19.41/5.71	NO
19.41/5.71	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
19.41/5.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.41/5.71	
19.41/5.71	
19.41/5.71	Outermost Termination of the given OTRS could be disproven:
19.41/5.71	
19.41/5.71	(0) OTRS
19.41/5.71	(1) OutermostNonTerminationProof [COMPLETE, 2402 ms]
19.41/5.71	(2) NO
19.41/5.71	
19.41/5.71	
19.41/5.71	----------------------------------------
19.41/5.71	
19.41/5.71	(0)
19.41/5.71	Obligation:
19.41/5.71	Term rewrite system R:
19.41/5.71	The TRS R consists of the following rules:
19.41/5.71	
19.41/5.71	   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
19.41/5.71	   sel(0, cons(X, Z)) -> X
19.41/5.71	   first(0, Z) -> nil
19.41/5.71	   first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
19.41/5.71	   from(X) -> cons(X, n__from(s(X)))
19.41/5.71	   sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
19.41/5.71	   sel1(0, cons(X, Z)) -> quote(X)
19.41/5.71	   first1(0, Z) -> nil1
19.41/5.71	   first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
19.41/5.71	   quote(n__0) -> 01
19.41/5.71	   quote1(n__cons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
19.41/5.71	   quote1(n__nil) -> nil1
19.41/5.71	   quote(n__s(X)) -> s1(quote(activate(X)))
19.41/5.71	   quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z))
19.41/5.71	   quote1(n__first(X, Z)) -> first1(activate(X), activate(Z))
19.41/5.71	   unquote(01) -> 0
19.41/5.71	   unquote(s1(X)) -> s(unquote(X))
19.41/5.71	   unquote1(nil1) -> nil
19.41/5.71	   unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
19.41/5.71	   fcons(X, Z) -> cons(X, Z)
19.41/5.71	   first(X1, X2) -> n__first(X1, X2)
19.41/5.71	   from(X) -> n__from(X)
19.41/5.71	   0 -> n__0
19.41/5.71	   cons(X1, X2) -> n__cons(X1, X2)
19.41/5.71	   nil -> n__nil
19.41/5.71	   s(X) -> n__s(X)
19.41/5.71	   sel(X1, X2) -> n__sel(X1, X2)
19.41/5.71	   activate(n__first(X1, X2)) -> first(X1, X2)
19.41/5.71	   activate(n__from(X)) -> from(X)
19.41/5.71	   activate(n__0) -> 0
19.41/5.71	   activate(n__cons(X1, X2)) -> cons(X1, X2)
19.41/5.71	   activate(n__nil) -> nil
19.41/5.71	   activate(n__s(X)) -> s(X)
19.41/5.71	   activate(n__sel(X1, X2)) -> sel(X1, X2)
19.41/5.71	   activate(X) -> X
19.41/5.71	
19.41/5.71	
19.41/5.71	
19.41/5.71	Outermost Strategy.
19.41/5.71	
19.41/5.71	----------------------------------------
19.41/5.71	
19.41/5.71	(1) OutermostNonTerminationProof (COMPLETE)
19.41/5.71	Term rewrite system R:
19.41/5.71	The TRS R consists of the following rules:
19.41/5.71	
19.41/5.71	   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
19.41/5.71	   sel(0, cons(X, Z)) -> X
19.41/5.71	   first(0, Z) -> nil
19.41/5.71	   first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
19.41/5.71	   from(X) -> cons(X, n__from(s(X)))
19.41/5.71	   sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
19.41/5.71	   sel1(0, cons(X, Z)) -> quote(X)
19.41/5.71	   first1(0, Z) -> nil1
19.41/5.71	   first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, activate(Z)))
19.41/5.71	   quote(n__0) -> 01
19.41/5.71	   quote1(n__cons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z)))
19.41/5.71	   quote1(n__nil) -> nil1
19.41/5.71	   quote(n__s(X)) -> s1(quote(activate(X)))
19.41/5.71	   quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z))
19.41/5.71	   quote1(n__first(X, Z)) -> first1(activate(X), activate(Z))
19.41/5.71	   unquote(01) -> 0
19.41/5.71	   unquote(s1(X)) -> s(unquote(X))
19.41/5.71	   unquote1(nil1) -> nil
19.41/5.71	   unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
19.41/5.71	   fcons(X, Z) -> cons(X, Z)
19.41/5.71	   first(X1, X2) -> n__first(X1, X2)
19.41/5.71	   from(X) -> n__from(X)
19.41/5.71	   0 -> n__0
19.41/5.71	   cons(X1, X2) -> n__cons(X1, X2)
19.41/5.71	   nil -> n__nil
19.41/5.71	   s(X) -> n__s(X)
19.41/5.71	   sel(X1, X2) -> n__sel(X1, X2)
19.41/5.71	   activate(n__first(X1, X2)) -> first(X1, X2)
19.41/5.71	   activate(n__from(X)) -> from(X)
19.41/5.71	   activate(n__0) -> 0
19.41/5.71	   activate(n__cons(X1, X2)) -> cons(X1, X2)
19.41/5.71	   activate(n__nil) -> nil
19.41/5.71	   activate(n__s(X)) -> s(X)
19.41/5.71	   activate(n__sel(X1, X2)) -> sel(X1, X2)
19.41/5.71	   activate(X) -> X
19.41/5.71	
19.41/5.71	
19.41/5.71	
19.41/5.71	Outermost Strategy.
19.41/5.71	
19.41/5.71	---------- Loop: ----------
19.41/5.71	
19.41/5.71	quote1(activate(n__from(X'))) -> quote1(from(X')) with rule activate(n__from(X'')) -> from(X'') at position [0] and matcher [X'' / X']
19.41/5.71	
19.41/5.71	quote1(from(X')) -> quote1(cons(X', n__from(s(X')))) with rule from(X) -> cons(X, n__from(s(X))) at position [0] and matcher [X / X']
19.41/5.71	
19.41/5.71	quote1(cons(X', n__from(s(X')))) -> quote1(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'))]
19.41/5.71	
19.41/5.71	quote1(n__cons(X', n__from(s(X')))) -> cons1(quote(activate(X')), quote1(activate(n__from(s(X'))))) with rule quote1(n__cons(X, Z)) -> cons1(quote(activate(X)), quote1(activate(Z))) at position [] and matcher [X / X', Z / n__from(s(X'))]
19.41/5.71	
19.41/5.71	Now an instance of the first term with Matcher [X' / s(X')] occurs in the last term at position [1].
19.41/5.71	
19.41/5.71	Context: cons1(quote(activate(X')), [])
19.41/5.71	
19.41/5.71	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
19.41/5.72	----------------------------------------
19.41/5.72	
19.41/5.72	(2)
19.41/5.72	NO
19.69/5.75	EOF