2.90/1.55 YES 2.90/1.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.90/1.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.90/1.55 2.90/1.55 2.90/1.55 Termination of the given ETRS could be proven: 2.90/1.55 2.90/1.55 (0) ETRS 2.90/1.55 (1) EDirectTerminationProof [EQUIVALENT, 0 ms] 2.90/1.55 (2) YES 2.90/1.55 2.90/1.55 2.90/1.55 ---------------------------------------- 2.90/1.55 2.90/1.55 (0) 2.90/1.55 Obligation: 2.90/1.55 Equational rewrite system: 2.90/1.55 The TRS R consists of the following rules: 2.90/1.55 2.90/1.55 plus(x, 0) -> x 2.90/1.55 plus(x, s(y)) -> s(plus(x, y)) 2.90/1.55 double(x) -> plus(x, x) 2.90/1.55 2.90/1.55 The set E consists of the following equations: 2.90/1.55 2.90/1.55 plus(x, y) == plus(y, x) 2.90/1.55 plus(plus(x, y), z) == plus(x, plus(y, z)) 2.90/1.55 2.90/1.55 2.90/1.55 ---------------------------------------- 2.90/1.55 2.90/1.55 (1) EDirectTerminationProof (EQUIVALENT) 2.90/1.55 We use [DA_FALKE] with the following order to prove termination. 2.90/1.55 2.90/1.55 Precedence: 2.90/1.55 double_1 > plus_2 > s_1 2.90/1.55 2.90/1.55 2.90/1.55 Status: 2.90/1.55 plus_2: flat status 2.90/1.55 2.90/1.55 2.90/1.55 2.90/1.55 ---------------------------------------- 2.90/1.55 2.90/1.55 (2) 2.90/1.55 YES 2.90/1.59 EOF