2.33/1.28	NO
2.33/1.28	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.33/1.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.33/1.28	
2.33/1.28	
2.33/1.28	Outermost Termination of the given OTRS could be disproven:
2.33/1.28	
2.33/1.28	(0) OTRS
2.33/1.28	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.33/1.28	(2) NO
2.33/1.28	
2.33/1.28	
2.33/1.28	----------------------------------------
2.33/1.28	
2.33/1.28	(0)
2.33/1.28	Obligation:
2.33/1.28	Term rewrite system R:
2.33/1.28	The TRS R consists of the following rules:
2.33/1.28	
2.33/1.28	   tail(cons(X)) -> Y
2.33/1.28	   if(true) -> X
2.33/1.28	   if(false) -> Y
2.33/1.28	   primes -> sieve(from(s(s(0))))
2.33/1.28	   from(X) -> cons(X)
2.33/1.28	   head(cons(X)) -> X
2.33/1.28	   filter(s(s(X)), cons(Y)) -> if(divides(s(s(X)), Y))
2.33/1.28	   sieve(cons(X)) -> cons(X)
2.33/1.28	
2.33/1.28	
2.33/1.28	
2.33/1.28	Outermost Strategy.
2.33/1.28	
2.33/1.28	----------------------------------------
2.33/1.28	
2.33/1.28	(1) OutermostNonTerminationProof (COMPLETE)
2.33/1.28	Term rewrite system R:
2.33/1.28	The TRS R consists of the following rules:
2.33/1.28	
2.33/1.28	   tail(cons(X)) -> Y
2.33/1.28	   if(true) -> X
2.33/1.28	   if(false) -> Y
2.33/1.28	   primes -> sieve(from(s(s(0))))
2.33/1.28	   from(X) -> cons(X)
2.33/1.28	   head(cons(X)) -> X
2.33/1.28	   filter(s(s(X)), cons(Y)) -> if(divides(s(s(X)), Y))
2.33/1.28	   sieve(cons(X)) -> cons(X)
2.33/1.28	
2.33/1.28	
2.33/1.28	
2.33/1.28	Outermost Strategy.
2.33/1.28	
2.33/1.28	---------- Loop: ----------
2.33/1.28	
2.33/1.28	tail(cons(X)) -> tail(cons(X)) with rule tail(cons(X'')) -> Y at position [] and matcher [X'' / X, Y / tail(cons(X))]
2.33/1.28	
2.33/1.28	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.33/1.28	
2.33/1.28	Context: []
2.33/1.28	
2.33/1.28	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.33/1.28	----------------------------------------
2.33/1.28	
2.33/1.28	(2)
2.33/1.28	NO
2.33/1.31	EOF