2.72/1.24 NO 2.72/1.25 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.72/1.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.72/1.25 2.72/1.25 2.72/1.25 Outermost Termination of the given OTRS could be disproven: 2.72/1.25 2.72/1.25 (0) OTRS 2.72/1.25 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.72/1.25 (2) NO 2.72/1.25 2.72/1.25 2.72/1.25 ---------------------------------------- 2.72/1.25 2.72/1.25 (0) 2.72/1.25 Obligation: 2.72/1.25 Term rewrite system R: 2.72/1.25 The TRS R consists of the following rules: 2.72/1.25 2.72/1.25 h(X, Z) -> f(X, s(X), Z) 2.72/1.25 f(X, Y, g(X, Y)) -> h(0, g(X, Y)) 2.72/1.25 g(0, Y) -> 0 2.72/1.25 g(X, s(Y)) -> g(X, Y) 2.72/1.25 2.72/1.25 2.72/1.25 2.72/1.25 Outermost Strategy. 2.72/1.25 2.72/1.25 ---------------------------------------- 2.72/1.25 2.72/1.25 (1) OutermostNonTerminationProof (COMPLETE) 2.72/1.25 Term rewrite system R: 2.72/1.25 The TRS R consists of the following rules: 2.72/1.25 2.72/1.25 h(X, Z) -> f(X, s(X), Z) 2.72/1.25 f(X, Y, g(X, Y)) -> h(0, g(X, Y)) 2.72/1.25 g(0, Y) -> 0 2.72/1.25 g(X, s(Y)) -> g(X, Y) 2.72/1.25 2.72/1.25 2.72/1.25 2.72/1.25 Outermost Strategy. 2.72/1.25 2.72/1.25 ---------- Loop: ---------- 2.72/1.25 2.72/1.25 f(0, s(0), g(0, s(0))) -> h(0, g(0, s(0))) with rule f(X, Y, g(X, Y)) -> h(0, g(X, Y)) at position [] and matcher [X / 0, Y / s(0)] 2.72/1.25 2.72/1.25 h(0, g(0, s(0))) -> f(0, s(0), g(0, s(0))) with rule h(X, Z) -> f(X, s(X), Z) at position [] and matcher [X / 0, Z / g(0, s(0))] 2.72/1.25 2.72/1.25 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.72/1.25 2.72/1.25 Context: [] 2.72/1.25 2.72/1.25 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.72/1.25 ---------------------------------------- 2.72/1.25 2.72/1.25 (2) 2.72/1.25 NO 2.72/1.30 EOF