2.36/1.20 NO 2.36/1.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.36/1.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.36/1.21 2.36/1.21 2.36/1.21 Outermost Termination of the given OTRS could be disproven: 2.36/1.21 2.36/1.21 (0) OTRS 2.36/1.21 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.36/1.21 (2) NO 2.36/1.21 2.36/1.21 2.36/1.21 ---------------------------------------- 2.36/1.21 2.36/1.21 (0) 2.36/1.21 Obligation: 2.36/1.21 Term rewrite system R: 2.36/1.21 The TRS R consists of the following rules: 2.36/1.21 2.36/1.21 tail(cons(X)) -> XS 2.36/1.21 nats -> cons(0) 2.36/1.21 pairs -> cons(0) 2.36/1.21 odds -> incr(pairs) 2.36/1.21 incr(cons(X)) -> cons(s(X)) 2.36/1.21 head(cons(X)) -> X 2.36/1.21 2.36/1.21 2.36/1.21 2.36/1.21 Outermost Strategy. 2.36/1.21 2.36/1.21 ---------------------------------------- 2.36/1.21 2.36/1.21 (1) OutermostNonTerminationProof (COMPLETE) 2.36/1.21 Term rewrite system R: 2.36/1.21 The TRS R consists of the following rules: 2.36/1.21 2.36/1.21 tail(cons(X)) -> XS 2.36/1.21 nats -> cons(0) 2.36/1.21 pairs -> cons(0) 2.36/1.21 odds -> incr(pairs) 2.36/1.21 incr(cons(X)) -> cons(s(X)) 2.36/1.21 head(cons(X)) -> X 2.36/1.21 2.36/1.21 2.36/1.21 2.36/1.21 Outermost Strategy. 2.36/1.21 2.36/1.21 ---------- Loop: ---------- 2.36/1.21 2.36/1.21 tail(cons(X)) -> tail(cons(X)) with rule tail(cons(X'')) -> XS at position [] and matcher [X'' / X, XS / tail(cons(X))] 2.36/1.21 2.36/1.21 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.36/1.21 2.36/1.21 Context: [] 2.36/1.21 2.36/1.21 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.36/1.21 ---------------------------------------- 2.36/1.21 2.36/1.21 (2) 2.36/1.21 NO 2.36/1.23 EOF