2.49/1.21	NO
2.49/1.22	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.49/1.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.49/1.22	
2.49/1.22	
2.49/1.22	Outermost Termination of the given OTRS could be disproven:
2.49/1.22	
2.49/1.22	(0) OTRS
2.49/1.22	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.49/1.22	(2) NO
2.49/1.22	
2.49/1.22	
2.49/1.22	----------------------------------------
2.49/1.22	
2.49/1.22	(0)
2.49/1.22	Obligation:
2.49/1.22	Term rewrite system R:
2.49/1.22	The TRS R consists of the following rules:
2.49/1.22	
2.49/1.22	   U12(tt) -> snd(splitAt(N, XS))
2.49/1.22	   U22(tt) -> X
2.49/1.22	   U32(tt) -> N
2.49/1.22	   U42(tt) -> head(afterNth(N, XS))
2.49/1.22	   U52(tt) -> Y
2.49/1.22	   U63(tt) -> U64(splitAt(N, XS))
2.49/1.22	   U64(pair(YS, ZS)) -> pair(cons(X), ZS)
2.49/1.22	   U72(tt) -> XS
2.49/1.22	   U82(tt) -> fst(splitAt(N, XS))
2.49/1.22	   U11(tt) -> U12(tt)
2.49/1.22	   U21(tt) -> U22(tt)
2.49/1.22	   U31(tt) -> U32(tt)
2.49/1.22	   U41(tt) -> U42(tt)
2.49/1.22	   U51(tt) -> U52(tt)
2.49/1.22	   U61(tt) -> U62(tt)
2.49/1.22	   U62(tt) -> U63(tt)
2.49/1.22	   U71(tt) -> U72(tt)
2.49/1.22	   U81(tt) -> U82(tt)
2.49/1.22	   afterNth(N, XS) -> U11(tt)
2.49/1.22	   fst(pair(X, Y)) -> U21(tt)
2.49/1.22	   head(cons(N)) -> U31(tt)
2.49/1.22	   natsFrom(N) -> cons(N)
2.49/1.22	   sel(N, XS) -> U41(tt)
2.49/1.22	   snd(pair(X, Y)) -> U51(tt)
2.49/1.22	   splitAt(0, XS) -> pair(nil, XS)
2.49/1.22	   splitAt(s(N), cons(X)) -> U61(tt)
2.49/1.22	   tail(cons(N)) -> U71(tt)
2.49/1.22	   take(N, XS) -> U81(tt)
2.49/1.22	
2.49/1.22	
2.49/1.22	
2.49/1.22	Outermost Strategy.
2.49/1.22	
2.49/1.22	----------------------------------------
2.49/1.22	
2.49/1.22	(1) OutermostNonTerminationProof (COMPLETE)
2.49/1.22	Term rewrite system R:
2.49/1.22	The TRS R consists of the following rules:
2.49/1.22	
2.49/1.22	   U12(tt) -> snd(splitAt(N, XS))
2.49/1.22	   U22(tt) -> X
2.49/1.22	   U32(tt) -> N
2.49/1.22	   U42(tt) -> head(afterNth(N, XS))
2.49/1.22	   U52(tt) -> Y
2.49/1.22	   U63(tt) -> U64(splitAt(N, XS))
2.49/1.22	   U64(pair(YS, ZS)) -> pair(cons(X), ZS)
2.49/1.22	   U72(tt) -> XS
2.49/1.22	   U82(tt) -> fst(splitAt(N, XS))
2.49/1.22	   U11(tt) -> U12(tt)
2.49/1.22	   U21(tt) -> U22(tt)
2.49/1.22	   U31(tt) -> U32(tt)
2.49/1.22	   U41(tt) -> U42(tt)
2.49/1.22	   U51(tt) -> U52(tt)
2.49/1.22	   U61(tt) -> U62(tt)
2.49/1.22	   U62(tt) -> U63(tt)
2.49/1.22	   U71(tt) -> U72(tt)
2.49/1.22	   U81(tt) -> U82(tt)
2.49/1.22	   afterNth(N, XS) -> U11(tt)
2.49/1.22	   fst(pair(X, Y)) -> U21(tt)
2.49/1.22	   head(cons(N)) -> U31(tt)
2.49/1.22	   natsFrom(N) -> cons(N)
2.49/1.22	   sel(N, XS) -> U41(tt)
2.49/1.22	   snd(pair(X, Y)) -> U51(tt)
2.49/1.22	   splitAt(0, XS) -> pair(nil, XS)
2.49/1.22	   splitAt(s(N), cons(X)) -> U61(tt)
2.49/1.22	   tail(cons(N)) -> U71(tt)
2.49/1.22	   take(N, XS) -> U81(tt)
2.49/1.22	
2.49/1.22	
2.49/1.22	
2.49/1.22	Outermost Strategy.
2.49/1.22	
2.49/1.22	---------- Loop: ----------
2.49/1.22	
2.49/1.22	U12(tt) -> snd(splitAt(U12(tt), U12(tt))) with rule U12(tt) -> snd(splitAt(N, XS)) at position [] and matcher [N / U12(tt), XS / U12(tt)]
2.49/1.22	
2.49/1.22	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.49/1.22	
2.49/1.22	Context: snd(splitAt([], U12(tt)))
2.49/1.22	
2.49/1.22	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.49/1.22	----------------------------------------
2.49/1.22	
2.49/1.22	(2)
2.49/1.22	NO
2.62/1.70	EOF