/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: terms(N) -> cons(recip(sqr(N)))
    2: sqr(0()) -> 0()
    3: sqr(s(X)) -> s(add(sqr(X),dbl(X)))
    4: dbl(0()) -> 0()
    5: dbl(s(X)) -> s(s(dbl(X)))
    6: add(0(),X) -> X
    7: add(s(X),Y) -> s(add(X,Y))
    8: first(0(),X) -> nil()
    9: first(s(X),cons(Y)) -> cons(Y)
    10: half(0()) -> 0()
    11: half(s(0())) -> 0()
    12: half(s(s(X))) -> s(half(X))
    13: half(dbl(X)) -> X
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #half(s(s(X))) -> #half(X)
   #2: #add(s(X),Y) -> #add(X,Y)
   #3: #dbl(s(X)) -> #dbl(X)
   #4: #sqr(s(X)) -> #add(sqr(X),dbl(X))
   #5: #sqr(s(X)) -> #sqr(X)
   #6: #sqr(s(X)) -> #dbl(X)
   #7: #terms(N) -> #sqr(N)
Number of SCCs: 4, DPs: 4
  SCC { #5 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      recip	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #half	w: 0
      half	w: 0
      #sqr	w: x1
      0 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      cons	w: 0
      #add	w: 0
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 3, DPs: 3
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      recip	w: 0
      dbl	w: 0
      #dbl	w: x1
      #terms	w: 0
      #half	w: 0
      half	w: 0
      #sqr	w: 0
      0 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      cons	w: 0
      #add	w: 0
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 2, DPs: 2
  SCC { #1 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      recip	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #half	w: x1
      half	w: 0
      #sqr	w: 0
      0 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      cons	w: 0
      #add	w: 0
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      recip	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #half	w: 0
      half	w: 0
      #sqr	w: 0
      0 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      cons	w: 0
      #add	w: x1
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0