2.46/1.31 NO 2.46/1.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.46/1.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.46/1.31 2.46/1.31 2.46/1.31 Outermost Termination of the given OTRS could be disproven: 2.46/1.31 2.46/1.31 (0) OTRS 2.46/1.31 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.46/1.31 (2) NO 2.46/1.31 2.46/1.31 2.46/1.31 ---------------------------------------- 2.46/1.31 2.46/1.31 (0) 2.46/1.31 Obligation: 2.46/1.31 Term rewrite system R: 2.46/1.31 The TRS R consists of the following rules: 2.46/1.31 2.46/1.31 f(x, y) -> f(x, x) 2.46/1.31 f(s(x), y) -> f(y, x) 2.46/1.31 2.46/1.31 2.46/1.31 2.46/1.31 Outermost Strategy. 2.46/1.31 2.46/1.31 ---------------------------------------- 2.46/1.31 2.46/1.31 (1) OutermostNonTerminationProof (COMPLETE) 2.46/1.31 Term rewrite system R: 2.46/1.31 The TRS R consists of the following rules: 2.46/1.31 2.46/1.31 f(x, y) -> f(x, x) 2.46/1.31 f(s(x), y) -> f(y, x) 2.46/1.31 2.46/1.31 2.46/1.31 2.46/1.31 Outermost Strategy. 2.46/1.31 2.46/1.31 ---------- Loop: ---------- 2.46/1.31 2.46/1.31 f(x, y) -> f(x, x) with rule f(x', y') -> f(x', x') at position [] and matcher [x' / x, y' / y] 2.46/1.31 2.46/1.31 Now an instance of the first term with Matcher [y / x] occurs in the last term at position []. 2.46/1.31 2.46/1.31 Context: [] 2.46/1.31 2.46/1.31 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.46/1.31 ---------------------------------------- 2.46/1.31 2.46/1.31 (2) 2.46/1.31 NO 2.46/1.34 EOF