #7 }
Sum... succeeded.
  s(x1)		w: (0)
  p❆1_s(x1)		w: (0)
  #j❆1_s(x1)		w: (0)
  #p❆1_0(x1)		w: (0)
  j❆1_s(x1)		w: (0)
  rd(x1)		w: (0)
  #half(x1)		w: (0)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #rd(x1)		w: (x1)
  f(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (1 + x1)
  p❆1_0(x1)		w: (0)
  #f(x1)		w: (0)
  #g(x1)		w: (0)
  j(x1)		w: (0)
  g(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 3, DPs: 8
	SCC { #12 #18 #19 }
Sum... succeeded.
  s(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #j❆1_s(x1)		w: (0)
  #p❆1_0(x1)		w: (1 + x1)
  j❆1_s(x1)		w: (0)
  rd(x1)		w: (0)
  #half(x1)		w: (0)
  #p(x1)		w: (x1)
  #p❆1_s(x1)		w: (0)
  #rd(x1)		w: (0)
  f(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (2 + x1)
  p❆1_0(x1)		w: (0)
  #f(x1)		w: (0)
  #g(x1)		w: (0)
  j(x1)		w: (0)
  g(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #12 #18 #19
Number of SCCs: 2, DPs: 5
	SCC { #9 #20 }
Sum... succeeded.
  s(x1)		w: (x1)
  p❆1_s(x1)		w: (x1)
  #j❆1_s(x1)		w: (0)
  #p❆1_0(x1)		w: (1)
  j❆1_s(x1)		w: (0)
  rd(x1)		w: (0)
  #half(x1)		w: (8855 + x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #rd(x1)		w: (0)
  f(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (x1)
  0(x1)		w: (1 + x1)
  p❆1_0(x1)		w: (1 + x1)
  #f(x1)		w: (0)
  #g(x1)		w: (0)
  j(x1)		w: (0)
  g(x1)		w: (0)
    USABLE RULES: { 1..3 10 11 }
    Removed DPs: #9
Number of SCCs: 2, DPs: 4
	SCC { #20 }
Sum... succeeded.
  s(x1)		w: (1 + x1)
  p❆1_s(x1)		w: (x1)
  #j❆1_s(x1)		w: (0)
  #p❆1_0(x1)		w: (1)
  j❆1_s(x1)		w: (0)
  rd(x1)		w: (0)
  #half(x1)		w: (8855 + x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #rd(x1)		w: (0)
  f(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (x1)
  0(x1)		w: (8367)
  p❆1_0(x1)		w: (8367)
  #f(x1)		w: (0)
  #g(x1)		w: (0)
  j(x1)		w: (0)
  g(x1)		w: (0)
    USABLE RULES: { 1..3 10 11 }
    Removed DPs: #20
Number of SCCs: 1, DPs: 3
	SCC { #3 #15 #24 }
Sum... succeeded.
  s(x1)		w: (30616 + x1)
  p❆1_s(x1)		w: (x1)
  #j❆1_s(x1)		w: (30615 + x1)
  #p❆1_0(x1)		w: (1)
  j❆1_s(x1)		w: (0)
  rd(x1)		w: (0)
  #half(x1)		w: (8855 + x1)
  #p(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #rd(x1)		w: (0)
  f(x1)		w: (0)
  half(x1)		w: (0)
  p(x1)		w: (1 + x1)
  0(x1)		w: (8367)
  p❆1_0(x1)		w: (8367)
  #f(x1)		w: (1 + x1)
  #g(x1)		w: (x1)
  j(x1)		w: (0)
  g(x1)		w: (0)
    USABLE RULES: { 1..3 10 11 }
    Removed DPs: #3 #15 #24
Number of SCCs: 0, DPs: 0