2.86/1.32	NO
2.86/1.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.86/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.86/1.33	
2.86/1.33	
2.86/1.33	Outermost Termination of the given OTRS could be disproven:
2.86/1.33	
2.86/1.33	(0) OTRS
2.86/1.33	(1) OutermostNonTerminationProof [COMPLETE, 49 ms]
2.86/1.33	(2) NO
2.86/1.33	
2.86/1.33	
2.86/1.33	----------------------------------------
2.86/1.33	
2.86/1.33	(0)
2.86/1.33	Obligation:
2.86/1.33	Term rewrite system R:
2.86/1.33	The TRS R consists of the following rules:
2.86/1.33	
2.86/1.33	   h(x, y) -> f(x, y, x)
2.86/1.33	   f(0, 1, x) -> h(x, x)
2.86/1.33	   g(x, y) -> x
2.86/1.33	   g(x, y) -> y
2.86/1.33	
2.86/1.33	
2.86/1.33	
2.86/1.33	Outermost Strategy.
2.86/1.33	
2.86/1.33	----------------------------------------
2.86/1.33	
2.86/1.33	(1) OutermostNonTerminationProof (COMPLETE)
2.86/1.33	Term rewrite system R:
2.86/1.33	The TRS R consists of the following rules:
2.86/1.33	
2.86/1.33	   h(x, y) -> f(x, y, x)
2.86/1.33	   f(0, 1, x) -> h(x, x)
2.86/1.33	   g(x, y) -> x
2.86/1.33	   g(x, y) -> y
2.86/1.33	
2.86/1.33	
2.86/1.33	
2.86/1.33	Outermost Strategy.
2.86/1.33	
2.86/1.33	---------- Loop: ----------
2.86/1.33	
2.86/1.33	f(g(0, 1), g(0, 1), g(0, 1)) -> f(g(0, 1), 1, g(0, 1)) with rule g(x, y') -> y' at position [1] and matcher [x / 0, y' / 1]
2.86/1.33	
2.86/1.33	f(g(0, 1), 1, g(0, 1)) -> f(0, 1, g(0, 1)) with rule g(x, y) -> x at position [0] and matcher [x / 0, y / 1]
2.86/1.33	
2.86/1.33	f(0, 1, g(0, 1)) -> h(g(0, 1), g(0, 1)) with rule f(0, 1, x) -> h(x, x) at position [] and matcher [x / g(0, 1)]
2.86/1.33	
2.86/1.33	h(g(0, 1), g(0, 1)) -> f(g(0, 1), g(0, 1), g(0, 1)) with rule h(x, y) -> f(x, y, x) at position [] and matcher [x / g(0, 1), y / g(0, 1)]
2.86/1.33	
2.86/1.33	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.86/1.33	
2.86/1.33	Context: []
2.86/1.33	
2.86/1.33	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.86/1.33	----------------------------------------
2.86/1.33	
2.86/1.33	(2)
2.86/1.33	NO
2.86/1.35	EOF