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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given GTRS could be disproven:

(0) GTRS
(1) CritRuleProof [COMPLETE, 0 ms]
(2) NO


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(0)
Obligation:
Generalized rewrite system (where rules with free variables on rhs are allowed):
The TRS R consists of the following rules:

   U12(tt) -> snd(splitAt(N, XS))
   U161(tt) -> cons(N)
   U172(tt) -> head(afterNth(N, XS))
   U182(tt) -> Y
   U191(tt) -> pair(nil, XS)
   U203(tt) -> U204(splitAt(N, XS))
   U204(pair(YS, ZS)) -> pair(cons(X), ZS)
   U212(tt) -> XS
   U22(tt) -> X
   U222(tt) -> fst(splitAt(N, XS))
   U32(tt) -> N
   U101(tt) -> U102(isLNat)
   U102(tt) -> tt
   U11(tt) -> U12(isLNat)
   U111(tt) -> tt
   U121(tt) -> tt
   U131(tt) -> U132(isLNat)
   U132(tt) -> tt
   U141(tt) -> U142(isLNat)
   U142(tt) -> tt
   U151(tt) -> U152(isLNat)
   U152(tt) -> tt
   U171(tt) -> U172(isLNat)
   U181(tt) -> U182(isLNat)
   U201(tt) -> U202(isNatural)
   U202(tt) -> U203(isLNat)
   U21(tt) -> U22(isLNat)
   U211(tt) -> U212(isLNat)
   U221(tt) -> U222(isLNat)
   U31(tt) -> U32(isLNat)
   U41(tt) -> U42(isLNat)
   U42(tt) -> tt
   U51(tt) -> U52(isLNat)
   U52(tt) -> tt
   U61(tt) -> tt
   U71(tt) -> tt
   U81(tt) -> tt
   U91(tt) -> tt
   afterNth(N, XS) -> U11(isNatural)
   fst(pair(X, Y)) -> U21(isLNat)
   head(cons(N)) -> U31(isNatural)
   isLNat -> tt
   isLNat -> U41(isNatural)
   isLNat -> U51(isNatural)
   isLNat -> U61(isPLNat)
   isLNat -> U71(isNatural)
   isLNat -> U81(isPLNat)
   isLNat -> U91(isLNat)
   isLNat -> U101(isNatural)
   isNatural -> tt
   isNatural -> U111(isLNat)
   isNatural -> U121(isNatural)
   isNatural -> U131(isNatural)
   isPLNat -> U141(isLNat)
   isPLNat -> U151(isNatural)
   natsFrom(N) -> U161(isNatural)
   sel(N, XS) -> U171(isNatural)
   snd(pair(X, Y)) -> U181(isLNat)
   splitAt(0, XS) -> U191(isLNat)
   splitAt(s(N), cons(X)) -> U201(isNatural)
   tail(cons(N)) -> U211(isNatural)
   take(N, XS) -> U221(isNatural)


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(1) CritRuleProof (COMPLETE)
The rule U12(tt) -> snd(splitAt(N, XS)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
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(2)
NO