/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(x)) -> f(c(f(x)))
    2: f(f(x)) -> f(d(f(x)))
    3: g(c(x)) -> x
    4: g(d(x)) -> x
    5: g(c(h(0()))) -> g(d(1()))
    6: g(c(1())) -> g(d(h(0())))
    7: g(h(x)) -> g(x)
Number of strict rules: 7
Direct poly ... removes: 4 3 7
  h(x1)		w: (30613 + x1)
  1()		w: (30614)
  d(x1)		w: (x1)
  c(x1)		w: (x1)
  f(x1)		w: (10451 + x1)
  0()		w: (1)
  g(x1)		w: (1 + 2 * x1)
Number of strict rules: 4
Direct poly ... failed.
Freezing g
1: f(f(x)) -> f(c(f(x)))
2: f(f(x)) -> f(d(f(x)))
5: g❆1_c(h(0())) -> g❆1_d(1())
6: g❆1_c(1()) -> g❆1_d(h(0()))
8: g(d(_1)) ->= g❆1_d(_1)
9: g(c(_1)) ->= g❆1_c(_1)
Number of strict rules: 4
Direct poly ... removes: 8 5 9 6
  h(x1)		w: (15921 + 2 * x1)
  1()		w: (15923)
  d(x1)		w: (x1)
  g❆1_c(x1)		w: (20538 + x1)
  c(x1)		w: (x1)
  g❆1_d(x1)		w: (20537 + x1)
  f(x1)		w: (282 + x1)
  0()		w: (1)
  g(x1)		w: (20540 + x1)
Number of strict rules: 2
Direct poly ... failed.
Dependency Pairs:
   #1: #f(f(x)) -> #f(d(f(x)))
   #2: #f(f(x)) -> #f(c(f(x)))
Number of SCCs: 0, DPs: 0