3.26/1.34 NO 3.26/1.35 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.26/1.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.26/1.35 3.26/1.35 3.26/1.35 Outermost Termination of the given OTRS could be disproven: 3.26/1.35 3.26/1.35 (0) OTRS 3.26/1.35 (1) OutermostNonTerminationProof [COMPLETE, 43 ms] 3.26/1.35 (2) NO 3.26/1.35 3.26/1.35 3.26/1.35 ---------------------------------------- 3.26/1.35 3.26/1.35 (0) 3.26/1.35 Obligation: 3.26/1.35 Term rewrite system R: 3.26/1.35 The TRS R consists of the following rules: 3.26/1.35 3.26/1.35 from(X) -> cons(X, from(s(X))) 3.26/1.35 sel(0, cons(X, XS)) -> X 3.26/1.35 sel(s(N), cons(X, XS)) -> sel(N, XS) 3.26/1.35 minus(X, 0) -> 0 3.26/1.35 minus(s(X), s(Y)) -> minus(X, Y) 3.26/1.35 quot(0, s(Y)) -> 0 3.26/1.35 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 3.26/1.35 zWquot(XS, nil) -> nil 3.26/1.35 zWquot(nil, XS) -> nil 3.26/1.35 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) 3.26/1.35 3.26/1.35 3.26/1.35 3.26/1.35 Outermost Strategy. 3.26/1.35 3.26/1.35 ---------------------------------------- 3.26/1.35 3.26/1.35 (1) OutermostNonTerminationProof (COMPLETE) 3.26/1.35 Term rewrite system R: 3.26/1.35 The TRS R consists of the following rules: 3.26/1.35 3.26/1.35 from(X) -> cons(X, from(s(X))) 3.26/1.35 sel(0, cons(X, XS)) -> X 3.26/1.35 sel(s(N), cons(X, XS)) -> sel(N, XS) 3.26/1.35 minus(X, 0) -> 0 3.26/1.35 minus(s(X), s(Y)) -> minus(X, Y) 3.26/1.35 quot(0, s(Y)) -> 0 3.26/1.35 quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 3.26/1.35 zWquot(XS, nil) -> nil 3.26/1.35 zWquot(nil, XS) -> nil 3.26/1.35 zWquot(cons(X, XS), cons(Y, YS)) -> cons(quot(X, Y), zWquot(XS, YS)) 3.26/1.35 3.26/1.35 3.26/1.35 3.26/1.35 Outermost Strategy. 3.26/1.35 3.26/1.35 ---------- Loop: ---------- 3.26/1.35 3.26/1.35 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 3.26/1.35 3.26/1.35 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 3.26/1.35 3.26/1.35 Context: cons(X, []) 3.26/1.35 3.26/1.35 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 3.26/1.35 ---------------------------------------- 3.26/1.35 3.26/1.35 (2) 3.26/1.35 NO 3.34/1.38 EOF