/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: f(c(s(x),y)) -> f(c(x,s(y)))
    2: f(c(s(x),s(y))) -> g(c(x,y))
    3: g(c(x,s(y))) -> g(c(s(x),y))
    4: g(c(s(x),s(y))) -> f(c(x,y))
Number of strict rules: 4
Direct poly ... removes: 4 2
  s(x1)		w: (1 + x1)
  c(x1,x2)		w: (8366 + 2 * x2 + 2 * x1)
  f(x1)		w: (3 + x1)
  g(x1)		w: (x1)
Number of strict rules: 2
Direct poly ... failed.
Freezing f g
1: f❆1_c(s(x),y) -> f❆1_c(x,s(y))
3: g❆1_c(x,s(y)) -> g❆1_c(s(x),y)
5: g(c(_1,_2)) ->= g❆1_c(_1,_2)
6: f(c(_1,_2)) ->= f❆1_c(_1,_2)
Number of strict rules: 2
Direct poly ... removes: 1 5 6
  s(x1)		w: (1 + x1)
  g❆1_c(x1,x2)		w: (x2 + x1)
  c(x1,x2)		w: (1 + x2 + x1)
  f❆1_c(x1,x2)		w: (x2 + 2 * x1)
  f(x1)		w: (2 * x1)
  g(x1)		w: (2 * x1)
Number of strict rules: 1
Direct poly ... removes: 3
  s(x1)		w: (1 + x1)
  g❆1_c(x1,x2)		w: (2 + 2 * x2 + x1)
  c(x1,x2)		w: (30613 + x2 + x1)
  f❆1_c(x1,x2)		w: (x2 + 2 * x1)
  f(x1)		w: (2 * x1)
  g(x1)		w: (10450 + 2 * x1)
Number of strict rules: 0