/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 fst(pair(XS,YS)) -> XS
 snd(pair(XS,YS)) -> YS
 splitAt(0(),XS) -> pair(nil(),XS)
 splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
 u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
 head(cons(N,XS)) -> N
 tail(cons(N,XS)) -> activate(XS)
 sel(N,XS) -> head(afterNth(N,XS))
 take(N,XS) -> fst(splitAt(N,XS))
 afterNth(N,XS) -> snd(splitAt(N,XS))
 natsFrom(X) -> n__natsFrom(X)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   splitAt#(s(N),cons(X,XS)) -> activate#(XS)
   splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
   splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS))
   u#(pair(YS,ZS),N,X,XS) -> activate#(X)
   tail#(cons(N,XS)) -> activate#(XS)
   sel#(N,XS) -> afterNth#(N,XS)
   sel#(N,XS) -> head#(afterNth(N,XS))
   take#(N,XS) -> splitAt#(N,XS)
   take#(N,XS) -> fst#(splitAt(N,XS))
   afterNth#(N,XS) -> splitAt#(N,XS)
   afterNth#(N,XS) -> snd#(splitAt(N,XS))
   activate#(n__natsFrom(X)) -> natsFrom#(X)
  TRS:
   natsFrom(N) -> cons(N,n__natsFrom(s(N)))
   fst(pair(XS,YS)) -> XS
   snd(pair(XS,YS)) -> YS
   splitAt(0(),XS) -> pair(nil(),XS)
   splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
   u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
   head(cons(N,XS)) -> N
   tail(cons(N,XS)) -> activate(XS)
   sel(N,XS) -> head(afterNth(N,XS))
   take(N,XS) -> fst(splitAt(N,XS))
   afterNth(N,XS) -> snd(splitAt(N,XS))
   natsFrom(X) -> n__natsFrom(X)
   activate(n__natsFrom(X)) -> natsFrom(X)
   activate(X) -> X
  TDG Processor:
   DPs:
    splitAt#(s(N),cons(X,XS)) -> activate#(XS)
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
    splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS))
    u#(pair(YS,ZS),N,X,XS) -> activate#(X)
    tail#(cons(N,XS)) -> activate#(XS)
    sel#(N,XS) -> afterNth#(N,XS)
    sel#(N,XS) -> head#(afterNth(N,XS))
    take#(N,XS) -> splitAt#(N,XS)
    take#(N,XS) -> fst#(splitAt(N,XS))
    afterNth#(N,XS) -> splitAt#(N,XS)
    afterNth#(N,XS) -> snd#(splitAt(N,XS))
    activate#(n__natsFrom(X)) -> natsFrom#(X)
   TRS:
    natsFrom(N) -> cons(N,n__natsFrom(s(N)))
    fst(pair(XS,YS)) -> XS
    snd(pair(XS,YS)) -> YS
    splitAt(0(),XS) -> pair(nil(),XS)
    splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
    u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
    head(cons(N,XS)) -> N
    tail(cons(N,XS)) -> activate(XS)
    sel(N,XS) -> head(afterNth(N,XS))
    take(N,XS) -> fst(splitAt(N,XS))
    afterNth(N,XS) -> snd(splitAt(N,XS))
    natsFrom(X) -> n__natsFrom(X)
    activate(n__natsFrom(X)) -> natsFrom(X)
    activate(X) -> X
   graph:
    take#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS))
    take#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
    take#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> activate#(XS)
    afterNth#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS))
    afterNth#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
    afterNth#(N,XS) -> splitAt#(N,XS) ->
    splitAt#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(N,XS) -> afterNth#(N,XS) ->
    afterNth#(N,XS) -> snd#(splitAt(N,XS))
    sel#(N,XS) -> afterNth#(N,XS) ->
    afterNth#(N,XS) -> splitAt#(N,XS)
    tail#(cons(N,XS)) -> activate#(XS) ->
    activate#(n__natsFrom(X)) -> natsFrom#(X)
    u#(pair(YS,ZS),N,X,XS) -> activate#(X) ->
    activate#(n__natsFrom(X)) -> natsFrom#(X)
    splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS)) ->
    u#(pair(YS,ZS),N,X,XS) -> activate#(X)
    splitAt#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__natsFrom(X)) -> natsFrom#(X)
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS)) ->
    splitAt#(s(N),cons(X,XS)) -> u#(splitAt(N,activate(XS)),N,X,activate(XS))
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS)) ->
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
    splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS)) ->
    splitAt#(s(N),cons(X,XS)) -> activate#(XS)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 15/144
    DPs:
     splitAt#(s(N),cons(X,XS)) -> splitAt#(N,activate(XS))
    TRS:
     natsFrom(N) -> cons(N,n__natsFrom(s(N)))
     fst(pair(XS,YS)) -> XS
     snd(pair(XS,YS)) -> YS
     splitAt(0(),XS) -> pair(nil(),XS)
     splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
     u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
     head(cons(N,XS)) -> N
     tail(cons(N,XS)) -> activate(XS)
     sel(N,XS) -> head(afterNth(N,XS))
     take(N,XS) -> fst(splitAt(N,XS))
     afterNth(N,XS) -> snd(splitAt(N,XS))
     natsFrom(X) -> n__natsFrom(X)
     activate(n__natsFrom(X)) -> natsFrom(X)
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(splitAt#) = 0
     problem:
      DPs:
       
      TRS:
       natsFrom(N) -> cons(N,n__natsFrom(s(N)))
       fst(pair(XS,YS)) -> XS
       snd(pair(XS,YS)) -> YS
       splitAt(0(),XS) -> pair(nil(),XS)
       splitAt(s(N),cons(X,XS)) -> u(splitAt(N,activate(XS)),N,X,activate(XS))
       u(pair(YS,ZS),N,X,XS) -> pair(cons(activate(X),YS),ZS)
       head(cons(N,XS)) -> N
       tail(cons(N,XS)) -> activate(XS)
       sel(N,XS) -> head(afterNth(N,XS))
       take(N,XS) -> fst(splitAt(N,XS))
       afterNth(N,XS) -> snd(splitAt(N,XS))
       natsFrom(X) -> n__natsFrom(X)
       activate(n__natsFrom(X)) -> natsFrom(X)
       activate(X) -> X
     Qed