9.92/3.10	NO
10.02/3.12	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.02/3.12	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.02/3.12	
10.02/3.12	
10.02/3.12	Outermost Termination of the given OTRS could be disproven:
10.02/3.12	
10.02/3.12	(0) OTRS
10.02/3.12	(1) OutermostNonTerminationProof [COMPLETE, 1307 ms]
10.02/3.12	(2) NO
10.02/3.12	
10.02/3.12	
10.02/3.12	----------------------------------------
10.02/3.12	
10.02/3.12	(0)
10.02/3.12	Obligation:
10.02/3.12	Term rewrite system R:
10.02/3.12	The TRS R consists of the following rules:
10.02/3.12	
10.02/3.12	   +(X, 0) -> X
10.02/3.12	   +(X, s(Y)) -> s(+(X, Y))
10.02/3.12	   f(0, s(0), X) -> f(X, +(X, X), X)
10.02/3.12	   g(X, Y) -> X
10.02/3.12	   g(X, Y) -> Y
10.02/3.12	
10.02/3.12	
10.02/3.12	
10.02/3.12	Outermost Strategy.
10.02/3.12	
10.02/3.12	----------------------------------------
10.02/3.12	
10.02/3.12	(1) OutermostNonTerminationProof (COMPLETE)
10.02/3.12	Term rewrite system R:
10.02/3.12	The TRS R consists of the following rules:
10.02/3.12	
10.02/3.12	   +(X, 0) -> X
10.02/3.12	   +(X, s(Y)) -> s(+(X, Y))
10.02/3.12	   f(0, s(0), X) -> f(X, +(X, X), X)
10.02/3.12	   g(X, Y) -> X
10.02/3.12	   g(X, Y) -> Y
10.02/3.12	
10.02/3.12	
10.02/3.12	
10.02/3.12	Outermost Strategy.
10.02/3.12	
10.02/3.12	---------- Loop: ----------
10.02/3.12	
10.02/3.12	f(g(0, s(0)), +(g(0, s(0)), g(0, s(0))), g(0, s(0))) -> f(g(0, s(0)), +(s(0), g(0, s(0))), g(0, s(0))) with rule g(X', Y'') -> Y'' at position [1,0] and matcher [X' / 0, Y'' / s(0)]
10.02/3.12	
10.02/3.12	f(g(0, s(0)), +(s(0), g(0, s(0))), g(0, s(0))) -> f(g(0, s(0)), +(s(0), 0), g(0, s(0))) with rule g(X', Y') -> X' at position [1,1] and matcher [X' / 0, Y' / s(0)]
10.02/3.12	
10.02/3.12	f(g(0, s(0)), +(s(0), 0), g(0, s(0))) -> f(g(0, s(0)), s(0), g(0, s(0))) with rule +(X', 0) -> X' at position [1] and matcher [X' / s(0)]
10.02/3.12	
10.02/3.12	f(g(0, s(0)), s(0), g(0, s(0))) -> f(0, s(0), g(0, s(0))) with rule g(X', Y) -> X' at position [0] and matcher [X' / 0, Y / s(0)]
10.02/3.12	
10.02/3.12	f(0, s(0), g(0, s(0))) -> f(g(0, s(0)), +(g(0, s(0)), g(0, s(0))), g(0, s(0))) with rule f(0, s(0), X) -> f(X, +(X, X), X) at position [] and matcher [X / g(0, s(0))]
10.02/3.12	
10.02/3.12	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
10.02/3.12	
10.02/3.12	Context: []
10.02/3.12	
10.02/3.12	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
10.02/3.12	----------------------------------------
10.02/3.12	
10.02/3.12	(2)
10.02/3.12	NO
10.02/3.17	EOF