2.46/1.33	NO
2.46/1.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.46/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.46/1.34	
2.46/1.34	
2.46/1.34	Outermost Termination of the given OTRS could be disproven:
2.46/1.34	
2.46/1.34	(0) OTRS
2.46/1.34	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.46/1.34	(2) NO
2.46/1.34	
2.46/1.34	
2.46/1.34	----------------------------------------
2.46/1.34	
2.46/1.34	(0)
2.46/1.34	Obligation:
2.46/1.34	Term rewrite system R:
2.46/1.34	The TRS R consists of the following rules:
2.46/1.34	
2.46/1.34	   U12(tt) -> s(length(L))
2.46/1.34	   U23(tt) -> cons(N)
2.46/1.34	   zeros -> cons(0)
2.46/1.34	   U11(tt) -> U12(tt)
2.46/1.34	   U21(tt) -> U22(tt)
2.46/1.34	   U22(tt) -> U23(tt)
2.46/1.34	   length(nil) -> 0
2.46/1.34	   length(cons(N)) -> U11(tt)
2.46/1.34	   take(0, IL) -> nil
2.46/1.34	   take(s(M), cons(N)) -> U21(tt)
2.46/1.34	
2.46/1.34	
2.46/1.34	
2.46/1.34	Outermost Strategy.
2.46/1.34	
2.46/1.34	----------------------------------------
2.46/1.34	
2.46/1.34	(1) OutermostNonTerminationProof (COMPLETE)
2.46/1.34	Term rewrite system R:
2.46/1.34	The TRS R consists of the following rules:
2.46/1.34	
2.46/1.34	   U12(tt) -> s(length(L))
2.46/1.34	   U23(tt) -> cons(N)
2.46/1.34	   zeros -> cons(0)
2.46/1.34	   U11(tt) -> U12(tt)
2.46/1.34	   U21(tt) -> U22(tt)
2.46/1.34	   U22(tt) -> U23(tt)
2.46/1.34	   length(nil) -> 0
2.46/1.34	   length(cons(N)) -> U11(tt)
2.46/1.34	   take(0, IL) -> nil
2.46/1.34	   take(s(M), cons(N)) -> U21(tt)
2.46/1.34	
2.46/1.34	
2.46/1.34	
2.46/1.34	Outermost Strategy.
2.46/1.34	
2.46/1.34	---------- Loop: ----------
2.46/1.34	
2.46/1.34	U12(tt) -> s(length(U12(tt))) with rule U12(tt) -> s(length(L)) at position [] and matcher [L / U12(tt)]
2.46/1.34	
2.46/1.34	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.46/1.34	
2.46/1.34	Context: s(length([]))
2.46/1.34	
2.46/1.34	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.46/1.34	----------------------------------------
2.46/1.34	
2.46/1.34	(2)
2.46/1.34	NO
2.46/1.38	EOF