/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: g(c(x,s(y))) -> g(c(s(x),y))
    2: f(c(s(x),y)) -> f(c(x,s(y)))
    3: f(f(x)) -> f(d(f(x)))
    4: f(x) -> x
Number of strict rules: 4
Direct poly ... removes: 4
  d(x1)		w: (x1)
  s(x1)		w: (1 + x1)
  c(x1,x2)		w: (2 * x2 + 2 * x1)
  f(x1)		w: (32286 + 2 * x1)
  g(x1)		w: (8365 + 2 * x1)
Number of strict rules: 3
Direct poly ... failed.
Freezing g
1: g❆1_c(x,s(y)) -> g❆1_c(s(x),y)
2: f(c(s(x),y)) -> f(c(x,s(y)))
3: f(f(x)) -> f(d(f(x)))
5: g(c(_1,_2)) ->= g❆1_c(_1,_2)
Number of strict rules: 3
Direct poly ... removes: 5
  d(x1)		w: (x1)
  s(x1)		w: (1 + x1)
  g❆1_c(x1,x2)		w: (3 + x2 + x1)
  c(x1,x2)		w: (1 + x2 + x1)
  f(x1)		w: (20538 + x1)
  g(x1)		w: (8 + 2 * x1)
Number of strict rules: 3
Direct poly ... removes: 1
  d(x1)		w: (x1)
  s(x1)		w: (1 + x1)
  g❆1_c(x1,x2)		w: (3 + 2 * x2 + x1)
  c(x1,x2)		w: (1 + x2 + x1)
  f(x1)		w: (23535 + x1)
  g(x1)		w: (8 + 2 * x1)
Number of strict rules: 2
Direct poly ... removes: 2
  d(x1)		w: (x1)
  s(x1)		w: (1 + x1)
  g❆1_c(x1,x2)		w: (3 + 2 * x2 + x1)
  c(x1,x2)		w: (1 + x2 + 2 * x1)
  f(x1)		w: (41992 + x1)
  g(x1)		w: (8 + 2 * x1)
Number of strict rules: 1
Direct poly ... failed.
Dependency Pairs:
   #1: #f(f(x)) -> #f(d(f(x)))
Number of SCCs: 0, DPs: 0