/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: f(f(x1)) -> b(b(b(x1)))
    2: a(f(x1)) -> f(a(a(x1)))
    3: b(b(x1)) -> c(c(a(c(x1))))
    4: d(b(x1)) -> d(a(b(x1)))
    5: c(c(x1)) -> d(d(d(x1)))
    6: b(d(x1)) -> d(b(x1))
    7: c(d(d(x1))) -> f(x1)
Number of strict rules: 7
Direct poly ... removes: 1 3 5 7
  a(x1)		w: (x1)
  d(x1)		w: (63707 + x1)
  b(x1)		w: (143342 + x1)
  c(x1)		w: (95561 + x1)
  f(x1)		w: (222974 + x1)
Number of strict rules: 3
Direct poly ... removes: 6
  a(x1)		w: (x1)
  d(x1)		w: (2 + 2 * x1)
  b(x1)		w: (1 + 2 * x1)
  c(x1)		w: (7 + x1)
  f(x1)		w: (13 + x1)
Number of strict rules: 2
Direct poly ... failed.
Freezing d a
2: a❆1_f(x1) -> f(a(a(x1)))
4: d❆1_b(x1) -> d❆1_a❆1_b(x1)
8: a(b(_1)) ->= a❆1_b(_1)
9: a(f(_1)) ->= a❆1_f(_1)
10: d(a❆1_b(_1)) ->= d❆1_a❆1_b(_1)
11: d(b(_1)) ->= d❆1_b(_1)
Number of strict rules: 2
Direct poly ... removes: 4 8 10 11
  a(x1)		w: (x1)
  d(x1)		w: (2 * x1)
  b(x1)		w: (283 + x1)
  a❆1_f(x1)		w: (20540 + x1)
  c(x1)		w: (x1)
  f(x1)		w: (20540 + x1)
  d❆1_b(x1)		w: (565 + x1)
  d❆1_a❆1_b(x1)		w: (563 + x1)
  a❆1_b(x1)		w: (282 + x1)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #a❆1_f(x1) -> #a(a(x1))
   #2: #a❆1_f(x1) -> #a(x1)
   #3: #a(f(_1)) ->? #a❆1_f(_1)
Number of SCCs: 1, DPs: 3
	SCC { #1..3 }
Sum... succeeded.
  a(x1)		w: (x1)
  d(x1)		w: (0)
  b(x1)		w: (0)
  a❆1_f(x1)		w: (2 + x1)
  c(x1)		w: (0)
  f(x1)		w: (2 + x1)
  d❆1_b(x1)		w: (0)
  d❆1_a❆1_b(x1)		w: (0)
  a❆1_b(x1)		w: (0)
  #a(x1)		w: (1 + x1)
  #a❆1_f(x1)		w: (2 + x1)
    USABLE RULES: { 2 9 }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0