3.54/1.50	NO
3.72/1.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.72/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.72/1.51	
3.72/1.51	
3.72/1.51	Outermost Termination of the given OTRS could be disproven:
3.72/1.51	
3.72/1.51	(0) OTRS
3.72/1.51	(1) OutermostNonTerminationProof [COMPLETE, 182 ms]
3.72/1.51	(2) NO
3.72/1.51	
3.72/1.51	
3.72/1.51	----------------------------------------
3.72/1.51	
3.72/1.51	(0)
3.72/1.51	Obligation:
3.72/1.51	Term rewrite system R:
3.72/1.51	The TRS R consists of the following rules:
3.72/1.51	
3.72/1.51	   from(X) -> cons(X, n__from(s(X)))
3.72/1.51	   length(n__nil) -> 0
3.72/1.51	   length(n__cons(X, Y)) -> s(length1(activate(Y)))
3.72/1.51	   length1(X) -> length(activate(X))
3.72/1.51	   from(X) -> n__from(X)
3.72/1.51	   nil -> n__nil
3.72/1.51	   cons(X1, X2) -> n__cons(X1, X2)
3.72/1.51	   activate(n__from(X)) -> from(X)
3.72/1.51	   activate(n__nil) -> nil
3.72/1.51	   activate(n__cons(X1, X2)) -> cons(X1, X2)
3.72/1.51	   activate(X) -> X
3.72/1.51	
3.72/1.51	
3.72/1.51	
3.72/1.51	Outermost Strategy.
3.72/1.51	
3.72/1.51	----------------------------------------
3.72/1.51	
3.72/1.51	(1) OutermostNonTerminationProof (COMPLETE)
3.72/1.51	Term rewrite system R:
3.72/1.51	The TRS R consists of the following rules:
3.72/1.51	
3.72/1.51	   from(X) -> cons(X, n__from(s(X)))
3.72/1.51	   length(n__nil) -> 0
3.72/1.51	   length(n__cons(X, Y)) -> s(length1(activate(Y)))
3.72/1.51	   length1(X) -> length(activate(X))
3.72/1.51	   from(X) -> n__from(X)
3.72/1.51	   nil -> n__nil
3.72/1.51	   cons(X1, X2) -> n__cons(X1, X2)
3.72/1.51	   activate(n__from(X)) -> from(X)
3.72/1.51	   activate(n__nil) -> nil
3.72/1.51	   activate(n__cons(X1, X2)) -> cons(X1, X2)
3.72/1.51	   activate(X) -> X
3.72/1.51	
3.72/1.51	
3.72/1.51	
3.72/1.51	Outermost Strategy.
3.72/1.51	
3.72/1.51	---------- Loop: ----------
3.72/1.51	
3.72/1.51	length1(activate(n__from(X'))) -> length(activate(activate(n__from(X')))) with rule length1(X) -> length(activate(X)) at position [] and matcher [X / activate(n__from(X'))]
3.72/1.51	
3.72/1.51	length(activate(activate(n__from(X')))) -> length(activate(n__from(X'))) with rule activate(X) -> X at position [0] and matcher [X / activate(n__from(X'))]
3.72/1.51	
3.72/1.51	length(activate(n__from(X'))) -> length(from(X')) with rule activate(n__from(X'')) -> from(X'') at position [0] and matcher [X'' / X']
3.72/1.51	
3.72/1.51	length(from(X')) -> length(cons(X', n__from(s(X')))) with rule from(X) -> cons(X, n__from(s(X))) at position [0] and matcher [X / X']
3.72/1.51	
3.72/1.51	length(cons(X', n__from(s(X')))) -> length(n__cons(X', n__from(s(X')))) with rule cons(X1, X2) -> n__cons(X1, X2) at position [0] and matcher [X1 / X', X2 / n__from(s(X'))]
3.72/1.51	
3.72/1.51	length(n__cons(X', n__from(s(X')))) -> s(length1(activate(n__from(s(X'))))) with rule length(n__cons(X, Y)) -> s(length1(activate(Y))) at position [] and matcher [X / X', Y / n__from(s(X'))]
3.72/1.51	
3.72/1.51	Now an instance of the first term with Matcher [X' / s(X')] occurs in the last term at position [0].
3.72/1.51	
3.72/1.51	Context: s([])
3.72/1.51	
3.72/1.51	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.72/1.51	----------------------------------------
3.72/1.51	
3.72/1.51	(2)
3.72/1.51	NO
3.74/1.54	EOF