2.48/1.20	NO
2.48/1.21	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.48/1.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.48/1.21	
2.48/1.21	
2.48/1.21	Outermost Termination of the given OTRS could be disproven:
2.48/1.21	
2.48/1.21	(0) OTRS
2.48/1.21	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.48/1.21	(2) NO
2.48/1.21	
2.48/1.21	
2.48/1.21	----------------------------------------
2.48/1.21	
2.48/1.21	(0)
2.48/1.21	Obligation:
2.48/1.21	Term rewrite system R:
2.48/1.21	The TRS R consists of the following rules:
2.48/1.21	
2.48/1.21	   sel(s(X), cons(Y)) -> sel(X, Z)
2.48/1.21	   from(X) -> cons(X)
2.48/1.21	   first(0, Z) -> nil
2.48/1.21	   first(s(X), cons(Y)) -> cons(Y)
2.48/1.21	   sel(0, cons(X)) -> X
2.48/1.21	
2.48/1.21	
2.48/1.21	
2.48/1.21	Outermost Strategy.
2.48/1.21	
2.48/1.21	----------------------------------------
2.48/1.21	
2.48/1.21	(1) OutermostNonTerminationProof (COMPLETE)
2.48/1.21	Term rewrite system R:
2.48/1.21	The TRS R consists of the following rules:
2.48/1.21	
2.48/1.21	   sel(s(X), cons(Y)) -> sel(X, Z)
2.48/1.21	   from(X) -> cons(X)
2.48/1.21	   first(0, Z) -> nil
2.48/1.21	   first(s(X), cons(Y)) -> cons(Y)
2.48/1.21	   sel(0, cons(X)) -> X
2.48/1.21	
2.48/1.21	
2.48/1.21	
2.48/1.21	Outermost Strategy.
2.48/1.21	
2.48/1.21	---------- Loop: ----------
2.48/1.21	
2.48/1.21	sel(s(X), cons(Y)) -> sel(X, sel(s(X), cons(Y))) with rule sel(s(X''), cons(Y'')) -> sel(X'', Z) at position [] and matcher [X'' / X, Y'' / Y, Z / sel(s(X), cons(Y))]
2.48/1.21	
2.48/1.21	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
2.48/1.21	
2.48/1.21	Context: sel(X, [])
2.48/1.21	
2.48/1.21	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.48/1.21	----------------------------------------
2.48/1.21	
2.48/1.21	(2)
2.48/1.21	NO
2.48/1.23	EOF