2.90/1.32 YES 2.90/1.33 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.90/1.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.90/1.33 2.90/1.33 2.90/1.33 Termination of the given CSR could be proven: 2.90/1.33 2.90/1.33 (0) CSR 2.90/1.33 (1) CSRRRRProof [EQUIVALENT, 53 ms] 2.90/1.33 (2) CSR 2.90/1.33 (3) CSRRRRProof [EQUIVALENT, 0 ms] 2.90/1.33 (4) CSR 2.90/1.33 (5) RisEmptyProof [EQUIVALENT, 0 ms] 2.90/1.33 (6) YES 2.90/1.33 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (0) 2.90/1.33 Obligation: 2.90/1.33 Context-sensitive rewrite system: 2.90/1.33 The TRS R consists of the following rules: 2.90/1.33 2.90/1.33 and(tt, X) -> X 2.90/1.33 plus(N, 0) -> N 2.90/1.33 plus(N, s(M)) -> s(plus(N, M)) 2.90/1.33 2.90/1.33 The replacement map contains the following entries: 2.90/1.33 2.90/1.33 and: {1} 2.90/1.33 tt: empty set 2.90/1.33 plus: {1, 2} 2.90/1.33 0: empty set 2.90/1.33 s: {1} 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (1) CSRRRRProof (EQUIVALENT) 2.90/1.33 The following CSR is given: Context-sensitive rewrite system: 2.90/1.33 The TRS R consists of the following rules: 2.90/1.33 2.90/1.33 and(tt, X) -> X 2.90/1.33 plus(N, 0) -> N 2.90/1.33 plus(N, s(M)) -> s(plus(N, M)) 2.90/1.33 2.90/1.33 The replacement map contains the following entries: 2.90/1.33 2.90/1.33 and: {1} 2.90/1.33 tt: empty set 2.90/1.33 plus: {1, 2} 2.90/1.33 0: empty set 2.90/1.33 s: {1} 2.90/1.33 Used ordering: 2.90/1.33 Polynomial interpretation [POLO]: 2.90/1.33 2.90/1.33 POL(0) = 1 2.90/1.33 POL(and(x_1, x_2)) = 2*x_1 + x_2 2.90/1.33 POL(plus(x_1, x_2)) = 2*x_1 + 2*x_2 2.90/1.33 POL(s(x_1)) = x_1 2.90/1.33 POL(tt) = 1 2.90/1.33 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.90/1.33 2.90/1.33 and(tt, X) -> X 2.90/1.33 plus(N, 0) -> N 2.90/1.33 2.90/1.33 2.90/1.33 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (2) 2.90/1.33 Obligation: 2.90/1.33 Context-sensitive rewrite system: 2.90/1.33 The TRS R consists of the following rules: 2.90/1.33 2.90/1.33 plus(N, s(M)) -> s(plus(N, M)) 2.90/1.33 2.90/1.33 The replacement map contains the following entries: 2.90/1.33 2.90/1.33 plus: {1, 2} 2.90/1.33 s: {1} 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (3) CSRRRRProof (EQUIVALENT) 2.90/1.33 The following CSR is given: Context-sensitive rewrite system: 2.90/1.33 The TRS R consists of the following rules: 2.90/1.33 2.90/1.33 plus(N, s(M)) -> s(plus(N, M)) 2.90/1.33 2.90/1.33 The replacement map contains the following entries: 2.90/1.33 2.90/1.33 plus: {1, 2} 2.90/1.33 s: {1} 2.90/1.33 Used ordering: 2.90/1.33 Polynomial interpretation [POLO]: 2.90/1.33 2.90/1.33 POL(plus(x_1, x_2)) = 2*x_1 + 2*x_2 2.90/1.33 POL(s(x_1)) = 1 + x_1 2.90/1.33 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 2.90/1.33 2.90/1.33 plus(N, s(M)) -> s(plus(N, M)) 2.90/1.33 2.90/1.33 2.90/1.33 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (4) 2.90/1.33 Obligation: 2.90/1.33 Context-sensitive rewrite system: 2.90/1.33 R is empty. 2.90/1.33 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (5) RisEmptyProof (EQUIVALENT) 2.90/1.33 The CSR R is empty. Hence, termination is trivially proven. 2.90/1.33 ---------------------------------------- 2.90/1.33 2.90/1.33 (6) 2.90/1.33 YES 2.90/1.35 EOF