3.00/1.38	NO
3.00/1.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.00/1.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.00/1.39	
3.00/1.39	
3.00/1.39	Outermost Termination of the given OTRS could be disproven:
3.00/1.39	
3.00/1.39	(0) OTRS
3.00/1.39	(1) OutermostNonTerminationProof [COMPLETE, 102 ms]
3.00/1.39	(2) NO
3.00/1.39	
3.00/1.39	
3.00/1.39	----------------------------------------
3.00/1.39	
3.00/1.39	(0)
3.00/1.39	Obligation:
3.00/1.39	Term rewrite system R:
3.00/1.39	The TRS R consists of the following rules:
3.00/1.39	
3.00/1.39	   f(0, 1, X) -> f(g(X, X), X, X)
3.00/1.39	   g(X, Y) -> X
3.00/1.39	   g(X, Y) -> Y
3.00/1.39	
3.00/1.39	
3.00/1.39	
3.00/1.39	Outermost Strategy.
3.00/1.39	
3.00/1.39	----------------------------------------
3.00/1.39	
3.00/1.39	(1) OutermostNonTerminationProof (COMPLETE)
3.00/1.39	Term rewrite system R:
3.00/1.39	The TRS R consists of the following rules:
3.00/1.39	
3.00/1.39	   f(0, 1, X) -> f(g(X, X), X, X)
3.00/1.39	   g(X, Y) -> X
3.00/1.39	   g(X, Y) -> Y
3.00/1.39	
3.00/1.39	
3.00/1.39	
3.00/1.39	Outermost Strategy.
3.00/1.39	
3.00/1.39	---------- Loop: ----------
3.00/1.39	
3.00/1.39	f(g(g(0, 1), g(0, 1)), g(0, 1), g(0, 1)) -> f(g(g(0, 1), g(0, 1)), 1, g(0, 1)) with rule g(X', Y'') -> Y'' at position [1] and matcher [X' / 0, Y'' / 1]
3.00/1.39	
3.00/1.39	f(g(g(0, 1), g(0, 1)), 1, g(0, 1)) -> f(g(0, 1), 1, g(0, 1)) with rule g(X', Y') -> X' at position [0] and matcher [X' / g(0, 1), Y' / g(0, 1)]
3.00/1.39	
3.00/1.39	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]
3.00/1.39	
3.00/1.39	f(0, 1, g(0, 1)) -> f(g(g(0, 1), g(0, 1)), g(0, 1), g(0, 1)) with rule f(0, 1, X) -> f(g(X, X), X, X) at position [] and matcher [X / g(0, 1)]
3.00/1.39	
3.00/1.39	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
3.00/1.39	
3.00/1.39	Context: []
3.00/1.39	
3.00/1.39	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.00/1.39	----------------------------------------
3.00/1.39	
3.00/1.39	(2)
3.00/1.39	NO
3.21/1.43	EOF