2.91/1.31	NO
3.01/1.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.01/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.01/1.33	
3.01/1.33	
3.01/1.33	Outermost Termination of the given OTRS could be disproven:
3.01/1.33	
3.01/1.33	(0) OTRS
3.01/1.33	(1) OutermostNonTerminationProof [COMPLETE, 39 ms]
3.01/1.33	(2) NO
3.01/1.33	
3.01/1.33	
3.01/1.33	----------------------------------------
3.01/1.33	
3.01/1.33	(0)
3.01/1.33	Obligation:
3.01/1.33	Term rewrite system R:
3.01/1.33	The TRS R consists of the following rules:
3.01/1.33	
3.01/1.33	   app(app(app(if, true), x), y) -> x
3.01/1.33	   app(app(app(if, false), x), y) -> y
3.01/1.33	   app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x)))
3.01/1.33	
3.01/1.33	
3.01/1.33	
3.01/1.33	Outermost Strategy.
3.01/1.33	
3.01/1.33	----------------------------------------
3.01/1.33	
3.01/1.33	(1) OutermostNonTerminationProof (COMPLETE)
3.01/1.33	Term rewrite system R:
3.01/1.33	The TRS R consists of the following rules:
3.01/1.33	
3.01/1.33	   app(app(app(if, true), x), y) -> x
3.01/1.33	   app(app(app(if, false), x), y) -> y
3.01/1.33	   app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x)))
3.01/1.33	
3.01/1.33	
3.01/1.33	
3.01/1.33	Outermost Strategy.
3.01/1.33	
3.01/1.33	---------- Loop: ----------
3.01/1.33	
3.01/1.33	app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x))) with rule app(app(app(until, p'), f'), x') -> app(app(app(if, app(p', x')), x'), app(app(app(until, p'), f'), app(f', x'))) at position [] and matcher [p' / p, f' / f, x' / x]
3.01/1.33	
3.01/1.33	Now an instance of the first term with Matcher [x / app(f, x)] occurs in the last term at position [1].
3.01/1.33	
3.01/1.33	Context: app(app(app(if, app(p, x)), x), [])
3.01/1.33	
3.01/1.33	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.01/1.33	----------------------------------------
3.01/1.33	
3.01/1.33	(2)
3.01/1.33	NO
3.01/1.36	EOF