/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(0()) -> s(0())
    2: f(s(0())) -> s(0())
    3: f(s(s(x))) -> f(f(s(x)))
    4: rand(x) ->= x
    5: rand(x) ->= rand(s(x))
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4
      s 	w: x1
      f 	w: x1
      rand	w: x1 + 1
      0 	w: 1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying f
1: f^1_0() -> s(0())
2: f^1_s(0()) -> s(0())
3: f^1_s(s(x)) -> f(f^1_s(x))
5: rand(x) ->= rand(s(x))
6: f(0()) ->= f^1_0()
7: f(s(_1)) ->= f^1_s(_1)
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #f(0()) ->? #f^1_0()
   #2: #f(s(_1)) ->? #f^1_s(_1)
   #3: #f^1_s(s(x)) -> #f(f^1_s(x))
   #4: #f^1_s(s(x)) -> #f^1_s(x)
Number of SCCs: 1, DPs: 3
  SCC { #2..4 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      #f^1_s	w: x1 + 1
      f 	w: x1 + 2
      rand	w: 0
      0 	w: 1
      #f 	w: x1
      #f^1_0	w: 0
      f^1_0	w: 3
      f^1_s	w: x1 + 2
    Removed DPs: #2..4
Number of SCCs: 0, DPs: 0