2.42/1.26	NO
2.42/1.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.42/1.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.42/1.26	
2.42/1.26	
2.42/1.26	Outermost Termination of the given OTRS could be disproven:
2.42/1.26	
2.42/1.26	(0) OTRS
2.42/1.26	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.42/1.26	(2) NO
2.42/1.26	
2.42/1.26	
2.42/1.26	----------------------------------------
2.42/1.26	
2.42/1.26	(0)
2.42/1.26	Obligation:
2.42/1.26	Term rewrite system R:
2.42/1.26	The TRS R consists of the following rules:
2.42/1.26	
2.42/1.26	   U61(tt) -> s(length(L))
2.42/1.26	   and(tt) -> X
2.42/1.26	   zeros -> cons(0)
2.42/1.26	   U11(tt) -> U12(isNatList)
2.42/1.26	   U12(tt) -> tt
2.42/1.26	   U21(tt) -> U22(isNat)
2.42/1.26	   U22(tt) -> tt
2.42/1.26	   U31(tt) -> U32(isNatList)
2.42/1.26	   U32(tt) -> tt
2.42/1.26	   U41(tt) -> U42(isNat)
2.42/1.26	   U42(tt) -> U43(isNatIList)
2.42/1.26	   U43(tt) -> tt
2.42/1.26	   U51(tt) -> U52(isNat)
2.42/1.26	   U52(tt) -> U53(isNatList)
2.42/1.26	   U53(tt) -> tt
2.42/1.26	   isNat -> tt
2.42/1.26	   isNat -> U11(isNatIListKind)
2.42/1.26	   isNat -> U21(isNatKind)
2.42/1.26	   isNatIList -> U31(isNatIListKind)
2.42/1.26	   isNatIList -> tt
2.42/1.26	   isNatIList -> U41(and(isNatKind))
2.42/1.26	   isNatIListKind -> tt
2.42/1.26	   isNatIListKind -> and(isNatKind)
2.42/1.26	   isNatKind -> tt
2.42/1.26	   isNatKind -> isNatIListKind
2.42/1.26	   isNatKind -> isNatKind
2.42/1.26	   isNatList -> tt
2.42/1.26	   isNatList -> U51(and(isNatKind))
2.42/1.26	   length(nil) -> 0
2.42/1.26	   length(cons(N)) -> U61(and(and(isNatList)))
2.42/1.26	
2.42/1.26	
2.42/1.26	
2.42/1.26	Outermost Strategy.
2.42/1.26	
2.42/1.26	----------------------------------------
2.42/1.26	
2.42/1.26	(1) OutermostNonTerminationProof (COMPLETE)
2.42/1.26	Term rewrite system R:
2.42/1.26	The TRS R consists of the following rules:
2.42/1.26	
2.42/1.26	   U61(tt) -> s(length(L))
2.42/1.26	   and(tt) -> X
2.42/1.26	   zeros -> cons(0)
2.42/1.26	   U11(tt) -> U12(isNatList)
2.42/1.26	   U12(tt) -> tt
2.42/1.26	   U21(tt) -> U22(isNat)
2.42/1.26	   U22(tt) -> tt
2.42/1.26	   U31(tt) -> U32(isNatList)
2.42/1.26	   U32(tt) -> tt
2.42/1.26	   U41(tt) -> U42(isNat)
2.42/1.26	   U42(tt) -> U43(isNatIList)
2.42/1.26	   U43(tt) -> tt
2.42/1.26	   U51(tt) -> U52(isNat)
2.42/1.26	   U52(tt) -> U53(isNatList)
2.42/1.26	   U53(tt) -> tt
2.42/1.26	   isNat -> tt
2.42/1.26	   isNat -> U11(isNatIListKind)
2.42/1.26	   isNat -> U21(isNatKind)
2.42/1.26	   isNatIList -> U31(isNatIListKind)
2.42/1.26	   isNatIList -> tt
2.42/1.26	   isNatIList -> U41(and(isNatKind))
2.42/1.26	   isNatIListKind -> tt
2.42/1.26	   isNatIListKind -> and(isNatKind)
2.42/1.26	   isNatKind -> tt
2.42/1.26	   isNatKind -> isNatIListKind
2.42/1.26	   isNatKind -> isNatKind
2.42/1.26	   isNatList -> tt
2.42/1.26	   isNatList -> U51(and(isNatKind))
2.42/1.27	   length(nil) -> 0
2.42/1.27	   length(cons(N)) -> U61(and(and(isNatList)))
2.42/1.27	
2.42/1.27	
2.42/1.27	
2.42/1.27	Outermost Strategy.
2.42/1.27	
2.42/1.27	---------- Loop: ----------
2.42/1.27	
2.42/1.27	U61(tt) -> s(length(U61(tt))) with rule U61(tt) -> s(length(L)) at position [] and matcher [L / U61(tt)]
2.42/1.27	
2.42/1.27	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.42/1.27	
2.42/1.27	Context: s(length([]))
2.42/1.27	
2.42/1.27	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.42/1.27	----------------------------------------
2.42/1.27	
2.42/1.27	(2)
2.42/1.27	NO
2.42/1.29	EOF