2.78/1.39	NO
2.78/1.39	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.78/1.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.78/1.39	
2.78/1.39	
2.78/1.39	Outermost Termination of the given OTRS could be disproven:
2.78/1.39	
2.78/1.39	(0) OTRS
2.78/1.39	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.78/1.39	(2) NO
2.78/1.39	
2.78/1.39	
2.78/1.39	----------------------------------------
2.78/1.39	
2.78/1.39	(0)
2.78/1.39	Obligation:
2.78/1.39	Term rewrite system R:
2.78/1.39	The TRS R consists of the following rules:
2.78/1.39	
2.78/1.39	   nats -> adx(zeros)
2.78/1.39	   zeros -> cons(0, zeros)
2.78/1.39	   incr(cons(X, Y)) -> cons(s(X), incr(Y))
2.78/1.39	   adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
2.78/1.39	   hd(cons(X, Y)) -> X
2.78/1.39	   tl(cons(X, Y)) -> Y
2.78/1.39	
2.78/1.39	
2.78/1.39	
2.78/1.39	Outermost Strategy.
2.78/1.39	
2.78/1.39	----------------------------------------
2.78/1.39	
2.78/1.39	(1) OutermostNonTerminationProof (COMPLETE)
2.78/1.39	Term rewrite system R:
2.78/1.39	The TRS R consists of the following rules:
2.78/1.39	
2.78/1.39	   nats -> adx(zeros)
2.78/1.39	   zeros -> cons(0, zeros)
2.78/1.39	   incr(cons(X, Y)) -> cons(s(X), incr(Y))
2.78/1.39	   adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
2.78/1.39	   hd(cons(X, Y)) -> X
2.78/1.39	   tl(cons(X, Y)) -> Y
2.78/1.39	
2.78/1.39	
2.78/1.39	
2.78/1.39	Outermost Strategy.
2.78/1.39	
2.78/1.39	---------- Loop: ----------
2.78/1.39	
2.78/1.39	zeros -> cons(0, zeros) with rule zeros -> cons(0, zeros) at position [] and matcher [ ]
2.78/1.39	
2.78/1.39	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
2.78/1.39	
2.78/1.39	Context: cons(0, [])
2.78/1.39	
2.78/1.39	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.78/1.39	----------------------------------------
2.78/1.39	
2.78/1.39	(2)
2.78/1.39	NO
2.88/1.42	EOF