2.40/1.20 NO 2.40/1.21 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.40/1.21 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.40/1.21 2.40/1.21 2.40/1.21 Outermost Termination of the given OTRS could be disproven: 2.40/1.21 2.40/1.21 (0) OTRS 2.40/1.21 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.40/1.21 (2) NO 2.40/1.21 2.40/1.21 2.40/1.21 ---------------------------------------- 2.40/1.21 2.40/1.21 (0) 2.40/1.21 Obligation: 2.40/1.21 Term rewrite system R: 2.40/1.21 The TRS R consists of the following rules: 2.40/1.21 2.40/1.21 tail(cons(X)) -> XS 2.40/1.21 pairNs -> cons(0) 2.40/1.21 oddNs -> incr(pairNs) 2.40/1.21 incr(cons(X)) -> cons(s(X)) 2.40/1.21 take(0, XS) -> nil 2.40/1.21 take(s(N), cons(X)) -> cons(X) 2.40/1.21 zip(nil, XS) -> nil 2.40/1.21 zip(X, nil) -> nil 2.40/1.21 zip(cons(X), cons(Y)) -> cons(pair(X, Y)) 2.40/1.21 repItems(nil) -> nil 2.40/1.21 repItems(cons(X)) -> cons(X) 2.40/1.21 2.40/1.21 2.40/1.21 2.40/1.21 Outermost Strategy. 2.40/1.21 2.40/1.21 ---------------------------------------- 2.40/1.21 2.40/1.21 (1) OutermostNonTerminationProof (COMPLETE) 2.40/1.21 Term rewrite system R: 2.40/1.21 The TRS R consists of the following rules: 2.40/1.21 2.40/1.21 tail(cons(X)) -> XS 2.40/1.21 pairNs -> cons(0) 2.40/1.21 oddNs -> incr(pairNs) 2.40/1.21 incr(cons(X)) -> cons(s(X)) 2.40/1.21 take(0, XS) -> nil 2.40/1.21 take(s(N), cons(X)) -> cons(X) 2.40/1.21 zip(nil, XS) -> nil 2.40/1.21 zip(X, nil) -> nil 2.40/1.21 zip(cons(X), cons(Y)) -> cons(pair(X, Y)) 2.40/1.21 repItems(nil) -> nil 2.40/1.21 repItems(cons(X)) -> cons(X) 2.40/1.21 2.40/1.21 2.40/1.21 2.40/1.21 Outermost Strategy. 2.40/1.21 2.40/1.21 ---------- Loop: ---------- 2.40/1.21 2.40/1.21 tail(cons(X)) -> tail(cons(X)) with rule tail(cons(X'')) -> XS at position [] and matcher [X'' / X, XS / tail(cons(X))] 2.40/1.21 2.40/1.21 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.40/1.21 2.40/1.21 Context: [] 2.40/1.21 2.40/1.21 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.40/1.21 ---------------------------------------- 2.40/1.21 2.40/1.21 (2) 2.40/1.21 NO 2.49/1.25 EOF