/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: U11(tt(),N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
    2: U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
    3: afterNth(N,XS) -> snd(splitAt(N,XS))
    4: and(tt(),X) -> activate(X)
    5: fst(pair(X,Y)) -> X
    6: head(cons(N,XS)) -> N
    7: natsFrom(N) -> cons(N,n__natsFrom(s(N)))
    8: sel(N,XS) -> head(afterNth(N,XS))
    9: snd(pair(X,Y)) -> Y
    10: splitAt(0(),XS) -> pair(nil(),XS)
    11: splitAt(s(N),cons(X,XS)) -> U11(tt(),N,X,activate(XS))
    12: tail(cons(N,XS)) -> activate(XS)
    13: take(N,XS) -> fst(splitAt(N,XS))
    14: natsFrom(X) -> n__natsFrom(X)
    15: activate(n__natsFrom(X)) -> natsFrom(X)
    16: activate(X) -> X
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying U11
1: U11^1_tt(N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
2: U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
3: afterNth(N,XS) -> snd(splitAt(N,XS))
4: and(tt(),X) -> activate(X)
5: fst(pair(X,Y)) -> X
6: head(cons(N,XS)) -> N
7: natsFrom(N) -> cons(N,n__natsFrom(s(N)))
8: sel(N,XS) -> head(afterNth(N,XS))
9: snd(pair(X,Y)) -> Y
10: splitAt(0(),XS) -> pair(nil(),XS)
11: splitAt(s(N),cons(X,XS)) -> U11^1_tt(N,X,activate(XS))
12: tail(cons(N,XS)) -> activate(XS)
13: take(N,XS) -> fst(splitAt(N,XS))
14: natsFrom(X) -> n__natsFrom(X)
15: activate(n__natsFrom(X)) -> natsFrom(X)
16: activate(X) -> X
17: U11(tt(),_3,_4,_5) ->= U11^1_tt(_3,_4,_5)
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #U12(pair(YS,ZS),X) -> #activate(X)
   #2: #take(N,XS) -> #fst(splitAt(N,XS))
   #3: #take(N,XS) -> #splitAt(N,XS)
   #4: #splitAt(s(N),cons(X,XS)) -> #U11^1_tt(N,X,activate(XS))
   #5: #splitAt(s(N),cons(X,XS)) -> #activate(XS)
   #6: #tail(cons(N,XS)) -> #activate(XS)
   #7: #U11(tt(),_3,_4,_5) ->? #U11^1_tt(_3,_4,_5)
   #8: #afterNth(N,XS) -> #snd(splitAt(N,XS))
   #9: #afterNth(N,XS) -> #splitAt(N,XS)
   #10: #U11^1_tt(N,X,XS) -> #U12(splitAt(activate(N),activate(XS)),activate(X))
   #11: #U11^1_tt(N,X,XS) -> #splitAt(activate(N),activate(XS))
   #12: #U11^1_tt(N,X,XS) -> #activate(N)
   #13: #U11^1_tt(N,X,XS) -> #activate(XS)
   #14: #U11^1_tt(N,X,XS) -> #activate(X)
   #15: #sel(N,XS) -> #head(afterNth(N,XS))
   #16: #sel(N,XS) -> #afterNth(N,XS)
   #17: #activate(n__natsFrom(X)) -> #natsFrom(X)
   #18: #and(tt(),X) -> #activate(X)
Number of SCCs: 1, DPs: 2
  SCC { #4 #11 }
POLO(Sum)... succeeded.
      U11	w: 0
      s 	w: x1 + 4
      #take	w: 0
      activate	w: x1 + 1
      take	w: 0
      and	w: 0
      pair	w: 0
      fst	w: 0
      #activate	w: 0
      natsFrom	w: x1 + 1
      #head	w: 0
      splitAt	w: 0
      #fst	w: 0
      U12	w: 0
      n__natsFrom	w: x1 + 1
      #U12	w: 0
      tail	w: 0
      0 	w: 0
      #sel	w: 0
      sel	w: 0
      afterNth	w: 0
      nil	w: 0
      U11^1_tt	w: 0
      #tail	w: 0
      #splitAt	w: x1 + 1
      #afterNth	w: 0
      #U11	w: 0
      head	w: 0
      #snd	w: 0
      cons	w: 1
      #natsFrom	w: 0
      snd	w: 0
      tt	w: 0
      #and	w: 0
      #U11^1_tt	w: x1 + 3
    USABLE RULES: { 7 14..16 }
    Removed DPs: #4 #11
Number of SCCs: 0, DPs: 0