2.66/1.26	NO
2.66/1.27	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.66/1.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.66/1.27	
2.66/1.27	
2.66/1.27	Outermost Termination of the given OTRS could be disproven:
2.66/1.27	
2.66/1.27	(0) OTRS
2.66/1.27	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.66/1.27	(2) NO
2.66/1.27	
2.66/1.27	
2.66/1.27	----------------------------------------
2.66/1.27	
2.66/1.27	(0)
2.66/1.27	Obligation:
2.66/1.27	Term rewrite system R:
2.66/1.27	The TRS R consists of the following rules:
2.66/1.27	
2.66/1.27	   U104(tt) -> plus(x(N, M), N)
2.66/1.27	   U72(tt) -> N
2.66/1.27	   U84(tt) -> s(plus(N, M))
2.66/1.27	   U101(tt) -> U102(isNatKind)
2.66/1.27	   U102(tt) -> U103(isNat)
2.66/1.27	   U103(tt) -> U104(isNatKind)
2.66/1.27	   U11(tt) -> U12(isNatKind)
2.66/1.27	   U12(tt) -> U13(isNatKind)
2.66/1.27	   U13(tt) -> U14(isNatKind)
2.66/1.27	   U14(tt) -> U15(isNat)
2.66/1.27	   U15(tt) -> U16(isNat)
2.66/1.27	   U16(tt) -> tt
2.66/1.27	   U21(tt) -> U22(isNatKind)
2.66/1.27	   U22(tt) -> U23(isNat)
2.66/1.27	   U23(tt) -> tt
2.66/1.27	   U31(tt) -> U32(isNatKind)
2.66/1.27	   U32(tt) -> U33(isNatKind)
2.66/1.27	   U33(tt) -> U34(isNatKind)
2.66/1.27	   U34(tt) -> U35(isNat)
2.66/1.27	   U35(tt) -> U36(isNat)
2.66/1.27	   U36(tt) -> tt
2.66/1.27	   U41(tt) -> U42(isNatKind)
2.66/1.27	   U42(tt) -> tt
2.66/1.27	   U51(tt) -> tt
2.66/1.27	   U61(tt) -> U62(isNatKind)
2.71/1.27	   U62(tt) -> tt
2.71/1.27	   U71(tt) -> U72(isNatKind)
2.71/1.27	   U81(tt) -> U82(isNatKind)
2.71/1.27	   U82(tt) -> U83(isNat)
2.71/1.27	   U83(tt) -> U84(isNatKind)
2.71/1.27	   U91(tt) -> U92(isNatKind)
2.71/1.27	   U92(tt) -> 0
2.71/1.27	   isNat -> tt
2.71/1.27	   isNat -> U11(isNatKind)
2.71/1.27	   isNat -> U21(isNatKind)
2.71/1.27	   isNat -> U31(isNatKind)
2.71/1.27	   isNatKind -> tt
2.71/1.27	   isNatKind -> U41(isNatKind)
2.71/1.27	   isNatKind -> U51(isNatKind)
2.71/1.27	   isNatKind -> U61(isNatKind)
2.71/1.27	   plus(N, 0) -> U71(isNat)
2.71/1.27	   plus(N, s(M)) -> U81(isNat)
2.71/1.27	   x(N, 0) -> U91(isNat)
2.71/1.27	   x(N, s(M)) -> U101(isNat)
2.71/1.27	
2.71/1.27	
2.71/1.27	
2.71/1.27	Outermost Strategy.
2.71/1.27	
2.71/1.27	----------------------------------------
2.71/1.27	
2.71/1.27	(1) OutermostNonTerminationProof (COMPLETE)
2.71/1.27	Term rewrite system R:
2.71/1.27	The TRS R consists of the following rules:
2.71/1.27	
2.71/1.27	   U104(tt) -> plus(x(N, M), N)
2.71/1.27	   U72(tt) -> N
2.71/1.27	   U84(tt) -> s(plus(N, M))
2.71/1.27	   U101(tt) -> U102(isNatKind)
2.71/1.27	   U102(tt) -> U103(isNat)
2.71/1.27	   U103(tt) -> U104(isNatKind)
2.71/1.27	   U11(tt) -> U12(isNatKind)
2.71/1.27	   U12(tt) -> U13(isNatKind)
2.71/1.27	   U13(tt) -> U14(isNatKind)
2.71/1.27	   U14(tt) -> U15(isNat)
2.71/1.27	   U15(tt) -> U16(isNat)
2.71/1.27	   U16(tt) -> tt
2.71/1.27	   U21(tt) -> U22(isNatKind)
2.71/1.27	   U22(tt) -> U23(isNat)
2.71/1.27	   U23(tt) -> tt
2.71/1.27	   U31(tt) -> U32(isNatKind)
2.71/1.27	   U32(tt) -> U33(isNatKind)
2.71/1.27	   U33(tt) -> U34(isNatKind)
2.71/1.27	   U34(tt) -> U35(isNat)
2.71/1.27	   U35(tt) -> U36(isNat)
2.71/1.27	   U36(tt) -> tt
2.71/1.27	   U41(tt) -> U42(isNatKind)
2.71/1.27	   U42(tt) -> tt
2.71/1.27	   U51(tt) -> tt
2.71/1.27	   U61(tt) -> U62(isNatKind)
2.71/1.27	   U62(tt) -> tt
2.71/1.27	   U71(tt) -> U72(isNatKind)
2.71/1.27	   U81(tt) -> U82(isNatKind)
2.71/1.27	   U82(tt) -> U83(isNat)
2.71/1.27	   U83(tt) -> U84(isNatKind)
2.71/1.27	   U91(tt) -> U92(isNatKind)
2.71/1.27	   U92(tt) -> 0
2.71/1.27	   isNat -> tt
2.71/1.27	   isNat -> U11(isNatKind)
2.71/1.27	   isNat -> U21(isNatKind)
2.71/1.27	   isNat -> U31(isNatKind)
2.71/1.27	   isNatKind -> tt
2.71/1.27	   isNatKind -> U41(isNatKind)
2.71/1.27	   isNatKind -> U51(isNatKind)
2.71/1.27	   isNatKind -> U61(isNatKind)
2.71/1.27	   plus(N, 0) -> U71(isNat)
2.71/1.27	   plus(N, s(M)) -> U81(isNat)
2.71/1.27	   x(N, 0) -> U91(isNat)
2.71/1.27	   x(N, s(M)) -> U101(isNat)
2.71/1.27	
2.71/1.27	
2.71/1.27	
2.71/1.27	Outermost Strategy.
2.71/1.27	
2.71/1.27	---------- Loop: ----------
2.71/1.27	
2.71/1.27	U104(tt) -> plus(x(U104(tt), U104(tt)), U104(tt)) with rule U104(tt) -> plus(x(N, M), N) at position [] and matcher [N / U104(tt), M / U104(tt)]
2.71/1.27	
2.71/1.27	Now an instance of the first term with Matcher [ ] occurs in the last term at position [1].
2.71/1.27	
2.71/1.27	Context: plus(x(U104(tt), U104(tt)), [])
2.71/1.27	
2.71/1.27	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.71/1.27	----------------------------------------
2.71/1.27	
2.71/1.27	(2)
2.71/1.27	NO
2.71/1.29	EOF