2.53/1.21	NO
2.53/1.22	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.53/1.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.53/1.22	
2.53/1.22	
2.53/1.22	Outermost Termination of the given OTRS could be disproven:
2.53/1.22	
2.53/1.22	(0) OTRS
2.53/1.22	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.53/1.22	(2) NO
2.53/1.22	
2.53/1.22	
2.53/1.22	----------------------------------------
2.53/1.22	
2.53/1.22	(0)
2.53/1.22	Obligation:
2.53/1.22	Term rewrite system R:
2.53/1.22	The TRS R consists of the following rules:
2.53/1.22	
2.53/1.22	   incr(nil) -> nil
2.53/1.22	   incr(cons(X, L)) -> cons(s(X), incr(L))
2.53/1.22	   adx(nil) -> nil
2.53/1.22	   adx(cons(X, L)) -> incr(cons(X, adx(L)))
2.53/1.22	   nats -> adx(zeros)
2.53/1.22	   zeros -> cons(0, zeros)
2.53/1.22	   head(cons(X, L)) -> X
2.53/1.22	   tail(cons(X, L)) -> L
2.53/1.22	
2.53/1.22	
2.53/1.22	
2.53/1.22	Outermost Strategy.
2.53/1.22	
2.53/1.22	----------------------------------------
2.53/1.22	
2.53/1.22	(1) OutermostNonTerminationProof (COMPLETE)
2.53/1.22	Term rewrite system R:
2.53/1.22	The TRS R consists of the following rules:
2.53/1.22	
2.53/1.22	   incr(nil) -> nil
2.53/1.22	   incr(cons(X, L)) -> cons(s(X), incr(L))
2.53/1.22	   adx(nil) -> nil
2.53/1.22	   adx(cons(X, L)) -> incr(cons(X, adx(L)))
2.53/1.22	   nats -> adx(zeros)
2.53/1.22	   zeros -> cons(0, zeros)
2.53/1.22	   head(cons(X, L)) -> X
2.53/1.22	   tail(cons(X, L)) -> L
2.53/1.22	
2.53/1.22	
2.53/1.22	
2.53/1.22	Outermost Strategy.
2.53/1.22	
2.53/1.22	---------- Loop: ----------
2.53/1.22	
2.53/1.22	zeros -> cons(0, zeros) with rule zeros -> cons(0, zeros) at position [] and matcher [ ]
2.53/1.22	
2.53/1.22	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
2.53/1.22	
2.53/1.22	Context: cons(0, [])
2.53/1.22	
2.53/1.22	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.53/1.22	----------------------------------------
2.53/1.22	
2.53/1.22	(2)
2.53/1.22	NO
2.64/1.25	EOF