2.74/1.34	NO
2.74/1.35	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.74/1.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.74/1.35	
2.74/1.35	
2.74/1.35	Outermost Termination of the given OTRS could be disproven:
2.74/1.35	
2.74/1.35	(0) OTRS
2.74/1.35	(1) OutermostNonTerminationProof [COMPLETE, 54 ms]
2.74/1.35	(2) NO
2.74/1.35	
2.74/1.35	
2.74/1.35	----------------------------------------
2.74/1.35	
2.74/1.35	(0)
2.74/1.35	Obligation:
2.74/1.35	Term rewrite system R:
2.74/1.35	The TRS R consists of the following rules:
2.74/1.35	
2.74/1.35	   zeros -> cons(0, n__zeros)
2.74/1.35	   and(tt, X) -> activate(X)
2.74/1.35	   length(nil) -> 0
2.74/1.35	   length(cons(N, L)) -> s(length(activate(L)))
2.74/1.35	   take(0, IL) -> nil
2.74/1.35	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
2.74/1.35	   zeros -> n__zeros
2.74/1.35	   take(X1, X2) -> n__take(X1, X2)
2.74/1.35	   activate(n__zeros) -> zeros
2.74/1.35	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
2.74/1.35	   activate(X) -> X
2.74/1.35	
2.74/1.35	
2.74/1.35	
2.74/1.35	Outermost Strategy.
2.74/1.35	
2.74/1.35	----------------------------------------
2.74/1.35	
2.74/1.35	(1) OutermostNonTerminationProof (COMPLETE)
2.74/1.35	Term rewrite system R:
2.74/1.35	The TRS R consists of the following rules:
2.74/1.35	
2.74/1.35	   zeros -> cons(0, n__zeros)
2.74/1.35	   and(tt, X) -> activate(X)
2.74/1.35	   length(nil) -> 0
2.74/1.35	   length(cons(N, L)) -> s(length(activate(L)))
2.74/1.35	   take(0, IL) -> nil
2.74/1.35	   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
2.74/1.35	   zeros -> n__zeros
2.74/1.35	   take(X1, X2) -> n__take(X1, X2)
2.74/1.35	   activate(n__zeros) -> zeros
2.74/1.35	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
2.74/1.35	   activate(X) -> X
2.74/1.35	
2.74/1.35	
2.74/1.35	
2.74/1.35	Outermost Strategy.
2.74/1.35	
2.74/1.35	---------- Loop: ----------
2.74/1.35	
2.74/1.35	length(activate(n__zeros)) -> length(zeros) with rule activate(n__zeros) -> zeros at position [0] and matcher [ ]
2.74/1.35	
2.74/1.35	length(zeros) -> length(cons(0, n__zeros)) with rule zeros -> cons(0, n__zeros) at position [0] and matcher [ ]
2.74/1.35	
2.74/1.35	length(cons(0, n__zeros)) -> s(length(activate(n__zeros))) with rule length(cons(N, L)) -> s(length(activate(L))) at position [] and matcher [N / 0, L / n__zeros]
2.74/1.35	
2.74/1.35	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
2.74/1.35	
2.74/1.35	Context: s([])
2.74/1.35	
2.74/1.35	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.74/1.35	----------------------------------------
2.74/1.35	
2.74/1.35	(2)
2.74/1.35	NO
2.89/1.75	EOF