2.43/1.30	NO
2.43/1.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.43/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.43/1.30	
2.43/1.30	
2.43/1.30	Outermost Termination of the given OTRS could be disproven:
2.43/1.30	
2.43/1.30	(0) OTRS
2.43/1.30	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.43/1.30	(2) NO
2.43/1.30	
2.43/1.30	
2.43/1.30	----------------------------------------
2.43/1.30	
2.43/1.30	(0)
2.43/1.30	Obligation:
2.43/1.30	Term rewrite system R:
2.43/1.30	The TRS R consists of the following rules:
2.43/1.30	
2.43/1.30	   U11(tt) -> N
2.43/1.30	   U21(tt) -> s(plus(N, M))
2.43/1.30	   U41(tt) -> plus(x(N, M), N)
2.43/1.30	   and(tt) -> X
2.43/1.30	   U31(tt) -> 0
2.43/1.30	   isNat -> tt
2.43/1.30	   isNat -> and(isNat)
2.43/1.30	   isNat -> isNat
2.43/1.30	   plus(N, 0) -> U11(isNat)
2.43/1.30	   plus(N, s(M)) -> U21(and(isNat))
2.43/1.30	   x(N, 0) -> U31(isNat)
2.43/1.30	   x(N, s(M)) -> U41(and(isNat))
2.43/1.30	
2.43/1.30	
2.43/1.30	
2.43/1.30	Outermost Strategy.
2.43/1.30	
2.43/1.30	----------------------------------------
2.43/1.30	
2.43/1.30	(1) OutermostNonTerminationProof (COMPLETE)
2.43/1.30	Term rewrite system R:
2.43/1.30	The TRS R consists of the following rules:
2.43/1.30	
2.43/1.30	   U11(tt) -> N
2.43/1.30	   U21(tt) -> s(plus(N, M))
2.43/1.30	   U41(tt) -> plus(x(N, M), N)
2.43/1.30	   and(tt) -> X
2.43/1.30	   U31(tt) -> 0
2.43/1.30	   isNat -> tt
2.43/1.30	   isNat -> and(isNat)
2.43/1.30	   isNat -> isNat
2.43/1.30	   plus(N, 0) -> U11(isNat)
2.43/1.30	   plus(N, s(M)) -> U21(and(isNat))
2.43/1.30	   x(N, 0) -> U31(isNat)
2.43/1.30	   x(N, s(M)) -> U41(and(isNat))
2.43/1.30	
2.43/1.30	
2.43/1.30	
2.43/1.30	Outermost Strategy.
2.43/1.30	
2.43/1.30	---------- Loop: ----------
2.43/1.30	
2.43/1.30	U11(tt) -> U11(tt) with rule U11(tt) -> N at position [] and matcher [N / U11(tt)]
2.43/1.30	
2.43/1.30	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.43/1.30	
2.43/1.30	Context: []
2.43/1.30	
2.43/1.30	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.43/1.30	----------------------------------------
2.43/1.30	
2.43/1.30	(2)
2.43/1.30	NO
2.43/1.34	EOF