2.55/1.25	NO
2.55/1.25	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.55/1.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.55/1.25	
2.55/1.25	
2.55/1.25	Outermost Termination of the given OTRS could be disproven:
2.55/1.25	
2.55/1.25	(0) OTRS
2.55/1.25	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.55/1.25	(2) NO
2.55/1.25	
2.55/1.25	
2.55/1.25	----------------------------------------
2.55/1.25	
2.55/1.25	(0)
2.55/1.25	Obligation:
2.55/1.25	Term rewrite system R:
2.55/1.25	The TRS R consists of the following rules:
2.55/1.25	
2.55/1.25	   eq(0, 0) -> true
2.55/1.25	   eq(s(X), s(Y)) -> eq(X, Y)
2.55/1.25	   eq(X, Y) -> false
2.55/1.25	   inf(X) -> cons(X, inf(s(X)))
2.55/1.25	   take(0, X) -> nil
2.55/1.25	   take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
2.55/1.25	   length(nil) -> 0
2.55/1.25	   length(cons(X, L)) -> s(length(L))
2.55/1.25	
2.55/1.25	
2.55/1.25	
2.55/1.25	Outermost Strategy.
2.55/1.25	
2.55/1.25	----------------------------------------
2.55/1.25	
2.55/1.25	(1) OutermostNonTerminationProof (COMPLETE)
2.55/1.25	Term rewrite system R:
2.55/1.25	The TRS R consists of the following rules:
2.55/1.25	
2.55/1.25	   eq(0, 0) -> true
2.55/1.25	   eq(s(X), s(Y)) -> eq(X, Y)
2.55/1.25	   eq(X, Y) -> false
2.55/1.25	   inf(X) -> cons(X, inf(s(X)))
2.55/1.25	   take(0, X) -> nil
2.55/1.25	   take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
2.55/1.25	   length(nil) -> 0
2.55/1.25	   length(cons(X, L)) -> s(length(L))
2.55/1.25	
2.55/1.25	
2.55/1.25	
2.55/1.25	Outermost Strategy.
2.55/1.25	
2.55/1.25	---------- Loop: ----------
2.55/1.25	
2.55/1.25	inf(X) -> cons(X, inf(s(X))) with rule inf(X') -> cons(X', inf(s(X'))) at position [] and matcher [X' / X]
2.55/1.25	
2.55/1.25	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.55/1.25	
2.55/1.25	Context: cons(X, [])
2.55/1.25	
2.55/1.25	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.55/1.25	----------------------------------------
2.55/1.25	
2.55/1.25	(2)
2.55/1.25	NO
2.68/1.27	EOF