/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 64 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d g(cons(x, k), d) -> g(k, cons(x, d)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(empty) = 2 POL(f(x_1, x_2)) = 1 + x_1 + 2*x_2 POL(g(x_1, x_2)) = x_1 + x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(cons(x, k), d) -> g(k, cons(x, d)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:cons_2 > g_2 and weight map: cons_2=0 g_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(cons(x, k), d) -> g(k, cons(x, d)) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES