2.64/1.23 NO 2.64/1.24 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.64/1.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.64/1.24 2.64/1.24 2.64/1.24 Outermost Termination of the given OTRS could be disproven: 2.64/1.24 2.64/1.24 (0) OTRS 2.64/1.24 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.64/1.24 (2) NO 2.64/1.24 2.64/1.24 2.64/1.24 ---------------------------------------- 2.64/1.24 2.64/1.24 (0) 2.64/1.24 Obligation: 2.64/1.24 Term rewrite system R: 2.64/1.24 The TRS R consists of the following rules: 2.64/1.24 2.64/1.24 primes -> sieve(from(s(s(0)))) 2.64/1.24 from(X) -> cons(X, from(s(X))) 2.64/1.24 head(cons(X, Y)) -> X 2.64/1.24 tail(cons(X, Y)) -> Y 2.64/1.24 if(true, X, Y) -> X 2.64/1.24 if(false, X, Y) -> Y 2.64/1.24 filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) 2.64/1.24 sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) 2.64/1.24 2.64/1.24 2.64/1.24 2.64/1.24 Outermost Strategy. 2.64/1.24 2.64/1.24 ---------------------------------------- 2.64/1.24 2.64/1.24 (1) OutermostNonTerminationProof (COMPLETE) 2.64/1.24 Term rewrite system R: 2.64/1.24 The TRS R consists of the following rules: 2.64/1.24 2.64/1.24 primes -> sieve(from(s(s(0)))) 2.64/1.24 from(X) -> cons(X, from(s(X))) 2.64/1.24 head(cons(X, Y)) -> X 2.64/1.24 tail(cons(X, Y)) -> Y 2.64/1.24 if(true, X, Y) -> X 2.64/1.24 if(false, X, Y) -> Y 2.64/1.24 filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) 2.64/1.24 sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) 2.64/1.24 2.64/1.24 2.64/1.24 2.64/1.24 Outermost Strategy. 2.64/1.24 2.64/1.24 ---------- Loop: ---------- 2.64/1.24 2.64/1.24 from(X) -> cons(X, from(s(X))) with rule from(X') -> cons(X', from(s(X'))) at position [] and matcher [X' / X] 2.64/1.24 2.64/1.24 Now an instance of the first term with Matcher [X / s(X)] occurs in the last term at position [1]. 2.64/1.24 2.64/1.24 Context: cons(X, []) 2.64/1.24 2.64/1.24 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.64/1.24 ---------------------------------------- 2.64/1.24 2.64/1.24 (2) 2.64/1.24 NO 2.64/1.27 EOF