/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
(2) NO


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(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   U101(tt) -> fst(splitAt(N, XS))
   U11(tt) -> snd(splitAt(N, XS))
   U21(tt) -> X
   U31(tt) -> N
   U41(tt) -> cons(N)
   U51(tt) -> head(afterNth(N, XS))
   U61(tt) -> Y
   U71(tt) -> pair(nil, XS)
   U81(tt) -> U82(splitAt(N, XS))
   U82(pair(YS, ZS)) -> pair(cons(X), ZS)
   U91(tt) -> XS
   and(tt) -> X
   afterNth(N, XS) -> U11(and(isNatural))
   fst(pair(X, Y)) -> U21(and(isLNat))
   head(cons(N)) -> U31(and(isNatural))
   isLNat -> tt
   isLNat -> and(isNatural)
   isLNat -> isPLNat
   isLNat -> isNatural
   isLNat -> isLNat
   isNatural -> tt
   isNatural -> isLNat
   isNatural -> isNatural
   isNatural -> and(isNatural)
   isPLNat -> and(isLNat)
   isPLNat -> and(isNatural)
   natsFrom(N) -> U41(isNatural)
   sel(N, XS) -> U51(and(isNatural))
   snd(pair(X, Y)) -> U61(and(isLNat))
   splitAt(0, XS) -> U71(isLNat)
   splitAt(s(N), cons(X)) -> U81(and(isNatural))
   tail(cons(N)) -> U91(and(isNatural))
   take(N, XS) -> U101(and(isNatural))



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   U101(tt) -> fst(splitAt(N, XS))
   U11(tt) -> snd(splitAt(N, XS))
   U21(tt) -> X
   U31(tt) -> N
   U41(tt) -> cons(N)
   U51(tt) -> head(afterNth(N, XS))
   U61(tt) -> Y
   U71(tt) -> pair(nil, XS)
   U81(tt) -> U82(splitAt(N, XS))
   U82(pair(YS, ZS)) -> pair(cons(X), ZS)
   U91(tt) -> XS
   and(tt) -> X
   afterNth(N, XS) -> U11(and(isNatural))
   fst(pair(X, Y)) -> U21(and(isLNat))
   head(cons(N)) -> U31(and(isNatural))
   isLNat -> tt
   isLNat -> and(isNatural)
   isLNat -> isPLNat
   isLNat -> isNatural
   isLNat -> isLNat
   isNatural -> tt
   isNatural -> isLNat
   isNatural -> isNatural
   isNatural -> and(isNatural)
   isPLNat -> and(isLNat)
   isPLNat -> and(isNatural)
   natsFrom(N) -> U41(isNatural)
   sel(N, XS) -> U51(and(isNatural))
   snd(pair(X, Y)) -> U61(and(isLNat))
   splitAt(0, XS) -> U71(isLNat)
   splitAt(s(N), cons(X)) -> U81(and(isNatural))
   tail(cons(N)) -> U91(and(isNatural))
   take(N, XS) -> U101(and(isNatural))



Outermost Strategy.

---------- Loop: ----------

U101(tt) -> fst(splitAt(U101(tt), U101(tt))) with rule U101(tt) -> fst(splitAt(N, XS)) at position [] and matcher [N / U101(tt), XS / U101(tt)]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].

Context: fst(splitAt([], U101(tt)))

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO