2.77/1.27 NO 2.77/1.28 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.77/1.28 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.77/1.28 2.77/1.28 2.77/1.28 Outermost Termination of the given OTRS could be disproven: 2.77/1.28 2.77/1.28 (0) OTRS 2.77/1.28 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.77/1.28 (2) NO 2.77/1.28 2.77/1.28 2.77/1.28 ---------------------------------------- 2.77/1.28 2.77/1.28 (0) 2.77/1.28 Obligation: 2.77/1.28 Term rewrite system R: 2.77/1.28 The TRS R consists of the following rules: 2.77/1.28 2.77/1.28 app(nil, YS) -> YS 2.77/1.28 app(cons(X, XS), YS) -> cons(X, app(XS, YS)) 2.77/1.28 from(X) -> cons(X, from(s(X))) 2.77/1.28 zWadr(nil, YS) -> nil 2.77/1.28 zWadr(XS, nil) -> nil 2.77/1.28 zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS)) 2.77/1.28 prefix(L) -> cons(nil, zWadr(L, prefix(L))) 2.77/1.28 2.77/1.28 2.77/1.28 2.77/1.28 Outermost Strategy. 2.77/1.28 2.77/1.28 ---------------------------------------- 2.77/1.28 2.77/1.28 (1) OutermostNonTerminationProof (COMPLETE) 2.77/1.28 Term rewrite system R: 2.77/1.28 The TRS R consists of the following rules: 2.77/1.28 2.77/1.28 app(nil, YS) -> YS 2.77/1.28 app(cons(X, XS), YS) -> cons(X, app(XS, YS)) 2.77/1.28 from(X) -> cons(X, from(s(X))) 2.77/1.28 zWadr(nil, YS) -> nil 2.77/1.28 zWadr(XS, nil) -> nil 2.77/1.28 zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS)) 2.77/1.28 prefix(L) -> cons(nil, zWadr(L, prefix(L))) 2.77/1.28 2.77/1.28 2.77/1.28 2.77/1.28 Outermost Strategy. 2.77/1.28 2.77/1.28 ---------- Loop: ---------- 2.77/1.28 2.77/1.28 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 2.77/1.28 2.77/1.28 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 2.77/1.28 2.77/1.28 Context: cons(X, []) 2.77/1.28 2.77/1.28 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.77/1.28 ---------------------------------------- 2.77/1.28 2.77/1.28 (2) 2.77/1.28 NO 2.96/1.33 EOF