5.69/2.26 YES 5.97/2.30 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.97/2.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.97/2.30 5.97/2.30 5.97/2.30 Termination of the given RelTRS could be proven: 5.97/2.30 5.97/2.30 (0) RelTRS 5.97/2.30 (1) RelTRS Reverse [EQUIVALENT, 0 ms] 5.97/2.30 (2) RelTRS 5.97/2.30 (3) RelTRSRRRProof [EQUIVALENT, 6 ms] 5.97/2.30 (4) RelTRS 5.97/2.30 (5) RIsEmptyProof [EQUIVALENT, 0 ms] 5.97/2.30 (6) YES 5.97/2.30 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (0) 5.97/2.30 Obligation: 5.97/2.30 Relative term rewrite system: 5.97/2.30 The relative TRS consists of the following R rules: 5.97/2.30 5.97/2.30 c(a(a(x1))) -> c(b(a(x1))) 5.97/2.30 c(b(c(x1))) -> a(c(b(x1))) 5.97/2.30 5.97/2.30 The relative TRS consists of the following S rules: 5.97/2.30 5.97/2.30 b(b(c(x1))) -> b(b(b(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(b(x1))) 5.97/2.30 b(b(a(x1))) -> c(a(c(x1))) 5.97/2.30 a(c(a(x1))) -> c(b(b(x1))) 5.97/2.30 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (1) RelTRS Reverse (EQUIVALENT) 5.97/2.30 We have reversed the following relative TRS [REVERSE]: 5.97/2.30 The set of rules R is 5.97/2.30 c(a(a(x1))) -> c(b(a(x1))) 5.97/2.30 c(b(c(x1))) -> a(c(b(x1))) 5.97/2.30 5.97/2.30 The set of rules S is 5.97/2.30 b(b(c(x1))) -> b(b(b(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(b(x1))) 5.97/2.30 b(b(a(x1))) -> c(a(c(x1))) 5.97/2.30 a(c(a(x1))) -> c(b(b(x1))) 5.97/2.30 5.97/2.30 We have obtained the following relative TRS: 5.97/2.30 The set of rules R is 5.97/2.30 a(a(c(x1))) -> a(b(c(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(a(x1))) 5.97/2.30 5.97/2.30 The set of rules S is 5.97/2.30 c(b(b(x1))) -> b(b(b(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(b(x1))) 5.97/2.30 a(b(b(x1))) -> c(a(c(x1))) 5.97/2.30 a(c(a(x1))) -> b(b(c(x1))) 5.97/2.30 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (2) 5.97/2.30 Obligation: 5.97/2.30 Relative term rewrite system: 5.97/2.30 The relative TRS consists of the following R rules: 5.97/2.30 5.97/2.30 a(a(c(x1))) -> a(b(c(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(a(x1))) 5.97/2.30 5.97/2.30 The relative TRS consists of the following S rules: 5.97/2.30 5.97/2.30 c(b(b(x1))) -> b(b(b(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(b(x1))) 5.97/2.30 a(b(b(x1))) -> c(a(c(x1))) 5.97/2.30 a(c(a(x1))) -> b(b(c(x1))) 5.97/2.30 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (3) RelTRSRRRProof (EQUIVALENT) 5.97/2.30 We used the following monotonic ordering for rule removal: 5.97/2.30 Knuth-Bendix order [KBO] with precedence:a_1 > c_1 > b_1 5.97/2.30 5.97/2.30 and weight map: 5.97/2.30 5.97/2.30 a_1=1 5.97/2.30 c_1=1 5.97/2.30 b_1=1 5.97/2.30 5.97/2.30 The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 5.97/2.30 Rules from R: 5.97/2.30 5.97/2.30 a(a(c(x1))) -> a(b(c(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(a(x1))) 5.97/2.30 Rules from S: 5.97/2.30 5.97/2.30 c(b(b(x1))) -> b(b(b(x1))) 5.97/2.30 c(b(c(x1))) -> b(c(b(x1))) 5.97/2.30 a(b(b(x1))) -> c(a(c(x1))) 5.97/2.30 a(c(a(x1))) -> b(b(c(x1))) 5.97/2.30 5.97/2.30 5.97/2.30 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (4) 5.97/2.30 Obligation: 5.97/2.30 Relative term rewrite system: 5.97/2.30 R is empty. 5.97/2.30 S is empty. 5.97/2.30 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (5) RIsEmptyProof (EQUIVALENT) 5.97/2.30 The TRS R is empty. Hence, termination is trivially proven. 5.97/2.30 ---------------------------------------- 5.97/2.30 5.97/2.30 (6) 5.97/2.30 YES 6.17/2.35 EOF