/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: + *
    1: dx(X()) -> 1()
    2: dx(0()) -> 0()
    3: dx(1()) -> 0()
    4: dx(a()) -> 0()
    5: dx(+(f,g)) -> +(dx(f),dx(g))
    6: dx(*(f,g)) -> +(*(dx(f),g),*(dx(g),f))
    7: dx(-(f,g)) -> -(dx(f),dx(g))
    8: dx(neg(f)) -> neg(dx(f))
    9: dx(/(f,g)) -> -(/(dx(f),g),/(*(dx(g),f),exp(g,2())))
    10: dx(ln(f)) -> /(dx(f),f)
    11: dx(exp(f,g)) -> +(*(dx(f),*(exp(f,-(g,1())),g)),*(dx(g),*(exp(f,g),ln(f))))
Number of strict rules: 11
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #dx(*(f,g)) -> #+(*(dx(f),g),*(dx(g),f))
   #2: #dx(*(f,g)) -> #*(dx(f),g)
   #3: #dx(*(f,g)) -> #dx(f)
   #4: #dx(*(f,g)) -> #*(dx(g),f)
   #5: #dx(*(f,g)) -> #dx(g)
   #6: #*(x,*(y,z)) ->= #*(*(x,y),z)
   #7: #*(x,*(y,z)) ->= #*(x,y)
   #8: #dx(/(f,g)) -> #dx(f)
   #9: #dx(/(f,g)) -> #*(dx(g),f)
   #10: #dx(/(f,g)) -> #dx(g)
   #11: #dx(exp(f,g)) -> #+(*(dx(f),*(exp(f,-(g,1())),g)),*(dx(g),*(exp(f,g),ln(f))))
   #12: #dx(exp(f,g)) -> #*(dx(f),*(exp(f,-(g,1())),g))
   #13: #dx(exp(f,g)) -> #dx(f)
   #14: #dx(exp(f,g)) -> #*(exp(f,-(g,1())),g)
   #15: #dx(exp(f,g)) -> #*(dx(g),*(exp(f,g),ln(f)))
   #16: #dx(exp(f,g)) -> #dx(g)
   #17: #dx(exp(f,g)) -> #*(exp(f,g),ln(f))
   #18: #+(x,+(y,z)) ->= #+(+(x,y),z)
   #19: #+(x,+(y,z)) ->= #+(x,y)
   #20: #dx(-(f,g)) -> #dx(f)
   #21: #dx(-(f,g)) -> #dx(g)
   #22: #dx(ln(f)) -> #dx(f)
   #23: #dx(+(f,g)) -> #+(dx(f),dx(g))
   #24: #dx(+(f,g)) -> #dx(f)
   #25: #dx(+(f,g)) -> #dx(g)
   #26: #dx(neg(f)) -> #dx(f)
Number of SCCs: 3, DPs: 16
  SCC { #6 #7 }
only weak rules.
Number of SCCs: 2, DPs: 14
  SCC { #18 #19 }
only weak rules.
Number of SCCs: 1, DPs: 12
  SCC { #3 #5 #8 #10 #13 #16 #20..22 #24..26 }
POLO(Sum)... succeeded.
      a 	w: 0
      1 	w: 0
      ln	w: x1 + 1
      / 	w: x1 + x2 + 1
      #dx	w: x1
      dx	w: 0
      0 	w: 0
      - 	w: x1 + x2 + 1
      neg	w: x1 + 1
      2 	w: 0
      exp	w: x1 + x2 + 1
      + 	w: x1 + x2 + 1
      X 	w: 0
      * 	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #3 #5 #8 #10 #13 #16 #20..22 #24..26
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
   #27: #*(x,*(y,z)) ->= #*(*(x,y),z)
   #28: #*(x,*(y,z)) ->= #*(x,y)
   #29: #+(x,+(y,z)) ->= #+(+(x,y),z)
   #30: #+(x,+(y,z)) ->= #+(x,y)
Number of SCCs: 2, DPs: 4
  SCC { #27 #28 }
only weak rules.
Number of SCCs: 1, DPs: 2
  SCC { #29 #30 }
only weak rules.
Number of SCCs: 0, DPs: 0