25.22/7.12	NO
25.22/7.13	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
25.22/7.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
25.22/7.13	
25.22/7.13	
25.22/7.13	Outermost Termination of the given OTRS could be disproven:
25.22/7.13	
25.22/7.13	(0) OTRS
25.22/7.13	(1) OutermostNonTerminationProof [COMPLETE, 3959 ms]
25.22/7.13	(2) NO
25.22/7.13	
25.22/7.13	
25.22/7.13	----------------------------------------
25.22/7.13	
25.22/7.13	(0)
25.22/7.13	Obligation:
25.22/7.13	Term rewrite system R:
25.22/7.13	The TRS R consists of the following rules:
25.22/7.13	
25.22/7.13	   zeros -> cons(0, n__zeros)
25.22/7.13	   U11(tt, L) -> U12(tt, activate(L))
25.22/7.13	   U12(tt, L) -> s(length(activate(L)))
25.22/7.13	   U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N))
25.22/7.13	   U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N))
25.22/7.13	   U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
25.22/7.13	   length(nil) -> 0
25.22/7.13	   length(cons(N, L)) -> U11(tt, activate(L))
25.22/7.13	   take(0, IL) -> nil
25.22/7.13	   take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N)
25.22/7.13	   zeros -> n__zeros
25.22/7.13	   take(X1, X2) -> n__take(X1, X2)
25.22/7.13	   activate(n__zeros) -> zeros
25.22/7.13	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
25.22/7.13	   activate(X) -> X
25.22/7.13	
25.22/7.13	
25.22/7.13	
25.22/7.13	Outermost Strategy.
25.22/7.13	
25.22/7.13	----------------------------------------
25.22/7.13	
25.22/7.13	(1) OutermostNonTerminationProof (COMPLETE)
25.22/7.13	Term rewrite system R:
25.22/7.13	The TRS R consists of the following rules:
25.22/7.13	
25.22/7.13	   zeros -> cons(0, n__zeros)
25.22/7.13	   U11(tt, L) -> U12(tt, activate(L))
25.22/7.13	   U12(tt, L) -> s(length(activate(L)))
25.22/7.13	   U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N))
25.22/7.13	   U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N))
25.22/7.13	   U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
25.22/7.13	   length(nil) -> 0
25.22/7.13	   length(cons(N, L)) -> U11(tt, activate(L))
25.22/7.13	   take(0, IL) -> nil
25.22/7.13	   take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N)
25.22/7.13	   zeros -> n__zeros
25.22/7.13	   take(X1, X2) -> n__take(X1, X2)
25.22/7.13	   activate(n__zeros) -> zeros
25.22/7.13	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
25.22/7.13	   activate(X) -> X
25.22/7.13	
25.22/7.13	
25.22/7.13	
25.22/7.13	Outermost Strategy.
25.22/7.13	
25.22/7.13	---------- Loop: ----------
25.22/7.13	
25.22/7.13	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))]
25.22/7.13	
25.22/7.13	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))]
25.22/7.13	
25.22/7.13	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)]
25.22/7.13	
25.22/7.13	s(length(activate(n__zeros))) -> s(length(zeros)) with rule activate(n__zeros) -> zeros at position [0,0] and matcher [ ]
25.22/7.13	
25.22/7.13	s(length(zeros)) -> s(length(cons(0, n__zeros))) with rule zeros -> cons(0, n__zeros) at position [0,0] and matcher [ ]
25.22/7.13	
25.22/7.13	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]
25.22/7.13	
25.22/7.13	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)]
25.22/7.13	
25.22/7.13	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
25.22/7.13	
25.22/7.13	Context: s([])
25.22/7.13	
25.22/7.13	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
25.22/7.13	----------------------------------------
25.22/7.13	
25.22/7.13	(2)
25.22/7.13	NO
25.50/7.93	EOF