/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 POLO(bPol) ... removes: 1 3 5 7
      a 	w: x1
      d 	w: x1 + 23
      b 	w: x1 + 53
      c 	w: x1 + 35
      f 	w: x1 + 80
Number of strict rules: 3
Direct POLO(bPol) ... removes: 6
      a 	w: x1
      d 	w: x1 + 23
      b 	w: 2 * x1 + 35
      c 	w: x1 + 35
      f 	w: x1 + 80
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying 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 POLO(bPol) ... removes: 4 8 10 11
      a 	w: x1
      d 	w: x1
      d^1_a^1_b	w: x1
      b 	w: 2 * x1 + 2
      a^1_f	w: x1 + 1
      c 	w: x1
      f 	w: x1 + 1
      a^1_b	w: x1 + 1
      d^1_b	w: 2 * x1 + 1
Number of strict rules: 1
Direct POLO(bPol) ... 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 }
POLO(Sum)... succeeded.
      a 	w: x1
      d 	w: 0
      d^1_a^1_b	w: 0
      b 	w: 0
      a^1_f	w: x1 + 2
      c 	w: 0
      f 	w: x1 + 2
      a^1_b	w: 0
      #a 	w: x1
      d^1_b	w: 0
      #a^1_f	w: x1 + 1
    USABLE RULES: { 2 9 }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0