2.63/1.25	NO
2.63/1.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.63/1.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.63/1.26	
2.63/1.26	
2.63/1.26	Outermost Termination of the given OTRS could be disproven:
2.63/1.26	
2.63/1.26	(0) OTRS
2.63/1.26	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.63/1.26	(2) NO
2.63/1.26	
2.63/1.26	
2.63/1.26	----------------------------------------
2.63/1.26	
2.63/1.26	(0)
2.63/1.26	Obligation:
2.63/1.26	Term rewrite system R:
2.63/1.26	The TRS R consists of the following rules:
2.63/1.26	
2.63/1.26	   f(X) -> cons(X, f(g(X)))
2.63/1.26	   g(0) -> s(0)
2.63/1.26	   g(s(X)) -> s(s(g(X)))
2.63/1.26	   sel(0, cons(X, Y)) -> X
2.63/1.26	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.63/1.26	
2.63/1.26	
2.63/1.26	
2.63/1.26	Outermost Strategy.
2.63/1.26	
2.63/1.26	----------------------------------------
2.63/1.26	
2.63/1.26	(1) OutermostNonTerminationProof (COMPLETE)
2.63/1.26	Term rewrite system R:
2.63/1.26	The TRS R consists of the following rules:
2.63/1.26	
2.63/1.26	   f(X) -> cons(X, f(g(X)))
2.63/1.26	   g(0) -> s(0)
2.63/1.26	   g(s(X)) -> s(s(g(X)))
2.63/1.26	   sel(0, cons(X, Y)) -> X
2.63/1.26	   sel(s(X), cons(Y, Z)) -> sel(X, Z)
2.63/1.26	
2.63/1.26	
2.63/1.26	
2.63/1.26	Outermost Strategy.
2.63/1.26	
2.63/1.26	---------- Loop: ----------
2.63/1.26	
2.63/1.26	f(X) -> cons(X, f(g(X))) with rule f(X') -> cons(X', f(g(X'))) at position [] and matcher [X' / X]
2.63/1.26	
2.63/1.26	Now an instance of the first term with Matcher [X / g(X)] occurs in the last term at position [1].
2.63/1.26	
2.63/1.26	Context: cons(X, [])
2.63/1.26	
2.63/1.26	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.63/1.26	----------------------------------------
2.63/1.26	
2.63/1.26	(2)
2.63/1.26	NO
2.63/1.29	EOF