/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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))
   U22(tt) -> X
   U32(tt) -> N
   U42(tt) -> head(afterNth(N, XS))
   U52(tt) -> Y
   U63(tt) -> U64(splitAt(N, XS))
   U64(pair(YS, ZS)) -> pair(cons(X), ZS)
   U72(tt) -> XS
   U82(tt) -> fst(splitAt(N, XS))
   U11(tt) -> U12(tt)
   U21(tt) -> U22(tt)
   U31(tt) -> U32(tt)
   U41(tt) -> U42(tt)
   U51(tt) -> U52(tt)
   U61(tt) -> U62(tt)
   U62(tt) -> U63(tt)
   U71(tt) -> U72(tt)
   U81(tt) -> U82(tt)
   afterNth(N, XS) -> U11(tt)
   fst(pair(X, Y)) -> U21(tt)
   head(cons(N)) -> U31(tt)
   natsFrom(N) -> cons(N)
   sel(N, XS) -> U41(tt)
   snd(pair(X, Y)) -> U51(tt)
   splitAt(0, XS) -> pair(nil, XS)
   splitAt(s(N), cons(X)) -> U61(tt)
   tail(cons(N)) -> U71(tt)
   take(N, XS) -> U81(tt)


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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