2.67/1.27	NO
2.67/1.28	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.67/1.28	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.67/1.28	
2.67/1.28	
2.67/1.28	Outermost Termination of the given OTRS could be disproven:
2.67/1.28	
2.67/1.28	(0) OTRS
2.67/1.28	(1) OutermostNonTerminationProof [COMPLETE, 50 ms]
2.67/1.28	(2) NO
2.67/1.28	
2.67/1.28	
2.67/1.28	----------------------------------------
2.67/1.28	
2.67/1.28	(0)
2.67/1.28	Obligation:
2.67/1.28	Term rewrite system R:
2.67/1.28	The TRS R consists of the following rules:
2.67/1.28	
2.67/1.28	   g(X) -> u(h(X), h(X), X)
2.67/1.28	   u(d, c(Y), X) -> k(Y)
2.67/1.28	   h(d) -> c(a)
2.67/1.28	   h(d) -> c(b)
2.67/1.28	   f(k(a), k(b), X) -> f(X, X, X)
2.67/1.28	
2.67/1.28	
2.67/1.28	
2.67/1.28	Outermost Strategy.
2.67/1.28	
2.67/1.28	----------------------------------------
2.67/1.28	
2.67/1.28	(1) OutermostNonTerminationProof (COMPLETE)
2.67/1.28	Term rewrite system R:
2.67/1.28	The TRS R consists of the following rules:
2.67/1.28	
2.67/1.28	   g(X) -> u(h(X), h(X), X)
2.67/1.28	   u(d, c(Y), X) -> k(Y)
2.67/1.28	   h(d) -> c(a)
2.67/1.28	   h(d) -> c(b)
2.67/1.28	   f(k(a), k(b), X) -> f(X, X, X)
2.67/1.28	
2.67/1.28	
2.67/1.28	
2.67/1.28	Outermost Strategy.
2.67/1.28	
2.67/1.28	---------- Loop: ----------
2.67/1.28	
2.67/1.28	f(u(d, h(d), X'), u(d, h(d), X'), u(d, h(d), X')) -> f(u(d, h(d), X'), u(d, c(b), X'), u(d, h(d), X')) with rule h(d) -> c(b) at position [1,1] and matcher [ ]
2.67/1.29	
2.67/1.29	f(u(d, h(d), X'), u(d, c(b), X'), u(d, h(d), X')) -> f(u(d, h(d), X'), k(b), u(d, h(d), X')) with rule u(d, c(Y), X'') -> k(Y) at position [1] and matcher [Y / b, X'' / X']
2.67/1.29	
2.67/1.29	f(u(d, h(d), X'), k(b), u(d, h(d), X')) -> f(u(d, c(a), X'), k(b), u(d, h(d), X')) with rule h(d) -> c(a) at position [0,1] and matcher [ ]
2.67/1.29	
2.67/1.29	f(u(d, c(a), X'), k(b), u(d, h(d), X')) -> f(k(a), k(b), u(d, h(d), X')) with rule u(d, c(Y), X'') -> k(Y) at position [0] and matcher [Y / a, X'' / X']
2.67/1.29	
2.67/1.29	f(k(a), k(b), u(d, h(d), X')) -> f(u(d, h(d), X'), u(d, h(d), X'), u(d, h(d), X')) with rule f(k(a), k(b), X) -> f(X, X, X) at position [] and matcher [X / u(d, h(d), X')]
2.67/1.29	
2.67/1.29	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.67/1.29	
2.67/1.29	Context: []
2.67/1.29	
2.67/1.29	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.67/1.29	----------------------------------------
2.67/1.29	
2.67/1.29	(2)
2.67/1.29	NO
2.67/1.32	EOF