2.54/1.21	NO
2.54/1.22	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.54/1.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.54/1.22	
2.54/1.22	
2.54/1.22	Outermost Termination of the given OTRS could be disproven:
2.54/1.22	
2.54/1.22	(0) OTRS
2.54/1.22	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.54/1.22	(2) NO
2.54/1.22	
2.54/1.22	
2.54/1.22	----------------------------------------
2.54/1.22	
2.54/1.22	(0)
2.54/1.22	Obligation:
2.54/1.22	Term rewrite system R:
2.54/1.22	The TRS R consists of the following rules:
2.54/1.22	
2.54/1.22	   from(X) -> cons(X, from(s(X)))
2.54/1.22	   first(0, Z) -> nil
2.54/1.22	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.54/1.22	   sel(0, cons(X, Z)) -> X
2.54/1.22	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.54/1.22	
2.54/1.22	
2.54/1.22	
2.54/1.22	Outermost Strategy.
2.54/1.22	
2.54/1.22	----------------------------------------
2.54/1.22	
2.54/1.22	(1) OutermostNonTerminationProof (COMPLETE)
2.54/1.22	Term rewrite system R:
2.54/1.22	The TRS R consists of the following rules:
2.54/1.22	
2.54/1.22	   from(X) -> cons(X, from(s(X)))
2.54/1.22	   first(0, Z) -> nil
2.54/1.22	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
2.54/1.22	   sel(0, cons(X, Z)) -> X
2.54/1.22	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.54/1.22	
2.54/1.22	
2.54/1.22	
2.54/1.22	Outermost Strategy.
2.54/1.22	
2.54/1.22	---------- Loop: ----------
2.54/1.22	
2.54/1.22	from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X]
2.54/1.22	
2.54/1.22	Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1].
2.54/1.22	
2.54/1.22	Context: cons(X, [])
2.54/1.22	
2.54/1.22	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.54/1.22	----------------------------------------
2.54/1.22	
2.54/1.22	(2)
2.54/1.22	NO
2.69/1.26	EOF