/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: a(a(x1)) -> b(b(b(x1)))
    2: a(x1) -> d(c(d(x1)))
    3: b(b(b(x1))) -> a(f(x1))
    4: b(b(x1)) -> c(c(c(x1)))
    5: c(c(x1)) -> d(d(d(x1)))
    6: c(d(d(x1))) -> f(x1)
    7: f(f(x1)) -> f(a(x1))
Number of strict rules: 7
Direct poly ... removes: 4 5
  a(x1)		w: (581169 + x1)
  d(x1)		w: (161436 + x1)
  b(x1)		w: (387446 + x1)
  c(x1)		w: (258297 + x1)
  f(x1)		w: (581169 + x1)
Number of strict rules: 5
Direct poly ... failed.
Freezing c
1: a(a(x1)) -> b(b(b(x1)))
2: a(x1) -> d(c❆1_d(x1))
3: b(b(b(x1))) -> a(f(x1))
6: c❆1_d(d(x1)) -> f(x1)
7: f(f(x1)) -> f(a(x1))
8: c(d(_1)) ->= c❆1_d(_1)
Number of strict rules: 5
Direct poly ... removes: 8
  a(x1)		w: (26571 + x1)
  d(x1)		w: (3 + x1)
  b(x1)		w: (17714 + x1)
  c(x1)		w: (26566 + x1)
  f(x1)		w: (26571 + x1)
  c❆1_d(x1)		w: (26568 + x1)
Number of strict rules: 5
Direct poly ... failed.
Dependency Pairs:
   #1: #a(x1) -> #c❆1_d(x1)
   #2: #c❆1_d(d(x1)) -> #f(x1)
   #3: #f(f(x1)) -> #f(a(x1))
   #4: #f(f(x1)) -> #a(x1)
   #5: #b(b(b(x1))) -> #a(f(x1))
   #6: #b(b(b(x1))) -> #f(x1)
   #7: #a(a(x1)) -> #b(b(b(x1)))
   #8: #a(a(x1)) -> #b(b(x1))
   #9: #a(a(x1)) -> #b(x1)
Number of SCCs: 1, DPs: 8
	SCC { #1 #2 #4..9 }
Sum... succeeded.
  a(x1)		w: (6 + x1)
  d(x1)		w: (6 + x1)
  b(x1)		w: (4 + x1)
  c(x1)		w: (0)
  f(x1)		w: (6 + x1)
  #f(x1)		w: (x1)
  #c❆1_d(x1)		w: (1 + x1)
  c❆1_d(x1)		w: (x1)
  #a(x1)		w: (2 + x1)
  #b(x1)		w: (x1)
    USABLE RULES: { 1..3 6 7 }
    Removed DPs: #1 #2 #4 #6 #8 #9
Number of SCCs: 0, DPs: 0