2.62/1.27 NO 2.62/1.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.62/1.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.62/1.28 2.62/1.28 2.62/1.28 Outermost Termination of the given OTRS could be disproven: 2.62/1.28 2.62/1.28 (0) OTRS 2.62/1.28 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.62/1.28 (2) NO 2.62/1.28 2.62/1.28 2.62/1.28 ---------------------------------------- 2.62/1.28 2.62/1.28 (0) 2.62/1.28 Obligation: 2.62/1.28 Term rewrite system R: 2.62/1.28 The TRS R consists of the following rules: 2.62/1.28 2.62/1.28 *(*(x, y), z) -> *(x, *(y, z)) 2.62/1.28 *(+(x, y), z) -> +(*(x, z), *(y, z)) 2.62/1.28 *(x, +(y, f(z))) -> *(g(x, z), +(y, y)) 2.62/1.28 2.62/1.28 2.62/1.28 2.62/1.28 Outermost Strategy. 2.62/1.28 2.62/1.28 ---------------------------------------- 2.62/1.28 2.62/1.28 (1) OutermostNonTerminationProof (COMPLETE) 2.62/1.28 Term rewrite system R: 2.62/1.28 The TRS R consists of the following rules: 2.62/1.28 2.62/1.28 *(*(x, y), z) -> *(x, *(y, z)) 2.62/1.28 *(+(x, y), z) -> +(*(x, z), *(y, z)) 2.62/1.28 *(x, +(y, f(z))) -> *(g(x, z), +(y, y)) 2.62/1.28 2.62/1.28 2.62/1.28 2.62/1.28 Outermost Strategy. 2.62/1.28 2.62/1.28 ---------- Loop: ---------- 2.62/1.28 2.62/1.28 *(x, +(f(z'), f(z))) -> *(g(x, z), +(f(z'), f(z'))) with rule *(x', +(y, f(z''))) -> *(g(x', z''), +(y, y)) at position [] and matcher [x' / x, y / f(z'), z'' / z] 2.62/1.28 2.62/1.28 Now an instance of the first term with Matcher [z / z', x / g(x, z)] occurs in the last term at position []. 2.62/1.28 2.62/1.28 Context: [] 2.62/1.28 2.62/1.28 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.62/1.28 ---------------------------------------- 2.62/1.28 2.62/1.28 (2) 2.62/1.28 NO 2.62/1.32 EOF