/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: foo(0(x1)) -> 0(s(p(p(p(s(s(s(p(s(x1))))))))))
    2: foo(s(x1)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(x1))))))))))))))))))))))))))
    3: bar(0(x1)) -> 0(p(s(s(s(x1)))))
    4: bar(s(x1)) -> p(s(p(p(s(s(foo(s(p(p(s(s(x1))))))))))))
    5: p(p(s(x1))) -> p(x1)
    6: p(s(x1)) -> x1
    7: p(0(x1)) -> 0(s(s(s(s(x1)))))
Number of strict rules: 7
Direct poly ... failed.
Freezing foo p
1: foo❆1_0(x1) -> 0(s(p(p(p❆1_s(s(s(p❆1_s(x1))))))))
2: foo❆1_s(x1) -> p❆1_s(p(p(p❆1_s(s(p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))))))))))))))
3: bar(0(x1)) -> 0(p❆1_s(s(s(x1))))
4: bar(s(x1)) -> p❆1_s(p(p❆1_s(s(foo❆1_s(p(p❆1_s(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(x1)))))
8: p(0(_1)) ->= p❆1_0(_1)
9: p(s(_1)) ->= p❆1_s(_1)
10: foo(0(_1)) ->= foo❆1_0(_1)
11: foo(s(_1)) ->= foo❆1_s(_1)
Number of strict rules: 7
Direct poly ... failed.
Dependency Pairs:
   #1: #foo❆1_s(x1) -> #p❆1_s(p(p(p❆1_s(s(p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))))))))))))))
   #2: #foo❆1_s(x1) -> #p(p(p❆1_s(s(p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1)))))))))))))))))
   #3: #foo❆1_s(x1) -> #p(p❆1_s(s(p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))))))))))))
   #4: #foo❆1_s(x1) -> #p❆1_s(s(p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1)))))))))))))))
   #5: #foo❆1_s(x1) -> #p❆1_s(s(p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1)))))))))))))
   #6: #foo❆1_s(x1) -> #p❆1_s(foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1)))))))))))
   #7: #foo❆1_s(x1) -> #foo(p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))))))
   #8: #foo❆1_s(x1) -> #p(p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1)))))))))
   #9: #foo❆1_s(x1) -> #p❆1_s(s(p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))))
   #10: #foo❆1_s(x1) -> #p❆1_s(bar(p(p❆1_s(s(p❆1_s(x1))))))
   #11: #foo❆1_s(x1) -> #bar(p(p❆1_s(s(p❆1_s(x1)))))
   #12: #foo❆1_s(x1) -> #p(p❆1_s(s(p❆1_s(x1))))
   #13: #foo❆1_s(x1) -> #p❆1_s(s(p❆1_s(x1)))
   #14: #foo❆1_s(x1) -> #p❆1_s(x1)
   #15: #p(s(_1)) ->? #p❆1_s(_1)
   #16: #foo(s(_1)) ->? #foo❆1_s(_1)
   #17: #foo(0(_1)) ->? #foo❆1_0(_1)
   #18: #p(p❆1_s(x1)) -> #p(x1)
   #19: #bar(0(x1)) -> #p❆1_s(s(s(x1)))
   #20: #foo❆1_0(x1) -> #p(p(p❆1_s(s(s(p❆1_s(x1))))))
   #21: #foo❆1_0(x1) -> #p(p❆1_s(s(s(p❆1_s(x1)))))
   #22: #foo❆1_0(x1) -> #p❆1_s(s(s(p❆1_s(x1))))
   #23: #foo❆1_0(x1) -> #p❆1_s(x1)
   #24: #p(0(_1)) ->? #p❆1_0(_1)
   #25: #bar(s(x1)) -> #p❆1_s(p(p❆1_s(s(foo❆1_s(p(p❆1_s(s(x1))))))))
   #26: #bar(s(x1)) -> #p(p❆1_s(s(foo❆1_s(p(p❆1_s(s(x1)))))))
   #27: #bar(s(x1)) -> #p❆1_s(s(foo❆1_s(p(p❆1_s(s(x1))))))
   #28: #bar(s(x1)) -> #foo❆1_s(p(p❆1_s(s(x1))))
   #29: #bar(s(x1)) -> #p(p❆1_s(s(x1)))
   #30: #bar(s(x1)) -> #p❆1_s(s(x1))
Number of SCCs: 2, DPs: 5
	SCC { #18 }
Sum... succeeded.
  s(x1)		w: (0)
  p❆1_s(x1)		w: (1 + x1)
  #p❆1_0(x1)		w: (0)
  #bar(x1)		w: (0)
  #p(x1)		w: (x1)
  foo❆1_0(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #foo❆1_s(x1)		w: (0)
  p(x1)		w: (0)
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  #foo(x1)		w: (0)
  #foo❆1_0(x1)		w: (0)
  bar(x1)		w: (0)
  foo(x1)		w: (0)
  foo❆1_s(x1)		w: (0)
    USABLE RULES: { }
    Removed DPs: #18
Number of SCCs: 1, DPs: 4
	SCC { #7 #11 #16 #28 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 2 + x1})
  p❆1_s(x1)		w: (max{0, x1})
  #p❆1_0(x1)		w: (0)
  #bar(x1)		w: (0)
  #p(x1)		w: (0)
  foo❆1_0(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #foo❆1_s(x1)		w: (0)
  p(x1)		w: (max{0, -2 + x1})
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  #foo(x1)		w: (max{0, x1})
  #foo❆1_0(x1)		w: (0)
  bar(x1)		w: (0)
  foo(x1)		w: (0)
  foo❆1_s(x1)		w: (0)
    USABLE RULES: { 1..11 }
    Removed DPs: #16
Number of SCCs: 1, DPs: 2
	SCC { #11 #28 }
Sum... Max... QLPOpS... NegMaxSum... succeeded.
  s(x1)		w: (max{0, 40783 + x1})
  p❆1_s(x1)		w: (max{0, x1})
  #p❆1_0(x1)		w: (0)
  #bar(x1)		w: (max{0, 40784 + x1})
  #p(x1)		w: (0)
  foo❆1_0(x1)		w: (0)
  #p❆1_s(x1)		w: (0)
  #foo❆1_s(x1)		w: (max{0, 40785 + x1})
  p(x1)		w: (max{0, -40783 + x1})
  0(x1)		w: (0)
  p❆1_0(x1)		w: (0)
  #foo(x1)		w: (max{0, x1})
  #foo❆1_0(x1)		w: (0)
  bar(x1)		w: (0)
  foo(x1)		w: (0)
  foo❆1_s(x1)		w: (0)
    USABLE RULES: { 1..11 }
    Removed DPs: #11 #28
Number of SCCs: 0, DPs: 0