3.29/1.60 NO 3.29/1.61 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.29/1.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.29/1.61 3.29/1.61 3.29/1.61 Termination of the given RelTRS could be disproven: 3.29/1.61 3.29/1.61 (0) RelTRS 3.29/1.61 (1) RelTRS Reverse [EQUIVALENT, 0 ms] 3.29/1.61 (2) RelTRS 3.29/1.61 (3) RelTRSLoopFinderProof [COMPLETE, 0 ms] 3.29/1.61 (4) NO 3.29/1.61 3.29/1.61 3.29/1.61 ---------------------------------------- 3.29/1.61 3.29/1.61 (0) 3.29/1.61 Obligation: 3.29/1.61 Relative term rewrite system: 3.29/1.61 The relative TRS consists of the following R rules: 3.29/1.61 3.29/1.61 a(b(c(x1))) -> c(x1) 3.29/1.61 3.29/1.61 The relative TRS consists of the following S rules: 3.29/1.61 3.29/1.61 c(x1) -> c(b(a(x1))) 3.29/1.61 3.29/1.61 3.29/1.61 ---------------------------------------- 3.29/1.61 3.29/1.61 (1) RelTRS Reverse (EQUIVALENT) 3.29/1.61 We have reversed the following relative TRS [REVERSE]: 3.29/1.61 The set of rules R is 3.29/1.61 a(b(c(x1))) -> c(x1) 3.29/1.61 3.29/1.61 The set of rules S is 3.29/1.61 c(x1) -> c(b(a(x1))) 3.29/1.61 3.29/1.61 We have obtained the following relative TRS: 3.29/1.61 The set of rules R is 3.29/1.61 c(b(a(x1))) -> c(x1) 3.29/1.61 3.29/1.61 The set of rules S is 3.29/1.61 c(x1) -> a(b(c(x1))) 3.29/1.61 3.29/1.61 3.29/1.61 ---------------------------------------- 3.29/1.61 3.29/1.61 (2) 3.29/1.61 Obligation: 3.29/1.61 Relative term rewrite system: 3.29/1.61 The relative TRS consists of the following R rules: 3.29/1.61 3.29/1.61 c(b(a(x1))) -> c(x1) 3.29/1.61 3.29/1.61 The relative TRS consists of the following S rules: 3.29/1.61 3.29/1.61 c(x1) -> a(b(c(x1))) 3.29/1.61 3.29/1.61 3.29/1.61 ---------------------------------------- 3.29/1.61 3.29/1.61 (3) RelTRSLoopFinderProof (COMPLETE) 3.29/1.61 The following loop was found: 3.29/1.61 3.29/1.61 ---------- Loop: ---------- 3.29/1.61 3.29/1.61 c(b(c(x1'))) -> c(b(a(b(c(x1'))))) with rule c(x1'') -> a(b(c(x1''))) at position [0,0] and matcher [x1'' / x1'] 3.29/1.61 3.29/1.61 c(b(a(b(c(x1'))))) -> c(b(c(x1'))) with rule c(b(a(x1))) -> c(x1) at position [] and matcher [x1 / b(c(x1'))] 3.29/1.61 3.29/1.61 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 3.29/1.61 3.29/1.61 Context: [] 3.29/1.61 3.29/1.61 Therefore, the relative TRS problem does not terminate. 3.29/1.61 ---------------------------------------- 3.29/1.61 3.29/1.61 (4) 3.29/1.61 NO 3.29/1.63 EOF