2.95/1.52 YES 2.95/1.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.95/1.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.95/1.53 2.95/1.53 2.95/1.53 Termination of the given ETRS could be proven: 2.95/1.53 2.95/1.53 (0) ETRS 2.95/1.53 (1) EDirectTerminationProof [EQUIVALENT, 0 ms] 2.95/1.53 (2) YES 2.95/1.53 2.95/1.53 2.95/1.53 ---------------------------------------- 2.95/1.53 2.95/1.53 (0) 2.95/1.53 Obligation: 2.95/1.53 Equational rewrite system: 2.95/1.53 The TRS R consists of the following rules: 2.95/1.53 2.95/1.53 plus(x, 0) -> x 2.95/1.53 plus(x, i(x)) -> 0 2.95/1.53 i(0) -> 0 2.95/1.53 i(i(x)) -> x 2.95/1.53 i(plus(x, y)) -> plus(i(x), i(y)) 2.95/1.53 times(x, plus(y, z)) -> plus(times(x, y), times(x, z)) 2.95/1.53 times(x, 0) -> 0 2.95/1.53 times(x, i(y)) -> i(times(x, y)) 2.95/1.53 2.95/1.53 The set E consists of the following equations: 2.95/1.53 2.95/1.53 plus(x, y) == plus(y, x) 2.95/1.53 times(x, y) == times(y, x) 2.95/1.53 plus(plus(x, y), z) == plus(x, plus(y, z)) 2.95/1.53 times(times(x, y), z) == times(x, times(y, z)) 2.95/1.53 2.95/1.53 2.95/1.53 ---------------------------------------- 2.95/1.53 2.95/1.53 (1) EDirectTerminationProof (EQUIVALENT) 2.95/1.53 We use [DA_FALKE] with the following order to prove termination. 2.95/1.53 2.95/1.53 Precedence: 2.95/1.53 times_2 > i_1 > plus_2 2.95/1.53 times_2 > i_1 > 0 2.95/1.53 2.95/1.53 2.95/1.53 Status: 2.95/1.53 plus_2: flat status 2.95/1.53 times_2: flat status 2.95/1.53 2.95/1.53 2.95/1.53 2.95/1.53 ---------------------------------------- 2.95/1.53 2.95/1.53 (2) 2.95/1.53 YES 3.10/1.56 EOF