2.59/1.23	NO
2.59/1.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.59/1.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.59/1.23	
2.59/1.23	
2.59/1.23	Outermost Termination of the given OTRS could be disproven:
2.59/1.23	
2.59/1.23	(0) OTRS
2.59/1.23	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.59/1.23	(2) NO
2.59/1.23	
2.59/1.23	
2.59/1.23	----------------------------------------
2.59/1.23	
2.59/1.23	(0)
2.59/1.23	Obligation:
2.59/1.23	Term rewrite system R:
2.59/1.23	The TRS R consists of the following rules:
2.59/1.23	
2.59/1.23	   U52(tt) -> N
2.59/1.23	   U64(tt) -> s(plus(N, M))
2.59/1.23	   U11(tt) -> U12(isNatKind)
2.59/1.23	   U12(tt) -> U13(isNatKind)
2.59/1.23	   U13(tt) -> U14(isNatKind)
2.59/1.23	   U14(tt) -> U15(isNat)
2.59/1.23	   U15(tt) -> U16(isNat)
2.59/1.23	   U16(tt) -> tt
2.59/1.23	   U21(tt) -> U22(isNatKind)
2.59/1.23	   U22(tt) -> U23(isNat)
2.59/1.23	   U23(tt) -> tt
2.59/1.23	   U31(tt) -> U32(isNatKind)
2.59/1.23	   U32(tt) -> tt
2.59/1.23	   U41(tt) -> tt
2.59/1.23	   U51(tt) -> U52(isNatKind)
2.59/1.23	   U61(tt) -> U62(isNatKind)
2.59/1.23	   U62(tt) -> U63(isNat)
2.59/1.23	   U63(tt) -> U64(isNatKind)
2.59/1.23	   isNat -> tt
2.59/1.23	   isNat -> U11(isNatKind)
2.59/1.23	   isNat -> U21(isNatKind)
2.59/1.23	   isNatKind -> tt
2.59/1.23	   isNatKind -> U31(isNatKind)
2.59/1.23	   isNatKind -> U41(isNatKind)
2.59/1.23	   plus(N, 0) -> U51(isNat)
2.59/1.23	   plus(N, s(M)) -> U61(isNat)
2.59/1.23	
2.59/1.23	
2.59/1.23	
2.59/1.23	Outermost Strategy.
2.59/1.23	
2.59/1.23	----------------------------------------
2.59/1.23	
2.59/1.23	(1) OutermostNonTerminationProof (COMPLETE)
2.59/1.23	Term rewrite system R:
2.59/1.23	The TRS R consists of the following rules:
2.59/1.23	
2.59/1.23	   U52(tt) -> N
2.59/1.23	   U64(tt) -> s(plus(N, M))
2.59/1.23	   U11(tt) -> U12(isNatKind)
2.59/1.23	   U12(tt) -> U13(isNatKind)
2.59/1.23	   U13(tt) -> U14(isNatKind)
2.59/1.23	   U14(tt) -> U15(isNat)
2.59/1.23	   U15(tt) -> U16(isNat)
2.59/1.23	   U16(tt) -> tt
2.59/1.23	   U21(tt) -> U22(isNatKind)
2.59/1.23	   U22(tt) -> U23(isNat)
2.59/1.23	   U23(tt) -> tt
2.59/1.23	   U31(tt) -> U32(isNatKind)
2.59/1.23	   U32(tt) -> tt
2.59/1.23	   U41(tt) -> tt
2.59/1.23	   U51(tt) -> U52(isNatKind)
2.59/1.23	   U61(tt) -> U62(isNatKind)
2.59/1.23	   U62(tt) -> U63(isNat)
2.59/1.23	   U63(tt) -> U64(isNatKind)
2.59/1.23	   isNat -> tt
2.59/1.23	   isNat -> U11(isNatKind)
2.59/1.23	   isNat -> U21(isNatKind)
2.59/1.23	   isNatKind -> tt
2.59/1.23	   isNatKind -> U31(isNatKind)
2.59/1.23	   isNatKind -> U41(isNatKind)
2.59/1.23	   plus(N, 0) -> U51(isNat)
2.59/1.23	   plus(N, s(M)) -> U61(isNat)
2.59/1.23	
2.59/1.23	
2.59/1.23	
2.59/1.23	Outermost Strategy.
2.59/1.23	
2.59/1.23	---------- Loop: ----------
2.59/1.23	
2.59/1.23	U52(tt) -> U52(tt) with rule U52(tt) -> N at position [] and matcher [N / U52(tt)]
2.59/1.23	
2.59/1.23	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.59/1.23	
2.59/1.23	Context: []
2.59/1.23	
2.59/1.23	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.59/1.23	----------------------------------------
2.59/1.23	
2.59/1.23	(2)
2.59/1.23	NO
2.59/1.25	EOF