2.92/1.61 YES 2.92/1.62 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.92/1.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.92/1.62 2.92/1.62 2.92/1.62 Termination of the given ETRS could be proven: 2.92/1.62 2.92/1.62 (0) ETRS 2.92/1.62 (1) EDirectTerminationProof [EQUIVALENT, 0 ms] 2.92/1.62 (2) YES 2.92/1.62 2.92/1.62 2.92/1.62 ---------------------------------------- 2.92/1.62 2.92/1.62 (0) 2.92/1.62 Obligation: 2.92/1.62 Equational rewrite system: 2.92/1.62 The TRS R consists of the following rules: 2.92/1.62 2.92/1.62 plus(x, 0) -> x 2.92/1.62 plus(x, x) -> x 2.92/1.62 plus(T(x), x) -> T(x) 2.92/1.62 plus(T(plus(x, y)), x) -> T(plus(x, y)) 2.92/1.62 L(T(x)) -> L(x) 2.92/1.62 L(plus(T(y), x)) -> plus(L(plus(x, y)), L(y)) 2.92/1.62 T(T(x)) -> T(x) 2.92/1.62 T(plus(T(y), x)) -> plus(T(plus(x, y)), T(y)) 2.92/1.62 2.92/1.62 The set E consists of the following equations: 2.92/1.62 2.92/1.62 plus(x, y) == plus(y, x) 2.92/1.62 plus(plus(x, y), z) == plus(x, plus(y, z)) 2.92/1.62 2.92/1.62 2.92/1.62 ---------------------------------------- 2.92/1.62 2.92/1.62 (1) EDirectTerminationProof (EQUIVALENT) 2.92/1.62 We use [DA_FALKE] with the following order to prove termination. 2.92/1.62 2.92/1.62 Precedence: 2.92/1.62 T_1 > plus_2 2.92/1.62 L_1 > plus_2 2.92/1.62 2.92/1.62 2.92/1.62 Status: 2.92/1.62 plus_2: flat status 2.92/1.62 2.92/1.62 2.92/1.62 2.92/1.62 ---------------------------------------- 2.92/1.62 2.92/1.62 (2) 2.92/1.62 YES 2.92/1.65 EOF