2.82/1.30 NO 2.82/1.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.82/1.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.82/1.31 2.82/1.31 2.82/1.31 Outermost Termination of the given OTRS could be disproven: 2.82/1.31 2.82/1.31 (0) OTRS 2.82/1.31 (1) OutermostNonTerminationProof [COMPLETE, 50 ms] 2.82/1.31 (2) NO 2.82/1.31 2.82/1.31 2.82/1.31 ---------------------------------------- 2.82/1.31 2.82/1.31 (0) 2.82/1.31 Obligation: 2.82/1.31 Term rewrite system R: 2.82/1.31 The TRS R consists of the following rules: 2.82/1.31 2.82/1.31 +(1, x) -> +(+(0, 1), x) 2.82/1.31 +(0, x) -> x 2.82/1.31 2.82/1.31 2.82/1.31 2.82/1.31 Outermost Strategy. 2.82/1.31 2.82/1.31 ---------------------------------------- 2.82/1.31 2.82/1.31 (1) OutermostNonTerminationProof (COMPLETE) 2.82/1.31 Term rewrite system R: 2.82/1.31 The TRS R consists of the following rules: 2.82/1.31 2.82/1.31 +(1, x) -> +(+(0, 1), x) 2.82/1.31 +(0, x) -> x 2.82/1.31 2.82/1.31 2.82/1.31 2.82/1.31 Outermost Strategy. 2.82/1.31 2.82/1.31 ---------- Loop: ---------- 2.82/1.31 2.82/1.31 +(+(0, 1), x) -> +(1, x) with rule +(0, x') -> x' at position [0] and matcher [x' / 1] 2.82/1.31 2.82/1.31 +(1, x) -> +(+(0, 1), x) with rule +(1, x') -> +(+(0, 1), x') at position [] and matcher [x' / x] 2.82/1.31 2.82/1.31 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.82/1.31 2.82/1.31 Context: [] 2.82/1.31 2.82/1.31 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.82/1.31 ---------------------------------------- 2.82/1.31 2.82/1.31 (2) 2.82/1.31 NO 3.01/1.34 EOF