2.89/1.37 YES 2.89/1.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.89/1.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.89/1.37 2.89/1.37 2.89/1.37 Termination of the given CSR could be proven: 2.89/1.37 2.89/1.37 (0) CSR 2.89/1.37 (1) CSRRRRProof [EQUIVALENT, 27 ms] 2.89/1.37 (2) CSR 2.89/1.37 (3) CSRRRRProof [EQUIVALENT, 0 ms] 2.89/1.37 (4) CSR 2.89/1.37 (5) RisEmptyProof [EQUIVALENT, 0 ms] 2.89/1.37 (6) YES 2.89/1.37 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (0) 2.89/1.37 Obligation: 2.89/1.37 Context-sensitive rewrite system: 2.89/1.37 The TRS R consists of the following rules: 2.89/1.37 2.89/1.37 f(b, X, c) -> f(X, c, X) 2.89/1.37 c -> b 2.89/1.37 2.89/1.37 The replacement map contains the following entries: 2.89/1.37 2.89/1.37 f: {2} 2.89/1.37 b: empty set 2.89/1.37 c: empty set 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (1) CSRRRRProof (EQUIVALENT) 2.89/1.37 The following CSR is given: Context-sensitive rewrite system: 2.89/1.37 The TRS R consists of the following rules: 2.89/1.37 2.89/1.37 f(b, X, c) -> f(X, c, X) 2.89/1.37 c -> b 2.89/1.37 2.89/1.37 The replacement map contains the following entries: 2.89/1.37 2.89/1.37 f: {2} 2.89/1.37 b: empty set 2.89/1.37 c: empty set 2.89/1.37 Used ordering: 2.89/1.37 Polynomial interpretation [POLO]: 2.89/1.37 2.89/1.37 POL(b) = 0 2.89/1.37 POL(c) = 1 2.89/1.37 POL(f(x_1, x_2, x_3)) = x_2 + x_3 2.89/1.37 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.89/1.37 2.89/1.37 c -> b 2.89/1.37 2.89/1.37 2.89/1.37 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (2) 2.89/1.37 Obligation: 2.89/1.37 Context-sensitive rewrite system: 2.89/1.37 The TRS R consists of the following rules: 2.89/1.37 2.89/1.37 f(b, X, c) -> f(X, c, X) 2.89/1.37 2.89/1.37 The replacement map contains the following entries: 2.89/1.37 2.89/1.37 f: {2} 2.89/1.37 b: empty set 2.89/1.37 c: empty set 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (3) CSRRRRProof (EQUIVALENT) 2.89/1.37 The following CSR is given: Context-sensitive rewrite system: 2.89/1.37 The TRS R consists of the following rules: 2.89/1.37 2.89/1.37 f(b, X, c) -> f(X, c, X) 2.89/1.37 2.89/1.37 The replacement map contains the following entries: 2.89/1.37 2.89/1.37 f: {2} 2.89/1.37 b: empty set 2.89/1.37 c: empty set 2.89/1.37 Used ordering: 2.89/1.37 Polynomial interpretation [POLO]: 2.89/1.37 2.89/1.37 POL(b) = 1 2.89/1.37 POL(c) = 0 2.89/1.37 POL(f(x_1, x_2, x_3)) = x_1 + x_2 2.89/1.37 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.89/1.37 2.89/1.37 f(b, X, c) -> f(X, c, X) 2.89/1.37 2.89/1.37 2.89/1.37 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (4) 2.89/1.37 Obligation: 2.89/1.37 Context-sensitive rewrite system: 2.89/1.37 R is empty. 2.89/1.37 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (5) RisEmptyProof (EQUIVALENT) 2.89/1.37 The CSR R is empty. Hence, termination is trivially proven. 2.89/1.37 ---------------------------------------- 2.89/1.37 2.89/1.37 (6) 2.89/1.37 YES 3.07/1.41 EOF