2.72/1.29 YES 2.72/1.30 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.72/1.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.72/1.30 2.72/1.30 2.72/1.30 Termination of the given CSR could be proven: 2.72/1.30 2.72/1.30 (0) CSR 2.72/1.30 (1) CSRRRRProof [EQUIVALENT, 0 ms] 2.72/1.30 (2) CSR 2.72/1.30 (3) RisEmptyProof [EQUIVALENT, 0 ms] 2.72/1.30 (4) YES 2.72/1.30 2.72/1.30 2.72/1.30 ---------------------------------------- 2.72/1.30 2.72/1.30 (0) 2.72/1.30 Obligation: 2.72/1.30 Context-sensitive rewrite system: 2.72/1.30 The TRS R consists of the following rules: 2.72/1.30 2.72/1.30 f(g(X), Y) -> f(X, f(g(X), Y)) 2.72/1.30 2.72/1.30 The replacement map contains the following entries: 2.72/1.30 2.72/1.30 f: {1} 2.72/1.30 g: {1} 2.72/1.30 2.72/1.30 ---------------------------------------- 2.72/1.30 2.72/1.30 (1) CSRRRRProof (EQUIVALENT) 2.72/1.30 The following CSR is given: Context-sensitive rewrite system: 2.72/1.30 The TRS R consists of the following rules: 2.72/1.30 2.72/1.30 f(g(X), Y) -> f(X, f(g(X), Y)) 2.72/1.30 2.72/1.30 The replacement map contains the following entries: 2.72/1.30 2.72/1.30 f: {1} 2.72/1.30 g: {1} 2.72/1.30 Used ordering: 2.72/1.30 Polynomial interpretation [POLO]: 2.72/1.30 2.72/1.30 POL(f(x_1, x_2)) = x_1 2.72/1.30 POL(g(x_1)) = 1 + x_1 2.72/1.30 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.72/1.30 2.72/1.30 f(g(X), Y) -> f(X, f(g(X), Y)) 2.72/1.30 2.72/1.30 2.72/1.30 2.72/1.30 2.72/1.30 ---------------------------------------- 2.72/1.30 2.72/1.30 (2) 2.72/1.30 Obligation: 2.72/1.30 Context-sensitive rewrite system: 2.72/1.30 R is empty. 2.72/1.30 2.72/1.30 ---------------------------------------- 2.72/1.30 2.72/1.30 (3) RisEmptyProof (EQUIVALENT) 2.72/1.30 The CSR R is empty. Hence, termination is trivially proven. 2.72/1.30 ---------------------------------------- 2.72/1.30 2.72/1.30 (4) 2.72/1.30 YES 2.92/1.38 EOF