2.56/1.22	NO
2.56/1.23	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.56/1.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.56/1.23	
2.56/1.23	
2.56/1.23	Outermost Termination of the given OTRS could be disproven:
2.56/1.23	
2.56/1.23	(0) OTRS
2.56/1.23	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.56/1.23	(2) NO
2.56/1.23	
2.56/1.23	
2.56/1.23	----------------------------------------
2.56/1.23	
2.56/1.23	(0)
2.56/1.23	Obligation:
2.56/1.23	Term rewrite system R:
2.56/1.23	The TRS R consists of the following rules:
2.56/1.23	
2.56/1.23	   uTake2(tt) -> cons(N)
2.56/1.23	   uLength(tt) -> s(length(L))
2.56/1.23	   and(tt, T) -> T
2.56/1.23	   isNatIList -> isNatList
2.56/1.23	   isNat -> tt
2.56/1.23	   isNat -> isNat
2.56/1.23	   isNat -> isNatList
2.56/1.23	   isNatIList -> tt
2.56/1.23	   isNatIList -> and(isNat, isNatIList)
2.56/1.23	   isNatList -> tt
2.56/1.23	   isNatList -> and(isNat, isNatList)
2.56/1.23	   isNatList -> and(isNat, isNatIList)
2.56/1.23	   zeros -> cons(0)
2.56/1.23	   take(0, IL) -> uTake1(isNatIList)
2.56/1.23	   uTake1(tt) -> nil
2.56/1.23	   take(s(M), cons(N)) -> uTake2(and(isNat, and(isNat, isNatIList)))
2.56/1.23	   length(cons(N)) -> uLength(and(isNat, isNatList))
2.56/1.23	
2.56/1.23	
2.56/1.23	
2.56/1.23	Outermost Strategy.
2.56/1.23	
2.56/1.23	----------------------------------------
2.56/1.23	
2.56/1.23	(1) OutermostNonTerminationProof (COMPLETE)
2.56/1.23	Term rewrite system R:
2.56/1.23	The TRS R consists of the following rules:
2.56/1.23	
2.56/1.23	   uTake2(tt) -> cons(N)
2.56/1.23	   uLength(tt) -> s(length(L))
2.56/1.23	   and(tt, T) -> T
2.56/1.23	   isNatIList -> isNatList
2.56/1.23	   isNat -> tt
2.56/1.23	   isNat -> isNat
2.56/1.23	   isNat -> isNatList
2.56/1.23	   isNatIList -> tt
2.56/1.23	   isNatIList -> and(isNat, isNatIList)
2.56/1.23	   isNatList -> tt
2.56/1.23	   isNatList -> and(isNat, isNatList)
2.56/1.23	   isNatList -> and(isNat, isNatIList)
2.56/1.23	   zeros -> cons(0)
2.56/1.23	   take(0, IL) -> uTake1(isNatIList)
2.56/1.23	   uTake1(tt) -> nil
2.56/1.23	   take(s(M), cons(N)) -> uTake2(and(isNat, and(isNat, isNatIList)))
2.56/1.23	   length(cons(N)) -> uLength(and(isNat, isNatList))
2.56/1.23	
2.56/1.23	
2.56/1.23	
2.56/1.23	Outermost Strategy.
2.56/1.23	
2.56/1.23	---------- Loop: ----------
2.56/1.23	
2.56/1.23	uTake2(tt) -> cons(uTake2(tt)) with rule uTake2(tt) -> cons(N) at position [] and matcher [N / uTake2(tt)]
2.56/1.23	
2.56/1.23	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
2.56/1.23	
2.56/1.23	Context: cons([])
2.56/1.23	
2.56/1.23	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.56/1.23	----------------------------------------
2.56/1.23	
2.56/1.23	(2)
2.56/1.23	NO
2.59/1.26	EOF