/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:
    AC symbols: f
    1: f(g(f(h(x),x)),x) -> f(h(x),f(x,x))
    2: f(h(x),g(x)) -> f(g(h(x)),x)
    3: f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x)
    4: f(g(g(x)),x) -> f(g(x),g(x))
Number of strict rules: 4
Direct POLO(bPol) ... removes: 1 3
      h 	w: x1 + 1
      f 	w: x1 + x2 + 1
      g 	w: x1 + 1
Number of strict rules: 2
Direct POLO(bPol) ... removes: 4
      h 	w: x1
      f 	w: x1 + x2 + 1
      g 	w: 2 * x1 + 1
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #f(h(x),g(x)) -> #f(g(h(x)),x)
   #2: #f(x,f(y,z)) ->= #f(f(x,y),z)
   #3: #f(x,f(y,z)) ->= #f(x,y)
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      f 	w: x1 + x2 + 1
      #f 	w: x1 + x2
      g 	w: 1
    USABLE RULES: { 2 5 }
    Removed DPs: #1 #3
Number of SCCs: 1, DPs: 1
  SCC { #2 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
   #4: #f(f(h(x),g(x)),_1) -> #f(f(g(h(x)),x),_1)
   #5: #f(x,f(y,z)) ->= #f(f(x,y),z)
   #6: #f(x,f(y,z)) ->= #f(x,y)
Number of SCCs: 1, DPs: 3
  SCC { #4..6 }
POLO(Sum)... succeeded.
      h 	w: x1 + 1
      f 	w: x1 + x2 + 1
      #f 	w: x1 + x2
      g 	w: 1
    USABLE RULES: { 2 5 }
    Removed DPs: #4 #6
Number of SCCs: 1, DPs: 1
  SCC { #5 }
only weak rules.
Number of SCCs: 0, DPs: 0