2.64/1.30	NO
2.64/1.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.64/1.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.64/1.30	
2.64/1.30	
2.64/1.30	Outermost Termination of the given OTRS could be disproven:
2.64/1.30	
2.64/1.30	(0) OTRS
2.64/1.30	(1) OutermostNonTerminationProof [COMPLETE, 50 ms]
2.64/1.30	(2) NO
2.64/1.30	
2.64/1.30	
2.64/1.30	----------------------------------------
2.64/1.30	
2.64/1.30	(0)
2.64/1.30	Obligation:
2.64/1.30	Term rewrite system R:
2.64/1.30	The TRS R consists of the following rules:
2.64/1.30	
2.64/1.30	   filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M))
2.64/1.30	   filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M))
2.64/1.30	   sieve(cons(0, Y)) -> cons(0, sieve(Y))
2.64/1.30	   sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N)))
2.64/1.30	   nats(N) -> cons(N, nats(s(N)))
2.64/1.30	   zprimes -> sieve(nats(s(s(0))))
2.64/1.30	
2.64/1.30	
2.64/1.30	
2.64/1.30	Outermost Strategy.
2.64/1.30	
2.64/1.30	----------------------------------------
2.64/1.30	
2.64/1.30	(1) OutermostNonTerminationProof (COMPLETE)
2.64/1.30	Term rewrite system R:
2.64/1.30	The TRS R consists of the following rules:
2.64/1.30	
2.64/1.30	   filter(cons(X, Y), 0, M) -> cons(0, filter(Y, M, M))
2.64/1.30	   filter(cons(X, Y), s(N), M) -> cons(X, filter(Y, N, M))
2.64/1.30	   sieve(cons(0, Y)) -> cons(0, sieve(Y))
2.64/1.30	   sieve(cons(s(N), Y)) -> cons(s(N), sieve(filter(Y, N, N)))
2.64/1.30	   nats(N) -> cons(N, nats(s(N)))
2.64/1.30	   zprimes -> sieve(nats(s(s(0))))
2.64/1.30	
2.64/1.30	
2.64/1.30	
2.64/1.30	Outermost Strategy.
2.64/1.30	
2.64/1.30	---------- Loop: ----------
2.64/1.30	
2.64/1.30	nats(N) -> cons(N, nats(s(N))) with rule nats(N') -> cons(N', nats(s(N'))) at position [] and matcher [N' / N]
2.64/1.30	
2.64/1.30	Now an instance of the first term with Matcher [N / s(N)] occurs in the last term at position [1].
2.64/1.30	
2.64/1.30	Context: cons(N, [])
2.64/1.30	
2.64/1.30	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.64/1.30	----------------------------------------
2.64/1.30	
2.64/1.30	(2)
2.64/1.30	NO
2.88/1.33	EOF