14.14/4.27	NO
14.14/4.29	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
14.14/4.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.14/4.29	
14.14/4.29	
14.14/4.29	Outermost Termination of the given OTRS could be disproven:
14.14/4.29	
14.14/4.29	(0) OTRS
14.14/4.29	(1) OutermostNonTerminationProof [COMPLETE, 1293 ms]
14.14/4.29	(2) NO
14.14/4.29	
14.14/4.29	
14.14/4.29	----------------------------------------
14.14/4.29	
14.14/4.29	(0)
14.14/4.29	Obligation:
14.14/4.29	Term rewrite system R:
14.14/4.29	The TRS R consists of the following rules:
14.14/4.29	
14.14/4.29	   and(tt, T) -> T
14.14/4.29	   isNatIList(IL) -> isNatList(activate(IL))
14.14/4.29	   isNat(n__0) -> tt
14.14/4.29	   isNat(n__s(N)) -> isNat(activate(N))
14.14/4.29	   isNat(n__length(L)) -> isNatList(activate(L))
14.14/4.29	   isNatIList(n__zeros) -> tt
14.14/4.29	   isNatIList(n__cons(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
14.14/4.29	   isNatList(n__nil) -> tt
14.14/4.29	   isNatList(n__cons(N, L)) -> and(isNat(activate(N)), isNatList(activate(L)))
14.14/4.29	   isNatList(n__take(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
14.14/4.29	   zeros -> cons(0, n__zeros)
14.14/4.29	   take(0, IL) -> uTake1(isNatIList(IL))
14.14/4.29	   uTake1(tt) -> nil
14.14/4.29	   take(s(M), cons(N, IL)) -> uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))), M, N, activate(IL))
14.14/4.29	   uTake2(tt, M, N, IL) -> cons(activate(N), n__take(activate(M), activate(IL)))
14.14/4.29	   length(cons(N, L)) -> uLength(and(isNat(N), isNatList(activate(L))), activate(L))
14.14/4.29	   uLength(tt, L) -> s(length(activate(L)))
14.14/4.29	   0 -> n__0
14.14/4.29	   s(X) -> n__s(X)
14.14/4.29	   length(X) -> n__length(X)
14.14/4.29	   zeros -> n__zeros
14.14/4.29	   cons(X1, X2) -> n__cons(X1, X2)
14.14/4.29	   nil -> n__nil
14.14/4.29	   take(X1, X2) -> n__take(X1, X2)
14.14/4.29	   activate(n__0) -> 0
14.14/4.29	   activate(n__s(X)) -> s(activate(X))
14.14/4.29	   activate(n__length(X)) -> length(activate(X))
14.14/4.29	   activate(n__zeros) -> zeros
14.14/4.29	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
14.14/4.29	   activate(n__nil) -> nil
14.14/4.29	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
14.14/4.29	   activate(X) -> X
14.14/4.29	
14.14/4.29	
14.14/4.29	
14.14/4.29	Outermost Strategy.
14.14/4.29	
14.14/4.29	----------------------------------------
14.14/4.29	
14.14/4.29	(1) OutermostNonTerminationProof (COMPLETE)
14.14/4.29	Term rewrite system R:
14.14/4.29	The TRS R consists of the following rules:
14.14/4.29	
14.14/4.29	   and(tt, T) -> T
14.14/4.29	   isNatIList(IL) -> isNatList(activate(IL))
14.14/4.29	   isNat(n__0) -> tt
14.14/4.29	   isNat(n__s(N)) -> isNat(activate(N))
14.14/4.29	   isNat(n__length(L)) -> isNatList(activate(L))
14.14/4.29	   isNatIList(n__zeros) -> tt
14.14/4.29	   isNatIList(n__cons(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
14.14/4.29	   isNatList(n__nil) -> tt
14.14/4.29	   isNatList(n__cons(N, L)) -> and(isNat(activate(N)), isNatList(activate(L)))
14.14/4.29	   isNatList(n__take(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
14.14/4.29	   zeros -> cons(0, n__zeros)
14.14/4.29	   take(0, IL) -> uTake1(isNatIList(IL))
14.14/4.29	   uTake1(tt) -> nil
14.14/4.29	   take(s(M), cons(N, IL)) -> uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))), M, N, activate(IL))
14.14/4.29	   uTake2(tt, M, N, IL) -> cons(activate(N), n__take(activate(M), activate(IL)))
14.14/4.29	   length(cons(N, L)) -> uLength(and(isNat(N), isNatList(activate(L))), activate(L))
14.14/4.29	   uLength(tt, L) -> s(length(activate(L)))
14.14/4.29	   0 -> n__0
14.14/4.29	   s(X) -> n__s(X)
14.14/4.29	   length(X) -> n__length(X)
14.14/4.29	   zeros -> n__zeros
14.14/4.29	   cons(X1, X2) -> n__cons(X1, X2)
14.14/4.29	   nil -> n__nil
14.14/4.29	   take(X1, X2) -> n__take(X1, X2)
14.14/4.29	   activate(n__0) -> 0
14.14/4.29	   activate(n__s(X)) -> s(activate(X))
14.14/4.29	   activate(n__length(X)) -> length(activate(X))
14.14/4.29	   activate(n__zeros) -> zeros
14.14/4.29	   activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
14.14/4.29	   activate(n__nil) -> nil
14.14/4.29	   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
14.14/4.29	   activate(X) -> X
14.14/4.29	
14.14/4.29	
14.14/4.29	
14.14/4.29	Outermost Strategy.
14.14/4.29	
14.14/4.29	---------- Loop: ----------
14.14/4.29	
14.14/4.29	isNatList(activate(n__zeros)) -> isNatList(zeros) with rule activate(n__zeros) -> zeros at position [0] and matcher [ ]
14.14/4.29	
14.14/4.29	isNatList(zeros) -> isNatList(cons(0, n__zeros)) with rule zeros -> cons(0, n__zeros) at position [0] and matcher [ ]
14.14/4.29	
14.14/4.29	isNatList(cons(0, n__zeros)) -> isNatList(n__cons(0, n__zeros)) with rule cons(X1, X2) -> n__cons(X1, X2) at position [0] and matcher [X1 / 0, X2 / n__zeros]
14.14/4.29	
14.14/4.29	isNatList(n__cons(0, n__zeros)) -> and(isNat(activate(0)), isNatList(activate(n__zeros))) with rule isNatList(n__cons(N, L)) -> and(isNat(activate(N)), isNatList(activate(L))) at position [] and matcher [N / 0, L / n__zeros]
14.14/4.29	
14.14/4.29	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
14.14/4.29	
14.14/4.29	Context: and(isNat(activate(0)), [])
14.14/4.29	
14.14/4.29	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
14.14/4.29	----------------------------------------
14.14/4.29	
14.14/4.29	(2)
14.14/4.29	NO
14.45/4.37	EOF