2.28/1.25	NO
2.28/1.25	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.28/1.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.28/1.25	
2.28/1.25	
2.28/1.25	Outermost Termination of the given OTRS could be disproven:
2.28/1.25	
2.28/1.25	(0) OTRS
2.28/1.25	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.28/1.25	(2) NO
2.28/1.25	
2.28/1.25	
2.28/1.25	----------------------------------------
2.28/1.25	
2.28/1.25	(0)
2.28/1.25	Obligation:
2.28/1.25	Term rewrite system R:
2.28/1.25	The TRS R consists of the following rules:
2.28/1.25	
2.28/1.25	   U41(tt) -> N
2.28/1.25	   U51(tt) -> s(plus(N, M))
2.28/1.25	   U71(tt) -> plus(x(N, M), N)
2.28/1.25	   and(tt) -> X
2.28/1.25	   U11(tt) -> U12(isNat)
2.28/1.25	   U12(tt) -> U13(isNat)
2.28/1.25	   U13(tt) -> tt
2.28/1.25	   U21(tt) -> U22(isNat)
2.28/1.25	   U22(tt) -> tt
2.28/1.25	   U31(tt) -> U32(isNat)
2.28/1.25	   U32(tt) -> U33(isNat)
2.28/1.25	   U33(tt) -> tt
2.28/1.25	   U61(tt) -> 0
2.28/1.25	   isNat -> tt
2.28/1.25	   isNat -> U11(and(isNatKind))
2.28/1.25	   isNat -> U21(isNatKind)
2.28/1.25	   isNat -> U31(and(isNatKind))
2.28/1.25	   isNatKind -> tt
2.28/1.25	   isNatKind -> and(isNatKind)
2.28/1.25	   isNatKind -> isNatKind
2.28/1.25	   plus(N, 0) -> U41(and(isNat))
2.28/1.25	   plus(N, s(M)) -> U51(and(and(isNat)))
2.28/1.25	   x(N, 0) -> U61(and(isNat))
2.28/1.25	   x(N, s(M)) -> U71(and(and(isNat)))
2.28/1.25	
2.28/1.25	
2.28/1.25	
2.28/1.25	Outermost Strategy.
2.28/1.25	
2.28/1.25	----------------------------------------
2.28/1.25	
2.28/1.25	(1) OutermostNonTerminationProof (COMPLETE)
2.28/1.25	Term rewrite system R:
2.28/1.25	The TRS R consists of the following rules:
2.28/1.25	
2.28/1.25	   U41(tt) -> N
2.28/1.25	   U51(tt) -> s(plus(N, M))
2.28/1.25	   U71(tt) -> plus(x(N, M), N)
2.28/1.25	   and(tt) -> X
2.28/1.25	   U11(tt) -> U12(isNat)
2.28/1.25	   U12(tt) -> U13(isNat)
2.28/1.25	   U13(tt) -> tt
2.28/1.25	   U21(tt) -> U22(isNat)
2.28/1.25	   U22(tt) -> tt
2.28/1.25	   U31(tt) -> U32(isNat)
2.28/1.25	   U32(tt) -> U33(isNat)
2.28/1.25	   U33(tt) -> tt
2.28/1.25	   U61(tt) -> 0
2.28/1.25	   isNat -> tt
2.28/1.25	   isNat -> U11(and(isNatKind))
2.28/1.25	   isNat -> U21(isNatKind)
2.28/1.25	   isNat -> U31(and(isNatKind))
2.28/1.25	   isNatKind -> tt
2.28/1.25	   isNatKind -> and(isNatKind)
2.28/1.25	   isNatKind -> isNatKind
2.28/1.25	   plus(N, 0) -> U41(and(isNat))
2.28/1.25	   plus(N, s(M)) -> U51(and(and(isNat)))
2.28/1.25	   x(N, 0) -> U61(and(isNat))
2.28/1.25	   x(N, s(M)) -> U71(and(and(isNat)))
2.28/1.25	
2.28/1.25	
2.28/1.25	
2.28/1.25	Outermost Strategy.
2.28/1.25	
2.28/1.25	---------- Loop: ----------
2.28/1.25	
2.28/1.25	U41(tt) -> U41(tt) with rule U41(tt) -> N at position [] and matcher [N / U41(tt)]
2.28/1.25	
2.28/1.25	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
2.28/1.25	
2.28/1.25	Context: []
2.28/1.25	
2.28/1.25	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.28/1.25	----------------------------------------
2.28/1.25	
2.28/1.25	(2)
2.28/1.25	NO
2.41/1.29	EOF