2.61/1.34	NO
2.61/1.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.61/1.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.61/1.34	
2.61/1.34	
2.61/1.34	Outermost Termination of the given OTRS could be disproven:
2.61/1.34	
2.61/1.34	(0) OTRS
2.61/1.34	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.61/1.34	(2) NO
2.61/1.34	
2.61/1.34	
2.61/1.34	----------------------------------------
2.61/1.34	
2.61/1.34	(0)
2.61/1.34	Obligation:
2.61/1.34	Term rewrite system R:
2.61/1.34	The TRS R consists of the following rules:
2.61/1.34	
2.61/1.34	   U71(tt) -> s(length(L))
2.61/1.34	   U91(tt) -> cons(N)
2.61/1.34	   and(tt) -> X
2.61/1.34	   zeros -> cons(0)
2.61/1.34	   U11(tt) -> U12(isNatList)
2.61/1.34	   U12(tt) -> tt
2.61/1.34	   U21(tt) -> U22(isNat)
2.61/1.34	   U22(tt) -> tt
2.61/1.34	   U31(tt) -> U32(isNatList)
2.61/1.34	   U32(tt) -> tt
2.61/1.34	   U41(tt) -> U42(isNat)
2.61/1.34	   U42(tt) -> U43(isNatIList)
2.61/1.34	   U43(tt) -> tt
2.61/1.34	   U51(tt) -> U52(isNat)
2.61/1.34	   U52(tt) -> U53(isNatList)
2.61/1.34	   U53(tt) -> tt
2.61/1.34	   U61(tt) -> U62(isNat)
2.61/1.34	   U62(tt) -> U63(isNatIList)
2.61/1.34	   U63(tt) -> tt
2.61/1.34	   U81(tt) -> nil
2.61/1.34	   isNat -> tt
2.61/1.34	   isNat -> U11(isNatIListKind)
2.61/1.34	   isNat -> U21(isNatKind)
2.61/1.34	   isNatIList -> U31(isNatIListKind)
2.61/1.34	   isNatIList -> tt
2.61/1.34	   isNatIList -> U41(and(isNatKind))
2.61/1.34	   isNatIListKind -> tt
2.61/1.34	   isNatIListKind -> and(isNatKind)
2.61/1.34	   isNatKind -> tt
2.61/1.34	   isNatKind -> isNatIListKind
2.61/1.34	   isNatKind -> isNatKind
2.61/1.34	   isNatList -> tt
2.61/1.34	   isNatList -> U51(and(isNatKind))
2.61/1.34	   isNatList -> U61(and(isNatKind))
2.61/1.34	   length(nil) -> 0
2.61/1.34	   length(cons(N)) -> U71(and(and(isNatList)))
2.61/1.34	   take(0, IL) -> U81(and(isNatIList))
2.61/1.34	   take(s(M), cons(N)) -> U91(and(and(isNatIList)))
2.61/1.34	
2.61/1.34	
2.61/1.34	
2.61/1.34	Outermost Strategy.
2.61/1.34	
2.61/1.34	----------------------------------------
2.61/1.34	
2.61/1.34	(1) OutermostNonTerminationProof (COMPLETE)
2.61/1.34	Term rewrite system R:
2.61/1.34	The TRS R consists of the following rules:
2.61/1.34	
2.61/1.34	   U71(tt) -> s(length(L))
2.61/1.34	   U91(tt) -> cons(N)
2.61/1.34	   and(tt) -> X
2.61/1.34	   zeros -> cons(0)
2.61/1.34	   U11(tt) -> U12(isNatList)
2.61/1.34	   U12(tt) -> tt
2.61/1.34	   U21(tt) -> U22(isNat)
2.61/1.34	   U22(tt) -> tt
2.61/1.34	   U31(tt) -> U32(isNatList)
2.61/1.34	   U32(tt) -> tt
2.61/1.34	   U41(tt) -> U42(isNat)
2.61/1.34	   U42(tt) -> U43(isNatIList)
2.61/1.34	   U43(tt) -> tt
2.61/1.34	   U51(tt) -> U52(isNat)
2.61/1.34	   U52(tt) -> U53(isNatList)
2.61/1.34	   U53(tt) -> tt
2.61/1.34	   U61(tt) -> U62(isNat)
2.61/1.34	   U62(tt) -> U63(isNatIList)
2.61/1.34	   U63(tt) -> tt
2.61/1.34	   U81(tt) -> nil
2.61/1.34	   isNat -> tt
2.61/1.35	   isNat -> U11(isNatIListKind)
2.61/1.35	   isNat -> U21(isNatKind)
2.61/1.35	   isNatIList -> U31(isNatIListKind)
2.61/1.35	   isNatIList -> tt
2.61/1.35	   isNatIList -> U41(and(isNatKind))
2.61/1.35	   isNatIListKind -> tt
2.61/1.35	   isNatIListKind -> and(isNatKind)
2.61/1.35	   isNatKind -> tt
2.61/1.35	   isNatKind -> isNatIListKind
2.61/1.35	   isNatKind -> isNatKind
2.61/1.35	   isNatList -> tt
2.61/1.35	   isNatList -> U51(and(isNatKind))
2.61/1.35	   isNatList -> U61(and(isNatKind))
2.61/1.35	   length(nil) -> 0
2.61/1.35	   length(cons(N)) -> U71(and(and(isNatList)))
2.61/1.35	   take(0, IL) -> U81(and(isNatIList))
2.61/1.35	   take(s(M), cons(N)) -> U91(and(and(isNatIList)))
2.61/1.35	
2.61/1.35	
2.61/1.35	
2.61/1.35	Outermost Strategy.
2.61/1.35	
2.61/1.35	---------- Loop: ----------
2.61/1.35	
2.61/1.35	U71(tt) -> s(length(U71(tt))) with rule U71(tt) -> s(length(L)) at position [] and matcher [L / U71(tt)]
2.61/1.35	
2.61/1.35	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0,0].
2.61/1.35	
2.61/1.35	Context: s(length([]))
2.61/1.35	
2.61/1.35	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.61/1.35	----------------------------------------
2.61/1.35	
2.61/1.35	(2)
2.61/1.35	NO
2.61/1.37	EOF