3.27/1.63 YES 3.27/1.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.27/1.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.27/1.63 3.27/1.63 3.27/1.63 Termination of the given ETRS could be proven: 3.27/1.63 3.27/1.63 (0) ETRS 3.27/1.63 (1) EDirectTerminationProof [EQUIVALENT, 0 ms] 3.27/1.63 (2) YES 3.27/1.63 3.27/1.63 3.27/1.63 ---------------------------------------- 3.27/1.63 3.27/1.63 (0) 3.27/1.63 Obligation: 3.27/1.63 Equational rewrite system: 3.27/1.63 The TRS R consists of the following rules: 3.27/1.63 3.27/1.63 f(g(f(h(a), a)), a) -> f(h(a), f(a, a)) 3.27/1.63 f(h(a), g(a)) -> f(g(h(a)), a) 3.27/1.63 f(g(h(a)), f(f(a, a), a)) -> f(g(f(h(a), a)), a) 3.27/1.63 f(h(a), a) -> f(h(a), b) 3.27/1.63 f(i(x, y), f(a, y)) -> f(g(i(x, y)), y) 3.27/1.63 3.27/1.63 The set E consists of the following equations: 3.27/1.63 3.27/1.63 f(x, y) == f(y, x) 3.27/1.63 f(f(x, y), z) == f(x, f(y, z)) 3.27/1.63 3.27/1.63 3.27/1.63 ---------------------------------------- 3.27/1.63 3.27/1.63 (1) EDirectTerminationProof (EQUIVALENT) 3.27/1.63 We use [DA_FALKE] with the following order to prove termination. 3.27/1.63 3.27/1.63 Precedence: 3.27/1.63 h_1 > f_2 > g_1 3.27/1.63 a > b 3.27/1.63 3.27/1.63 3.27/1.63 Status: 3.27/1.63 f_2: flat status 3.27/1.63 3.27/1.63 3.27/1.63 3.27/1.63 ---------------------------------------- 3.27/1.63 3.27/1.63 (2) 3.27/1.63 YES 3.27/1.66 EOF