3.35/1.46	NO
3.35/1.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.47	
3.35/1.47	
3.35/1.47	Outermost Termination of the given OTRS could be disproven:
3.35/1.47	
3.35/1.47	(0) OTRS
3.35/1.47	(1) OutermostNonTerminationProof [COMPLETE, 253 ms]
3.35/1.47	(2) NO
3.35/1.47	
3.35/1.47	
3.35/1.47	----------------------------------------
3.35/1.47	
3.35/1.47	(0)
3.35/1.47	Obligation:
3.35/1.47	Term rewrite system R:
3.35/1.47	The TRS R consists of the following rules:
3.35/1.47	
3.35/1.47	   ap(ap(f, x), x) -> ap(ap(x, ap(f, x)), ap(ap(cons, x), nil))
3.35/1.47	   ap(ap(ap(foldr, g), h), nil) -> h
3.35/1.47	   ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs))
3.35/1.47	
3.35/1.47	
3.35/1.47	
3.35/1.47	Outermost Strategy.
3.35/1.47	
3.35/1.47	----------------------------------------
3.35/1.47	
3.35/1.47	(1) OutermostNonTerminationProof (COMPLETE)
3.35/1.47	Term rewrite system R:
3.35/1.47	The TRS R consists of the following rules:
3.35/1.47	
3.35/1.47	   ap(ap(f, x), x) -> ap(ap(x, ap(f, x)), ap(ap(cons, x), nil))
3.35/1.47	   ap(ap(ap(foldr, g), h), nil) -> h
3.35/1.47	   ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs))
3.35/1.47	
3.35/1.47	
3.35/1.47	
3.35/1.47	Outermost Strategy.
3.35/1.47	
3.35/1.47	---------- Loop: ----------
3.35/1.47	
3.35/1.47	ap(ap(ap(f, foldr), foldr), ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), nil)) -> ap(ap(ap(f, foldr), foldr), ap(ap(cons, foldr), nil)) with rule ap(ap(ap(foldr, g), h), nil) -> h at position [1] and matcher [g / ap(f, foldr), h / ap(ap(cons, foldr), nil)]
3.35/1.47	
3.35/1.47	ap(ap(ap(f, foldr), foldr), ap(ap(cons, foldr), nil)) -> ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), ap(ap(cons, foldr), nil)) with rule ap(ap(f, x'), x') -> ap(ap(x', ap(f, x')), ap(ap(cons, x'), nil)) at position [0] and matcher [x' / foldr]
3.35/1.47	
3.35/1.47	ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), ap(ap(cons, foldr), nil)) -> ap(ap(ap(f, foldr), foldr), ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), nil)) with rule ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs)) at position [] and matcher [g / ap(f, foldr), h / ap(ap(cons, foldr), nil), x / foldr, xs / nil]
3.35/1.47	
3.35/1.47	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
3.35/1.47	
3.35/1.47	Context: []
3.35/1.47	
3.35/1.47	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.35/1.47	----------------------------------------
3.35/1.47	
3.35/1.47	(2)
3.35/1.47	NO
3.56/1.50	EOF