/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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:

   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))


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(1) CritRuleProof (COMPLETE)
The rule U101(tt) -> fst(splitAt(N, XS)) contains free variables in its right-hand side. Hence the TRS is not-terminating.
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(2)
NO