2.57/1.27	NO
2.57/1.27	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.57/1.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.57/1.27	
2.57/1.27	
2.57/1.27	Outermost Termination of the given OTRS could be disproven:
2.57/1.27	
2.57/1.27	(0) OTRS
2.57/1.27	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.57/1.27	(2) NO
2.57/1.27	
2.57/1.27	
2.57/1.27	----------------------------------------
2.57/1.27	
2.57/1.27	(0)
2.57/1.27	Obligation:
2.57/1.27	Term rewrite system R:
2.57/1.27	The TRS R consists of the following rules:
2.57/1.27	
2.57/1.27	   U41(tt) -> N
2.57/1.27	   U52(tt) -> s(plus(N, M))
2.57/1.27	   U72(tt) -> plus(x(N, M), N)
2.57/1.27	   U11(tt) -> U12(isNat)
2.57/1.27	   U12(tt) -> tt
2.57/1.27	   U21(tt) -> tt
2.57/1.27	   U31(tt) -> U32(isNat)
2.57/1.27	   U32(tt) -> tt
2.57/1.27	   U51(tt) -> U52(isNat)
2.57/1.27	   U61(tt) -> 0
2.57/1.27	   U71(tt) -> U72(isNat)
2.57/1.27	   isNat -> tt
2.57/1.27	   isNat -> U11(isNat)
2.57/1.27	   isNat -> U21(isNat)
2.57/1.27	   isNat -> U31(isNat)
2.57/1.27	   plus(N, 0) -> U41(isNat)
2.57/1.27	   plus(N, s(M)) -> U51(isNat)
2.57/1.27	   x(N, 0) -> U61(isNat)
2.57/1.27	   x(N, s(M)) -> U71(isNat)
2.57/1.27	
2.57/1.27	
2.57/1.27	
2.57/1.27	Outermost Strategy.
2.57/1.27	
2.57/1.27	----------------------------------------
2.57/1.27	
2.57/1.27	(1) OutermostNonTerminationProof (COMPLETE)
2.57/1.27	Term rewrite system R:
2.57/1.27	The TRS R consists of the following rules:
2.57/1.28	
2.57/1.28	   U41(tt) -> N
2.57/1.28	   U52(tt) -> s(plus(N, M))
2.57/1.28	   U72(tt) -> plus(x(N, M), N)
2.57/1.28	   U11(tt) -> U12(isNat)
2.57/1.28	   U12(tt) -> tt
2.57/1.28	   U21(tt) -> tt
2.57/1.28	   U31(tt) -> U32(isNat)
2.57/1.28	   U32(tt) -> tt
2.57/1.28	   U51(tt) -> U52(isNat)
2.57/1.28	   U61(tt) -> 0
2.57/1.28	   U71(tt) -> U72(isNat)
2.57/1.28	   isNat -> tt
2.57/1.28	   isNat -> U11(isNat)
2.57/1.28	   isNat -> U21(isNat)
2.57/1.28	   isNat -> U31(isNat)
2.57/1.28	   plus(N, 0) -> U41(isNat)
2.57/1.28	   plus(N, s(M)) -> U51(isNat)
2.57/1.28	   x(N, 0) -> U61(isNat)
2.57/1.28	   x(N, s(M)) -> U71(isNat)
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	U41(tt) -> U41(tt) with rule U41(tt) -> N at position [] and matcher [N / U41(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 [].
2.57/1.28	
2.57/1.28	Context: []
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
2.75/1.31	EOF