3.98/1.60	NO
3.98/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.98/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.98/1.61	
3.98/1.61	
3.98/1.61	Outermost Termination of the given OTRS could be disproven:
3.98/1.61	
3.98/1.61	(0) OTRS
3.98/1.61	(1) OutermostNonTerminationProof [COMPLETE, 208 ms]
3.98/1.61	(2) NO
3.98/1.61	
3.98/1.61	
3.98/1.61	----------------------------------------
3.98/1.61	
3.98/1.61	(0)
3.98/1.61	Obligation:
3.98/1.61	Term rewrite system R:
3.98/1.61	The TRS R consists of the following rules:
3.98/1.61	
3.98/1.61	   zeros -> cons(0, n__zeros)
3.98/1.61	   U11(tt, L) -> U12(tt, activate(L))
3.98/1.61	   U12(tt, L) -> s(length(activate(L)))
3.98/1.61	   length(nil) -> 0
3.98/1.61	   length(cons(N, L)) -> U11(tt, activate(L))
3.98/1.61	   zeros -> n__zeros
3.98/1.61	   activate(n__zeros) -> zeros
3.98/1.61	   activate(X) -> X
3.98/1.61	
3.98/1.61	
3.98/1.61	
3.98/1.61	Outermost Strategy.
3.98/1.61	
3.98/1.61	----------------------------------------
3.98/1.61	
3.98/1.61	(1) OutermostNonTerminationProof (COMPLETE)
3.98/1.61	Term rewrite system R:
3.98/1.61	The TRS R consists of the following rules:
3.98/1.61	
3.98/1.61	   zeros -> cons(0, n__zeros)
3.98/1.61	   U11(tt, L) -> U12(tt, activate(L))
3.98/1.61	   U12(tt, L) -> s(length(activate(L)))
3.98/1.61	   length(nil) -> 0
3.98/1.61	   length(cons(N, L)) -> U11(tt, activate(L))
3.98/1.61	   zeros -> n__zeros
3.98/1.61	   activate(n__zeros) -> zeros
3.98/1.61	   activate(X) -> X
3.98/1.61	
3.98/1.61	
3.98/1.61	
3.98/1.61	Outermost Strategy.
3.98/1.61	
3.98/1.61	---------- Loop: ----------
3.98/1.61	
3.98/1.61	U12(tt, activate(activate(n__zeros))) -> s(length(activate(activate(activate(n__zeros))))) with rule U12(tt, L) -> s(length(activate(L))) at position [] and matcher [L / activate(activate(n__zeros))]
3.98/1.61	
3.98/1.61	s(length(activate(activate(activate(n__zeros))))) -> s(length(activate(activate(n__zeros)))) with rule activate(X) -> X at position [0,0] and matcher [X / activate(activate(n__zeros))]
3.98/1.61	
3.98/1.61	s(length(activate(activate(n__zeros)))) -> s(length(activate(n__zeros))) with rule activate(X) -> X at position [0,0] and matcher [X / activate(n__zeros)]
3.98/1.61	
3.98/1.61	s(length(activate(n__zeros))) -> s(length(zeros)) with rule activate(n__zeros) -> zeros at position [0,0] and matcher [ ]
3.98/1.61	
3.98/1.61	s(length(zeros)) -> s(length(cons(0, n__zeros))) with rule zeros -> cons(0, n__zeros) at position [0,0] and matcher [ ]
3.98/1.61	
3.98/1.61	s(length(cons(0, n__zeros))) -> s(U11(tt, activate(n__zeros))) with rule length(cons(N, L)) -> U11(tt, activate(L)) at position [0] and matcher [N / 0, L / n__zeros]
3.98/1.61	
3.98/1.61	s(U11(tt, activate(n__zeros))) -> s(U12(tt, activate(activate(n__zeros)))) with rule U11(tt, L) -> U12(tt, activate(L)) at position [0] and matcher [L / activate(n__zeros)]
3.98/1.61	
3.98/1.61	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
3.98/1.61	
3.98/1.61	Context: s([])
3.98/1.61	
3.98/1.61	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
3.98/1.61	----------------------------------------
3.98/1.61	
3.98/1.61	(2)
3.98/1.61	NO
4.23/1.68	EOF