2.82/2.19 NO 2.82/2.20 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.82/2.20 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.82/2.20 2.82/2.20 2.82/2.20 Outermost Termination of the given OTRS could be disproven: 2.82/2.20 2.82/2.20 (0) OTRS 2.82/2.20 (1) OutermostNonTerminationProof [COMPLETE, 54 ms] 2.82/2.20 (2) NO 2.82/2.20 2.82/2.20 2.82/2.20 ---------------------------------------- 2.82/2.20 2.82/2.20 (0) 2.82/2.20 Obligation: 2.82/2.20 Term rewrite system R: 2.82/2.20 The TRS R consists of the following rules: 2.82/2.20 2.82/2.20 from(X) -> cons(X, from(s(X))) 2.82/2.20 2ndspos(0, Z) -> rnil 2.82/2.20 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z)) 2.82/2.20 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2.82/2.20 2ndsneg(0, Z) -> rnil 2.82/2.20 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z)) 2.82/2.20 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z)) 2.82/2.20 pi(X) -> 2ndspos(X, from(0)) 2.82/2.20 plus(0, Y) -> Y 2.82/2.20 plus(s(X), Y) -> s(plus(X, Y)) 2.82/2.20 times(0, Y) -> 0 2.82/2.20 times(s(X), Y) -> plus(Y, times(X, Y)) 2.82/2.20 square(X) -> times(X, X) 2.82/2.20 2.82/2.20 2.82/2.20 2.82/2.20 Outermost Strategy. 2.82/2.20 2.82/2.20 ---------------------------------------- 2.82/2.20 2.82/2.20 (1) OutermostNonTerminationProof (COMPLETE) 2.82/2.20 Term rewrite system R: 2.82/2.20 The TRS R consists of the following rules: 2.82/2.20 2.82/2.20 from(X) -> cons(X, from(s(X))) 2.82/2.20 2ndspos(0, Z) -> rnil 2.82/2.20 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z)) 2.82/2.20 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2.82/2.20 2ndsneg(0, Z) -> rnil 2.82/2.20 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z)) 2.82/2.20 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, Z)) 2.82/2.20 pi(X) -> 2ndspos(X, from(0)) 2.82/2.20 plus(0, Y) -> Y 2.82/2.20 plus(s(X), Y) -> s(plus(X, Y)) 2.82/2.20 times(0, Y) -> 0 2.82/2.20 times(s(X), Y) -> plus(Y, times(X, Y)) 2.82/2.20 square(X) -> times(X, X) 2.82/2.20 2.82/2.20 2.82/2.20 2.82/2.20 Outermost Strategy. 2.82/2.20 2.82/2.20 ---------- Loop: ---------- 2.82/2.20 2.82/2.20 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 2.82/2.20 2.82/2.20 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 2.82/2.20 2.82/2.20 Context: cons(X, []) 2.82/2.20 2.82/2.20 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.82/2.20 ---------------------------------------- 2.82/2.20 2.82/2.20 (2) 2.82/2.20 NO 2.82/2.23 EOF