2.60/1.24	NO
2.69/1.25	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.69/1.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.69/1.25	
2.69/1.25	
2.69/1.25	Outermost Termination of the given OTRS could be disproven:
2.69/1.25	
2.69/1.25	(0) OTRS
2.69/1.25	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.69/1.25	(2) NO
2.69/1.25	
2.69/1.25	
2.69/1.25	----------------------------------------
2.69/1.25	
2.69/1.25	(0)
2.69/1.25	Obligation:
2.69/1.25	Term rewrite system R:
2.69/1.25	The TRS R consists of the following rules:
2.69/1.25	
2.69/1.25	   U11(tt) -> s(length(L))
2.69/1.25	   U31(tt) -> cons(N)
2.69/1.25	   and(tt) -> X
2.69/1.25	   zeros -> cons(0)
2.69/1.25	   U21(tt) -> nil
2.69/1.25	   isNat -> tt
2.69/1.25	   isNat -> isNatList
2.69/1.25	   isNat -> isNat
2.69/1.25	   isNatIList -> isNatList
2.69/1.25	   isNatIList -> tt
2.69/1.25	   isNatIList -> and(isNat)
2.69/1.25	   isNatList -> tt
2.69/1.25	   isNatList -> and(isNat)
2.69/1.25	   length(nil) -> 0
2.69/1.25	   length(cons(N)) -> U11(and(isNatList))
2.69/1.25	   take(0, IL) -> U21(isNatIList)
2.69/1.25	   take(s(M), cons(N)) -> U31(and(isNatIList))
2.69/1.25	
2.69/1.25	
2.69/1.25	
2.69/1.25	Outermost Strategy.
2.69/1.25	
2.69/1.25	----------------------------------------
2.69/1.25	
2.69/1.25	(1) OutermostNonTerminationProof (COMPLETE)
2.69/1.25	Term rewrite system R:
2.69/1.25	The TRS R consists of the following rules:
2.69/1.25	
2.69/1.25	   U11(tt) -> s(length(L))
2.69/1.25	   U31(tt) -> cons(N)
2.69/1.25	   and(tt) -> X
2.69/1.25	   zeros -> cons(0)
2.69/1.25	   U21(tt) -> nil
2.69/1.25	   isNat -> tt
2.69/1.25	   isNat -> isNatList
2.69/1.25	   isNat -> isNat
2.69/1.25	   isNatIList -> isNatList
2.69/1.25	   isNatIList -> tt
2.69/1.25	   isNatIList -> and(isNat)
2.69/1.25	   isNatList -> tt
2.69/1.25	   isNatList -> and(isNat)
2.69/1.25	   length(nil) -> 0
2.69/1.25	   length(cons(N)) -> U11(and(isNatList))
2.69/1.25	   take(0, IL) -> U21(isNatIList)
2.69/1.25	   take(s(M), cons(N)) -> U31(and(isNatIList))
2.69/1.25	
2.69/1.25	
2.69/1.25	
2.69/1.25	Outermost Strategy.
2.69/1.25	
2.69/1.25	---------- Loop: ----------
2.69/1.25	
2.69/1.25	U11(tt) -> s(length(U11(tt))) with rule U11(tt) -> s(length(L)) at position [] and matcher [L / U11(tt)]
2.69/1.25	
2.69/1.25	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.69/1.25	
2.69/1.25	Context: s(length([]))
2.69/1.25	
2.69/1.25	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.69/1.25	----------------------------------------
2.69/1.25	
2.69/1.25	(2)
2.69/1.25	NO
2.69/1.27	EOF