3.18/1.37	NO
3.18/1.38	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.18/1.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.38	
3.18/1.38	
3.18/1.38	Outermost Termination of the given OTRS could be disproven:
3.18/1.38	
3.18/1.38	(0) OTRS
3.18/1.38	(1) OutermostNonTerminationProof [COMPLETE, 107 ms]
3.18/1.38	(2) NO
3.18/1.38	
3.18/1.38	
3.18/1.38	----------------------------------------
3.18/1.38	
3.18/1.38	(0)
3.18/1.38	Obligation:
3.18/1.38	Term rewrite system R:
3.18/1.38	The TRS R consists of the following rules:
3.18/1.38	
3.18/1.38	   f(0, 1, X) -> h(X, X)
3.18/1.38	   h(0, X) -> f(0, X, X)
3.18/1.38	   g(X, Y) -> X
3.18/1.38	   g(X, Y) -> Y
3.18/1.38	
3.18/1.38	
3.18/1.38	
3.18/1.38	Outermost Strategy.
3.18/1.38	
3.18/1.38	----------------------------------------
3.18/1.38	
3.18/1.38	(1) OutermostNonTerminationProof (COMPLETE)
3.18/1.38	Term rewrite system R:
3.18/1.38	The TRS R consists of the following rules:
3.18/1.38	
3.18/1.38	   f(0, 1, X) -> h(X, X)
3.18/1.38	   h(0, X) -> f(0, X, X)
3.18/1.38	   g(X, Y) -> X
3.18/1.38	   g(X, Y) -> Y
3.18/1.38	
3.18/1.38	
3.18/1.38	
3.18/1.38	Outermost Strategy.
3.18/1.38	
3.18/1.38	---------- Loop: ----------
3.18/1.38	
3.18/1.38	h(g(1, 0), g(1, 0)) -> h(0, g(1, 0)) with rule g(X, Y') -> Y' at position [0] and matcher [X / 1, Y' / 0]
3.18/1.38	
3.18/1.38	h(0, g(1, 0)) -> f(0, g(1, 0), g(1, 0)) with rule h(0, X) -> f(0, X, X) at position [] and matcher [X / g(1, 0)]
3.18/1.38	
3.18/1.38	f(0, g(1, 0), g(1, 0)) -> f(0, 1, g(1, 0)) with rule g(X', Y) -> X' at position [1] and matcher [X' / 1, Y / 0]
3.18/1.38	
3.18/1.38	f(0, 1, g(1, 0)) -> h(g(1, 0), g(1, 0)) with rule f(0, 1, X) -> h(X, X) at position [] and matcher [X / g(1, 0)]
3.18/1.38	
3.18/1.38	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
3.18/1.38	
3.18/1.38	Context: []
3.18/1.38	
3.18/1.38	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.18/1.38	----------------------------------------
3.18/1.38	
3.18/1.38	(2)
3.18/1.38	NO
3.18/1.40	EOF