2.42/1.20	NO
2.42/1.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.42/1.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.42/1.21	
2.42/1.21	
2.42/1.21	Outermost Termination of the given OTRS could be disproven:
2.42/1.21	
2.42/1.21	(0) OTRS
2.42/1.21	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.42/1.21	(2) NO
2.42/1.21	
2.42/1.21	
2.42/1.21	----------------------------------------
2.42/1.21	
2.42/1.21	(0)
2.42/1.21	Obligation:
2.42/1.21	Term rewrite system R:
2.42/1.21	The TRS R consists of the following rules:
2.42/1.21	
2.42/1.21	   f(s(x), x) -> f(s(x), round(x))
2.42/1.21	   round(0) -> 0
2.42/1.21	   round(0) -> s(0)
2.42/1.21	   round(s(0)) -> s(0)
2.42/1.21	   round(s(s(x))) -> s(s(round(x)))
2.42/1.21	
2.42/1.21	
2.42/1.21	
2.42/1.21	Outermost Strategy.
2.42/1.21	
2.42/1.21	----------------------------------------
2.42/1.21	
2.42/1.21	(1) OutermostNonTerminationProof (COMPLETE)
2.42/1.21	Term rewrite system R:
2.42/1.21	The TRS R consists of the following rules:
2.42/1.21	
2.42/1.21	   f(s(x), x) -> f(s(x), round(x))
2.42/1.21	   round(0) -> 0
2.42/1.21	   round(0) -> s(0)
2.42/1.21	   round(s(0)) -> s(0)
2.42/1.21	   round(s(s(x))) -> s(s(round(x)))
2.42/1.21	
2.42/1.21	
2.42/1.21	
2.42/1.21	Outermost Strategy.
2.42/1.21	
2.42/1.21	---------- Loop: ----------
2.42/1.21	
2.42/1.21	f(s(0), round(0)) -> f(s(0), 0) with rule round(0) -> 0 at position [1] and matcher [ ]
2.42/1.21	
2.42/1.21	f(s(0), 0) -> f(s(0), round(0)) with rule f(s(x), x) -> f(s(x), round(x)) at position [] and matcher [x / 0]
2.42/1.21	
2.42/1.21	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.42/1.21	
2.42/1.21	Context: []
2.42/1.21	
2.42/1.21	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.42/1.21	----------------------------------------
2.42/1.21	
2.42/1.21	(2)
2.42/1.21	NO
2.65/1.24	EOF