2.52/1.22 NO 2.52/1.23 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.52/1.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.52/1.23 2.52/1.23 2.52/1.23 Outermost Termination of the given OTRS could be disproven: 2.52/1.23 2.52/1.23 (0) OTRS 2.52/1.23 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.52/1.23 (2) NO 2.52/1.23 2.52/1.23 2.52/1.23 ---------------------------------------- 2.52/1.23 2.52/1.23 (0) 2.52/1.23 Obligation: 2.52/1.23 Term rewrite system R: 2.52/1.23 The TRS R consists of the following rules: 2.52/1.23 2.52/1.23 2ndspos(s(N), cons(X)) -> 2ndspos(s(N), cons2(Z)) 2.52/1.23 2ndspos(s(N), cons2(cons(Y))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2.52/1.23 2ndsneg(s(N), cons(X)) -> 2ndsneg(s(N), cons2(Z)) 2.52/1.23 2ndsneg(s(N), cons2(cons(Y))) -> rcons(negrecip(Y), 2ndspos(N, Z)) 2.52/1.23 from(X) -> cons(X) 2.52/1.23 2ndspos(0, Z) -> rnil 2.52/1.23 2ndsneg(0, Z) -> rnil 2.52/1.23 pi(X) -> 2ndspos(X, from(0)) 2.52/1.23 plus(0, Y) -> Y 2.52/1.23 plus(s(X), Y) -> s(plus(X, Y)) 2.52/1.23 times(0, Y) -> 0 2.52/1.23 times(s(X), Y) -> plus(Y, times(X, Y)) 2.52/1.23 square(X) -> times(X, X) 2.52/1.23 2.52/1.23 2.52/1.23 2.52/1.23 Outermost Strategy. 2.52/1.23 2.52/1.23 ---------------------------------------- 2.52/1.23 2.52/1.23 (1) OutermostNonTerminationProof (COMPLETE) 2.52/1.23 Term rewrite system R: 2.52/1.23 The TRS R consists of the following rules: 2.52/1.23 2.52/1.23 2ndspos(s(N), cons(X)) -> 2ndspos(s(N), cons2(Z)) 2.52/1.23 2ndspos(s(N), cons2(cons(Y))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2.52/1.23 2ndsneg(s(N), cons(X)) -> 2ndsneg(s(N), cons2(Z)) 2.52/1.23 2ndsneg(s(N), cons2(cons(Y))) -> rcons(negrecip(Y), 2ndspos(N, Z)) 2.52/1.23 from(X) -> cons(X) 2.52/1.23 2ndspos(0, Z) -> rnil 2.52/1.23 2ndsneg(0, Z) -> rnil 2.52/1.23 pi(X) -> 2ndspos(X, from(0)) 2.52/1.23 plus(0, Y) -> Y 2.52/1.23 plus(s(X), Y) -> s(plus(X, Y)) 2.52/1.23 times(0, Y) -> 0 2.52/1.23 times(s(X), Y) -> plus(Y, times(X, Y)) 2.52/1.23 square(X) -> times(X, X) 2.52/1.23 2.52/1.23 2.52/1.23 2.52/1.23 Outermost Strategy. 2.52/1.23 2.52/1.23 ---------- Loop: ---------- 2.52/1.23 2.52/1.23 2ndspos(s(N), cons(X)) -> 2ndspos(s(N), cons2(2ndspos(s(N), cons(X)))) with rule 2ndspos(s(N''), cons(X'')) -> 2ndspos(s(N''), cons2(Z)) at position [] and matcher [N'' / N, X'' / X, Z / 2ndspos(s(N), cons(X))] 2.52/1.23 2.52/1.23 Now an instance of the first term with Matcher [ ] occurs in the last term at position [1,0]. 2.52/1.23 2.52/1.23 Context: 2ndspos(s(N), cons2([])) 2.52/1.23 2.52/1.23 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.52/1.23 ---------------------------------------- 2.52/1.23 2.52/1.23 (2) 2.52/1.23 NO 2.52/1.25 EOF