2.50/1.23	NO
2.50/1.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.50/1.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.50/1.23	
2.50/1.23	
2.50/1.23	Outermost Termination of the given OTRS could be disproven:
2.50/1.23	
2.50/1.23	(0) OTRS
2.50/1.23	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.50/1.23	(2) NO
2.50/1.23	
2.50/1.23	
2.50/1.23	----------------------------------------
2.50/1.23	
2.50/1.23	(0)
2.50/1.23	Obligation:
2.50/1.23	Term rewrite system R:
2.50/1.23	The TRS R consists of the following rules:
2.50/1.23	
2.50/1.23	   U12(tt) -> s(plus(N, M))
2.50/1.23	   U11(tt) -> U12(tt)
2.50/1.23	   plus(N, 0) -> N
2.50/1.23	   plus(N, s(M)) -> U11(tt)
2.50/1.23	
2.50/1.23	
2.50/1.23	
2.50/1.23	Outermost Strategy.
2.50/1.23	
2.50/1.23	----------------------------------------
2.50/1.23	
2.50/1.23	(1) OutermostNonTerminationProof (COMPLETE)
2.50/1.23	Term rewrite system R:
2.50/1.23	The TRS R consists of the following rules:
2.50/1.23	
2.50/1.23	   U12(tt) -> s(plus(N, M))
2.50/1.23	   U11(tt) -> U12(tt)
2.50/1.23	   plus(N, 0) -> N
2.50/1.23	   plus(N, s(M)) -> U11(tt)
2.50/1.23	
2.50/1.23	
2.50/1.23	
2.50/1.23	Outermost Strategy.
2.50/1.23	
2.50/1.23	---------- Loop: ----------
2.50/1.23	
2.50/1.23	plus(N, U12(tt)) -> plus(N, s(plus(U12(tt), U12(tt)))) with rule U12(tt) -> s(plus(N, M)) at position [1] and matcher [N / U12(tt), M / U12(tt)]
2.50/1.23	
2.50/1.23	plus(N, s(plus(U12(tt), U12(tt)))) -> U11(tt) with rule plus(N', s(M)) -> U11(tt) at position [] and matcher [N' / N, M / plus(U12(tt), U12(tt))]
2.58/1.23	
2.58/1.23	U11(tt) -> U12(tt) with rule U11(tt) -> U12(tt) at position [] and matcher [ ]
2.58/1.23	
2.58/1.23	U12(tt) -> s(plus(U12(tt), U12(tt))) with rule U12(tt) -> s(plus(N, M)) at position [] and matcher [N / U12(tt), M / U12(tt)]
2.58/1.23	
2.58/1.23	Now an instance of the first term with Matcher [N / U12(tt)] occurs in the last term at position [0].
2.58/1.23	
2.58/1.23	Context: s([])
2.58/1.23	
2.58/1.23	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.58/1.23	----------------------------------------
2.58/1.23	
2.58/1.23	(2)
2.58/1.23	NO
2.58/1.26	EOF