2.47/1.26 NO 2.47/1.27 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.47/1.27 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.47/1.27 2.47/1.27 2.47/1.27 Outermost Termination of the given OTRS could be disproven: 2.47/1.27 2.47/1.27 (0) OTRS 2.47/1.27 (1) OutermostNonTerminationProof [COMPLETE, 0 ms] 2.47/1.27 (2) NO 2.47/1.27 2.47/1.27 2.47/1.27 ---------------------------------------- 2.47/1.27 2.47/1.27 (0) 2.47/1.27 Obligation: 2.47/1.27 Term rewrite system R: 2.47/1.27 The TRS R consists of the following rules: 2.47/1.27 2.47/1.27 if(true) -> X 2.47/1.27 if(false) -> Y 2.47/1.27 p(0) -> 0 2.47/1.27 p(s(X)) -> X 2.47/1.27 leq(0, Y) -> true 2.47/1.27 leq(s(X), 0) -> false 2.47/1.27 leq(s(X), s(Y)) -> leq(X, Y) 2.47/1.27 diff(X, Y) -> if(leq(X, Y)) 2.47/1.27 2.47/1.27 2.47/1.27 2.47/1.27 Outermost Strategy. 2.47/1.27 2.47/1.27 ---------------------------------------- 2.47/1.27 2.47/1.27 (1) OutermostNonTerminationProof (COMPLETE) 2.47/1.27 Term rewrite system R: 2.47/1.27 The TRS R consists of the following rules: 2.47/1.27 2.47/1.27 if(true) -> X 2.47/1.27 if(false) -> Y 2.47/1.27 p(0) -> 0 2.47/1.27 p(s(X)) -> X 2.47/1.27 leq(0, Y) -> true 2.47/1.27 leq(s(X), 0) -> false 2.47/1.27 leq(s(X), s(Y)) -> leq(X, Y) 2.47/1.27 diff(X, Y) -> if(leq(X, Y)) 2.47/1.27 2.47/1.27 2.47/1.27 2.47/1.27 Outermost Strategy. 2.47/1.27 2.47/1.27 ---------- Loop: ---------- 2.47/1.27 2.47/1.27 if(true) -> if(true) with rule if(true) -> X at position [] and matcher [X / if(true)] 2.47/1.27 2.47/1.27 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.47/1.27 2.47/1.27 Context: [] 2.47/1.27 2.47/1.27 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.47/1.27 ---------------------------------------- 2.47/1.27 2.47/1.27 (2) 2.47/1.27 NO 2.62/1.29 EOF