2.57/1.27	NO
2.57/1.28	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.57/1.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.57/1.28	
2.57/1.28	
2.57/1.28	Outermost Termination of the given OTRS could be disproven:
2.57/1.28	
2.57/1.28	(0) OTRS
2.57/1.28	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.57/1.28	(2) NO
2.57/1.28	
2.57/1.28	
2.57/1.28	----------------------------------------
2.57/1.28	
2.57/1.28	(0)
2.57/1.28	Obligation:
2.57/1.28	Term rewrite system R:
2.57/1.28	The TRS R consists of the following rules:
2.57/1.28	
2.57/1.28	   U101(tt) -> fst(splitAt(N, XS))
2.57/1.28	   U11(tt) -> snd(splitAt(N, XS))
2.57/1.28	   U21(tt) -> X
2.57/1.28	   U31(tt) -> N
2.57/1.28	   U41(tt) -> cons(N)
2.57/1.28	   U51(tt) -> head(afterNth(N, XS))
2.57/1.28	   U61(tt) -> Y
2.57/1.28	   U71(tt) -> pair(nil, XS)
2.57/1.28	   U81(tt) -> U82(splitAt(N, XS))
2.57/1.28	   U82(pair(YS, ZS)) -> pair(cons(X), ZS)
2.57/1.28	   U91(tt) -> XS
2.57/1.28	   and(tt) -> X
2.57/1.28	   afterNth(N, XS) -> U11(and(isNatural))
2.57/1.28	   fst(pair(X, Y)) -> U21(and(isLNat))
2.57/1.28	   head(cons(N)) -> U31(and(isNatural))
2.57/1.28	   isLNat -> tt
2.57/1.28	   isLNat -> and(isNatural)
2.57/1.28	   isLNat -> isPLNat
2.57/1.28	   isLNat -> isNatural
2.57/1.28	   isLNat -> isLNat
2.57/1.28	   isNatural -> tt
2.57/1.28	   isNatural -> isLNat
2.57/1.28	   isNatural -> isNatural
2.57/1.28	   isNatural -> and(isNatural)
2.57/1.28	   isPLNat -> and(isLNat)
2.57/1.28	   isPLNat -> and(isNatural)
2.57/1.28	   natsFrom(N) -> U41(isNatural)
2.57/1.28	   sel(N, XS) -> U51(and(isNatural))
2.57/1.28	   snd(pair(X, Y)) -> U61(and(isLNat))
2.57/1.28	   splitAt(0, XS) -> U71(isLNat)
2.57/1.28	   splitAt(s(N), cons(X)) -> U81(and(isNatural))
2.57/1.28	   tail(cons(N)) -> U91(and(isNatural))
2.57/1.28	   take(N, XS) -> U101(and(isNatural))
2.57/1.28	
2.57/1.28	
2.57/1.28	
2.57/1.28	Outermost Strategy.
2.57/1.28	
2.57/1.28	----------------------------------------
2.57/1.28	
2.57/1.28	(1) OutermostNonTerminationProof (COMPLETE)
2.57/1.28	Term rewrite system R:
2.57/1.28	The TRS R consists of the following rules:
2.57/1.28	
2.57/1.28	   U101(tt) -> fst(splitAt(N, XS))
2.57/1.28	   U11(tt) -> snd(splitAt(N, XS))
2.57/1.28	   U21(tt) -> X
2.57/1.28	   U31(tt) -> N
2.57/1.28	   U41(tt) -> cons(N)
2.57/1.28	   U51(tt) -> head(afterNth(N, XS))
2.57/1.28	   U61(tt) -> Y
2.57/1.28	   U71(tt) -> pair(nil, XS)
2.57/1.28	   U81(tt) -> U82(splitAt(N, XS))
2.57/1.28	   U82(pair(YS, ZS)) -> pair(cons(X), ZS)
2.57/1.28	   U91(tt) -> XS
2.57/1.28	   and(tt) -> X
2.57/1.28	   afterNth(N, XS) -> U11(and(isNatural))
2.57/1.28	   fst(pair(X, Y)) -> U21(and(isLNat))
2.57/1.28	   head(cons(N)) -> U31(and(isNatural))
2.57/1.28	   isLNat -> tt
2.57/1.28	   isLNat -> and(isNatural)
2.57/1.28	   isLNat -> isPLNat
2.57/1.28	   isLNat -> isNatural
2.57/1.28	   isLNat -> isLNat
2.57/1.28	   isNatural -> tt
2.57/1.28	   isNatural -> isLNat
2.57/1.28	   isNatural -> isNatural
2.57/1.28	   isNatural -> and(isNatural)
2.57/1.28	   isPLNat -> and(isLNat)
2.57/1.28	   isPLNat -> and(isNatural)
2.57/1.28	   natsFrom(N) -> U41(isNatural)
2.57/1.28	   sel(N, XS) -> U51(and(isNatural))
2.57/1.28	   snd(pair(X, Y)) -> U61(and(isLNat))
2.57/1.28	   splitAt(0, XS) -> U71(isLNat)
2.57/1.28	   splitAt(s(N), cons(X)) -> U81(and(isNatural))
2.57/1.28	   tail(cons(N)) -> U91(and(isNatural))
2.57/1.28	   take(N, XS) -> U101(and(isNatural))
2.57/1.28	
2.57/1.28	
2.57/1.28	
2.57/1.28	Outermost Strategy.
2.57/1.28	
2.57/1.28	---------- Loop: ----------
2.57/1.28	
2.57/1.28	U101(tt) -> fst(splitAt(U101(tt), U101(tt))) with rule U101(tt) -> fst(splitAt(N, XS)) at position [] and matcher [N / U101(tt), XS / U101(tt)]
2.57/1.28	
2.57/1.28	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.57/1.28	
2.57/1.28	Context: fst(splitAt([], U101(tt)))
2.57/1.28	
2.57/1.28	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.57/1.28	----------------------------------------
2.57/1.28	
2.57/1.28	(2)
2.57/1.28	NO
2.70/1.45	EOF