5.70/2.28 YES 5.97/2.34 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.97/2.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.97/2.34 5.97/2.34 5.97/2.34 Termination of the given RelTRS could be proven: 5.97/2.34 5.97/2.34 (0) RelTRS 5.97/2.34 (1) RelTRS S Cleaner [EQUIVALENT, 0 ms] 5.97/2.34 (2) RelTRS 5.97/2.34 (3) RelTRSRRRProof [EQUIVALENT, 40 ms] 5.97/2.34 (4) RelTRS 5.97/2.34 (5) RIsEmptyProof [EQUIVALENT, 1 ms] 5.97/2.34 (6) YES 5.97/2.34 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (0) 5.97/2.34 Obligation: 5.97/2.34 Relative term rewrite system: 5.97/2.34 The relative TRS consists of the following R rules: 5.97/2.34 5.97/2.34 a(b(c(x1))) -> b(a(a(x1))) 5.97/2.34 a(b(b(x1))) -> b(c(a(x1))) 5.97/2.34 5.97/2.34 The relative TRS consists of the following S rules: 5.97/2.34 5.97/2.34 a(b(a(x1))) -> a(b(a(x1))) 5.97/2.34 c(b(a(x1))) -> a(a(b(x1))) 5.97/2.34 c(a(a(x1))) -> c(a(b(x1))) 5.97/2.34 c(b(c(x1))) -> a(c(c(x1))) 5.97/2.34 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (1) RelTRS S Cleaner (EQUIVALENT) 5.97/2.34 We have deleted all rules from S that have the shape t -> t: 5.97/2.34 5.97/2.34 a(b(a(x1))) -> a(b(a(x1))) 5.97/2.34 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (2) 5.97/2.34 Obligation: 5.97/2.34 Relative term rewrite system: 5.97/2.34 The relative TRS consists of the following R rules: 5.97/2.34 5.97/2.34 a(b(c(x1))) -> b(a(a(x1))) 5.97/2.34 a(b(b(x1))) -> b(c(a(x1))) 5.97/2.34 5.97/2.34 The relative TRS consists of the following S rules: 5.97/2.34 5.97/2.34 c(b(a(x1))) -> a(a(b(x1))) 5.97/2.34 c(a(a(x1))) -> c(a(b(x1))) 5.97/2.34 c(b(c(x1))) -> a(c(c(x1))) 5.97/2.34 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (3) RelTRSRRRProof (EQUIVALENT) 5.97/2.34 We used the following monotonic ordering for rule removal: 5.97/2.34 Knuth-Bendix order [KBO] with precedence:c_1 > a_1 > b_1 5.97/2.34 5.97/2.34 and weight map: 5.97/2.34 5.97/2.34 a_1=1 5.97/2.34 b_1=1 5.97/2.34 c_1=1 5.97/2.34 5.97/2.34 The variable weight is 1With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 5.97/2.34 Rules from R: 5.97/2.34 5.97/2.34 a(b(c(x1))) -> b(a(a(x1))) 5.97/2.34 a(b(b(x1))) -> b(c(a(x1))) 5.97/2.34 Rules from S: 5.97/2.34 5.97/2.34 c(b(a(x1))) -> a(a(b(x1))) 5.97/2.34 c(a(a(x1))) -> c(a(b(x1))) 5.97/2.34 c(b(c(x1))) -> a(c(c(x1))) 5.97/2.34 5.97/2.34 5.97/2.34 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (4) 5.97/2.34 Obligation: 5.97/2.34 Relative term rewrite system: 5.97/2.34 R is empty. 5.97/2.34 S is empty. 5.97/2.34 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (5) RIsEmptyProof (EQUIVALENT) 5.97/2.34 The TRS R is empty. Hence, termination is trivially proven. 5.97/2.34 ---------------------------------------- 5.97/2.34 5.97/2.34 (6) 5.97/2.34 YES 5.97/2.38 EOF