2.37/1.21 NO 2.52/1.22 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.52/1.22 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.52/1.22 2.52/1.22 2.52/1.22 Outermost Termination of the given OTRS could be disproven: 2.52/1.22 2.52/1.22 (0) OTRS 2.52/1.22 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.52/1.22 (2) NO 2.52/1.22 2.52/1.22 2.52/1.22 ---------------------------------------- 2.52/1.22 2.52/1.22 (0) 2.52/1.22 Obligation: 2.52/1.22 Term rewrite system R: 2.52/1.22 The TRS R consists of the following rules: 2.52/1.22 2.52/1.22 U31(tt) -> N 2.52/1.22 U42(tt) -> s(plus(N, M)) 2.52/1.22 U11(tt) -> U12(isNat) 2.52/1.22 U12(tt) -> tt 2.52/1.22 U21(tt) -> tt 2.52/1.22 U41(tt) -> U42(isNat) 2.52/1.22 isNat -> tt 2.52/1.22 isNat -> U11(isNat) 2.52/1.22 isNat -> U21(isNat) 2.52/1.22 plus(N, 0) -> U31(isNat) 2.52/1.22 plus(N, s(M)) -> U41(isNat) 2.52/1.22 2.52/1.22 2.52/1.22 2.52/1.22 Outermost Strategy. 2.52/1.22 2.52/1.22 ---------------------------------------- 2.52/1.22 2.52/1.22 (1) OutermostNonTerminationProof (COMPLETE) 2.52/1.22 Term rewrite system R: 2.52/1.22 The TRS R consists of the following rules: 2.52/1.22 2.52/1.22 U31(tt) -> N 2.52/1.22 U42(tt) -> s(plus(N, M)) 2.52/1.22 U11(tt) -> U12(isNat) 2.52/1.22 U12(tt) -> tt 2.52/1.22 U21(tt) -> tt 2.52/1.22 U41(tt) -> U42(isNat) 2.52/1.22 isNat -> tt 2.52/1.22 isNat -> U11(isNat) 2.52/1.22 isNat -> U21(isNat) 2.52/1.22 plus(N, 0) -> U31(isNat) 2.52/1.22 plus(N, s(M)) -> U41(isNat) 2.52/1.22 2.52/1.22 2.52/1.22 2.52/1.22 Outermost Strategy. 2.52/1.22 2.52/1.22 ---------- Loop: ---------- 2.52/1.22 2.52/1.22 U31(tt) -> U31(tt) with rule U31(tt) -> N at position [] and matcher [N / U31(tt)] 2.52/1.22 2.52/1.22 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.52/1.22 2.52/1.22 Context: [] 2.52/1.22 2.52/1.22 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.52/1.22 ---------------------------------------- 2.52/1.22 2.52/1.22 (2) 2.52/1.22 NO 2.52/1.25 EOF