2.51/1.23	NO
2.51/1.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.51/1.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.51/1.23	
2.51/1.23	
2.51/1.23	Outermost Termination of the given OTRS could be disproven:
2.51/1.23	
2.51/1.23	(0) OTRS
2.51/1.23	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.51/1.23	(2) NO
2.51/1.23	
2.51/1.23	
2.51/1.23	----------------------------------------
2.51/1.23	
2.51/1.23	(0)
2.51/1.23	Obligation:
2.51/1.23	Term rewrite system R:
2.51/1.23	The TRS R consists of the following rules:
2.51/1.23	
2.51/1.23	   U72(tt) -> s(length(L))
2.51/1.23	   U93(tt) -> cons(N)
2.51/1.23	   zeros -> cons(0)
2.51/1.23	   U11(tt) -> tt
2.51/1.23	   U21(tt) -> tt
2.51/1.23	   U31(tt) -> tt
2.51/1.23	   U41(tt) -> U42(isNatIList)
2.51/1.23	   U42(tt) -> tt
2.51/1.23	   U51(tt) -> U52(isNatList)
2.51/1.23	   U52(tt) -> tt
2.51/1.23	   U61(tt) -> U62(isNatIList)
2.51/1.23	   U62(tt) -> tt
2.51/1.23	   U71(tt) -> U72(isNat)
2.51/1.23	   U81(tt) -> nil
2.51/1.23	   U91(tt) -> U92(isNat)
2.51/1.23	   U92(tt) -> U93(isNat)
2.51/1.23	   isNat -> tt
2.51/1.23	   isNat -> U11(isNatList)
2.51/1.23	   isNat -> U21(isNat)
2.51/1.23	   isNatIList -> U31(isNatList)
2.51/1.23	   isNatIList -> tt
2.51/1.23	   isNatIList -> U41(isNat)
2.51/1.23	   isNatList -> tt
2.51/1.23	   isNatList -> U51(isNat)
2.51/1.23	   isNatList -> U61(isNat)
2.51/1.23	   length(nil) -> 0
2.51/1.23	   length(cons(N)) -> U71(isNatList)
2.51/1.24	   take(0, IL) -> U81(isNatIList)
2.51/1.24	   take(s(M), cons(N)) -> U91(isNatIList)
2.51/1.24	
2.51/1.24	
2.51/1.24	
2.51/1.24	Outermost Strategy.
2.51/1.24	
2.51/1.24	----------------------------------------
2.51/1.24	
2.51/1.24	(1) OutermostNonTerminationProof (COMPLETE)
2.51/1.24	Term rewrite system R:
2.51/1.24	The TRS R consists of the following rules:
2.51/1.24	
2.51/1.24	   U72(tt) -> s(length(L))
2.51/1.24	   U93(tt) -> cons(N)
2.51/1.24	   zeros -> cons(0)
2.51/1.24	   U11(tt) -> tt
2.51/1.24	   U21(tt) -> tt
2.51/1.24	   U31(tt) -> tt
2.51/1.24	   U41(tt) -> U42(isNatIList)
2.51/1.24	   U42(tt) -> tt
2.51/1.24	   U51(tt) -> U52(isNatList)
2.51/1.24	   U52(tt) -> tt
2.51/1.24	   U61(tt) -> U62(isNatIList)
2.51/1.24	   U62(tt) -> tt
2.51/1.24	   U71(tt) -> U72(isNat)
2.51/1.24	   U81(tt) -> nil
2.51/1.24	   U91(tt) -> U92(isNat)
2.51/1.24	   U92(tt) -> U93(isNat)
2.51/1.24	   isNat -> tt
2.51/1.24	   isNat -> U11(isNatList)
2.51/1.24	   isNat -> U21(isNat)
2.51/1.24	   isNatIList -> U31(isNatList)
2.51/1.24	   isNatIList -> tt
2.51/1.24	   isNatIList -> U41(isNat)
2.51/1.24	   isNatList -> tt
2.51/1.24	   isNatList -> U51(isNat)
2.51/1.24	   isNatList -> U61(isNat)
2.51/1.24	   length(nil) -> 0
2.51/1.24	   length(cons(N)) -> U71(isNatList)
2.51/1.24	   take(0, IL) -> U81(isNatIList)
2.51/1.24	   take(s(M), cons(N)) -> U91(isNatIList)
2.51/1.24	
2.51/1.24	
2.51/1.24	
2.51/1.24	Outermost Strategy.
2.51/1.24	
2.51/1.24	---------- Loop: ----------
2.51/1.24	
2.51/1.24	U72(tt) -> s(length(U72(tt))) with rule U72(tt) -> s(length(L)) at position [] and matcher [L / U72(tt)]
2.51/1.24	
2.51/1.24	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.51/1.24	
2.51/1.24	Context: s(length([]))
2.51/1.24	
2.51/1.24	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.51/1.24	----------------------------------------
2.51/1.24	
2.51/1.24	(2)
2.51/1.24	NO
2.55/1.26	EOF