2.50/1.23	NO
2.68/1.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.68/1.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.68/1.24	
2.68/1.24	
2.68/1.24	Outermost Termination of the given OTRS could be disproven:
2.68/1.24	
2.68/1.24	(0) OTRS
2.68/1.24	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.68/1.24	(2) NO
2.68/1.24	
2.68/1.24	
2.68/1.24	----------------------------------------
2.68/1.24	
2.68/1.24	(0)
2.68/1.24	Obligation:
2.68/1.24	Term rewrite system R:
2.68/1.24	The TRS R consists of the following rules:
2.68/1.24	
2.68/1.24	   nats -> cons(0, n__incr(nats))
2.68/1.24	   pairs -> cons(0, n__incr(odds))
2.68/1.24	   odds -> incr(pairs)
2.68/1.24	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
2.68/1.24	   head(cons(X, XS)) -> X
2.68/1.24	   tail(cons(X, XS)) -> activate(XS)
2.68/1.24	   incr(X) -> n__incr(X)
2.68/1.24	   activate(n__incr(X)) -> incr(X)
2.68/1.24	   activate(X) -> X
2.68/1.24	
2.68/1.24	
2.68/1.24	
2.68/1.24	Outermost Strategy.
2.68/1.24	
2.68/1.24	----------------------------------------
2.68/1.24	
2.68/1.24	(1) OutermostNonTerminationProof (COMPLETE)
2.68/1.24	Term rewrite system R:
2.68/1.24	The TRS R consists of the following rules:
2.68/1.24	
2.68/1.24	   nats -> cons(0, n__incr(nats))
2.68/1.24	   pairs -> cons(0, n__incr(odds))
2.68/1.24	   odds -> incr(pairs)
2.68/1.24	   incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS)))
2.68/1.24	   head(cons(X, XS)) -> X
2.68/1.24	   tail(cons(X, XS)) -> activate(XS)
2.68/1.24	   incr(X) -> n__incr(X)
2.68/1.24	   activate(n__incr(X)) -> incr(X)
2.68/1.24	   activate(X) -> X
2.68/1.24	
2.68/1.24	
2.68/1.24	
2.68/1.24	Outermost Strategy.
2.68/1.24	
2.68/1.24	---------- Loop: ----------
2.68/1.24	
2.68/1.24	nats -> cons(0, n__incr(nats)) with rule nats -> cons(0, n__incr(nats)) at position [] and matcher [ ]
2.68/1.24	
2.68/1.24	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1,0].
2.68/1.24	
2.68/1.24	Context: cons(0, n__incr([]))
2.68/1.24	
2.68/1.24	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.68/1.24	----------------------------------------
2.68/1.24	
2.68/1.24	(2)
2.68/1.24	NO
2.70/1.26	EOF