2.45/1.26	NO
2.45/1.27	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.45/1.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.45/1.27	
2.45/1.27	
2.45/1.27	Outermost Termination of the given OTRS could be disproven:
2.45/1.27	
2.45/1.27	(0) OTRS
2.45/1.27	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.45/1.27	(2) NO
2.45/1.27	
2.45/1.27	
2.45/1.27	----------------------------------------
2.45/1.27	
2.45/1.27	(0)
2.45/1.27	Obligation:
2.45/1.27	Term rewrite system R:
2.45/1.27	The TRS R consists of the following rules:
2.45/1.27	
2.45/1.27	   U11(tt) -> U12(splitAt(N, XS))
2.45/1.27	   U12(pair(YS, ZS)) -> pair(cons(X), ZS)
2.45/1.27	   and(tt) -> X
2.45/1.27	   tail(cons(N)) -> XS
2.45/1.27	   afterNth(N, XS) -> snd(splitAt(N, XS))
2.45/1.27	   fst(pair(X, Y)) -> X
2.45/1.27	   head(cons(N)) -> N
2.45/1.27	   natsFrom(N) -> cons(N)
2.45/1.27	   sel(N, XS) -> head(afterNth(N, XS))
2.45/1.27	   snd(pair(X, Y)) -> Y
2.45/1.27	   splitAt(0, XS) -> pair(nil, XS)
2.45/1.27	   splitAt(s(N), cons(X)) -> U11(tt)
2.45/1.27	   take(N, XS) -> fst(splitAt(N, XS))
2.45/1.27	
2.45/1.27	
2.45/1.27	
2.45/1.27	Outermost Strategy.
2.45/1.27	
2.45/1.27	----------------------------------------
2.45/1.27	
2.45/1.27	(1) OutermostNonTerminationProof (COMPLETE)
2.45/1.27	Term rewrite system R:
2.45/1.27	The TRS R consists of the following rules:
2.45/1.27	
2.45/1.27	   U11(tt) -> U12(splitAt(N, XS))
2.45/1.27	   U12(pair(YS, ZS)) -> pair(cons(X), ZS)
2.45/1.27	   and(tt) -> X
2.45/1.27	   tail(cons(N)) -> XS
2.45/1.27	   afterNth(N, XS) -> snd(splitAt(N, XS))
2.45/1.27	   fst(pair(X, Y)) -> X
2.45/1.27	   head(cons(N)) -> N
2.45/1.27	   natsFrom(N) -> cons(N)
2.45/1.27	   sel(N, XS) -> head(afterNth(N, XS))
2.45/1.27	   snd(pair(X, Y)) -> Y
2.45/1.27	   splitAt(0, XS) -> pair(nil, XS)
2.45/1.27	   splitAt(s(N), cons(X)) -> U11(tt)
2.45/1.27	   take(N, XS) -> fst(splitAt(N, XS))
2.45/1.27	
2.45/1.27	
2.45/1.27	
2.45/1.27	Outermost Strategy.
2.45/1.27	
2.45/1.27	---------- Loop: ----------
2.45/1.27	
2.45/1.27	U11(tt) -> U12(splitAt(U11(tt), U11(tt))) with rule U11(tt) -> U12(splitAt(N, XS)) at position [] and matcher [N / U11(tt), XS / U11(tt)]
2.45/1.27	
2.45/1.27	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.45/1.27	
2.45/1.27	Context: U12(splitAt([], U11(tt)))
2.45/1.27	
2.45/1.27	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.45/1.27	----------------------------------------
2.45/1.27	
2.45/1.27	(2)
2.45/1.27	NO
2.69/1.30	EOF