/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

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



Outermost Strategy.

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

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



Outermost Strategy.

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

splitAt(s(N), cons(X)) -> u(splitAt(N, splitAt(s(N), cons(X)))) with rule splitAt(s(N''), cons(X'')) -> u(splitAt(N'', XS)) at position [] and matcher [N'' / N, X'' / X, XS / splitAt(s(N), cons(X))]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,1].

Context: u(splitAt(N, []))

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