2.56/1.32	NO
2.56/1.32	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.56/1.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.56/1.32	
2.56/1.32	
2.56/1.32	Outermost Termination of the given OTRS could be disproven:
2.56/1.32	
2.56/1.32	(0) OTRS
2.56/1.32	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.56/1.32	(2) NO
2.56/1.32	
2.56/1.32	
2.56/1.32	----------------------------------------
2.56/1.32	
2.56/1.32	(0)
2.56/1.32	Obligation:
2.56/1.32	Term rewrite system R:
2.56/1.32	The TRS R consists of the following rules:
2.56/1.32	
2.56/1.32	   from(X) -> cons(X, from(s(X)))
2.56/1.32	   head(cons(X, XS)) -> X
2.56/1.32	   2nd(cons(X, XS)) -> head(XS)
2.56/1.32	   take(0, XS) -> nil
2.56/1.32	   take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
2.56/1.32	   sel(0, cons(X, XS)) -> X
2.56/1.32	   sel(s(N), cons(X, XS)) -> sel(N, XS)
2.56/1.32	
2.56/1.32	
2.56/1.32	
2.56/1.32	Outermost Strategy.
2.56/1.32	
2.56/1.32	----------------------------------------
2.56/1.32	
2.56/1.32	(1) OutermostNonTerminationProof (COMPLETE)
2.56/1.32	Term rewrite system R:
2.56/1.32	The TRS R consists of the following rules:
2.56/1.32	
2.56/1.32	   from(X) -> cons(X, from(s(X)))
2.56/1.32	   head(cons(X, XS)) -> X
2.56/1.32	   2nd(cons(X, XS)) -> head(XS)
2.56/1.32	   take(0, XS) -> nil
2.56/1.32	   take(s(N), cons(X, XS)) -> cons(X, take(N, XS))
2.56/1.32	   sel(0, cons(X, XS)) -> X
2.56/1.32	   sel(s(N), cons(X, XS)) -> sel(N, XS)
2.56/1.32	
2.56/1.32	
2.56/1.32	
2.56/1.32	Outermost Strategy.
2.56/1.32	
2.56/1.32	---------- Loop: ----------
2.56/1.32	
2.56/1.32	from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]
2.56/1.32	
2.56/1.32	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.56/1.32	
2.56/1.32	Context: cons(X, [])
2.56/1.32	
2.56/1.32	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.56/1.32	----------------------------------------
2.56/1.32	
2.56/1.32	(2)
2.56/1.32	NO
2.78/1.35	EOF