/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(a()) -> g(h(a()))
    2: h(g(x)) -> g(h(f(x)))
    3: k(x,h(x),a()) -> h(x)
    4: k(f(x),y,x) -> f(x)
Number of strict rules: 4
Direct poly ... removes: 4 3
  a()		w: (282)
  h(x1)		w: (x1)
  k(x1,x2,x3)		w: (1 + 2 * x3 + x2 + 2 * x1)
  f(x1)		w: (x1)
  g(x1)		w: (x1)
Number of strict rules: 2
Direct poly ... failed.
Freezing h
1: f(a()) -> g(h❆1_a())
2: h❆1_g(x) -> g(h(f(x)))
5: h(a()) ->= h❆1_a()
6: h(g(_1)) ->= h❆1_g(_1)
Number of strict rules: 2
Direct poly ... removes: 1 5
  a()		w: (3)
  h(x1)		w: (2438 + x1)
  h❆1_a()		w: (1)
  k(x1,x2,x3)		w: (x3 + x2 + x1)
  f(x1)		w: (x1)
  h❆1_g(x1)		w: (2439 + x1)
  g(x1)		w: (1 + x1)
Number of strict rules: 1
Direct poly ... removes: 6 2
  a()		w: (32288)
  h(x1)		w: (2438 + 2 * x1)
  h❆1_a()		w: (1)
  k(x1,x2,x3)		w: (x3 + x2 + x1)
  f(x1)		w: (x1)
  h❆1_g(x1)		w: (2441 + 2 * x1)
  g(x1)		w: (2 + x1)
Number of strict rules: 0