2.84/1.34 NO 2.84/1.34 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 2.84/1.34 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.84/1.34 2.84/1.34 2.84/1.34 Outermost Termination of the given OTRS could be disproven: 2.84/1.34 2.84/1.34 (0) OTRS 2.84/1.34 (1) OutermostNonTerminationProof [COMPLETE, 66 ms] 2.84/1.34 (2) NO 2.84/1.34 2.84/1.34 2.84/1.34 ---------------------------------------- 2.84/1.34 2.84/1.34 (0) 2.84/1.34 Obligation: 2.84/1.34 Term rewrite system R: 2.84/1.34 The TRS R consists of the following rules: 2.84/1.34 2.84/1.34 f(s(a), s(b), x) -> f(x, x, x) 2.84/1.34 g(f(s(x), s(y), z)) -> g(f(x, y, z)) 2.84/1.34 cons(x, y) -> x 2.84/1.34 cons(x, y) -> y 2.84/1.34 2.84/1.34 2.84/1.34 2.84/1.34 Outermost Strategy. 2.84/1.34 2.84/1.34 ---------------------------------------- 2.84/1.34 2.84/1.34 (1) OutermostNonTerminationProof (COMPLETE) 2.84/1.34 Term rewrite system R: 2.84/1.34 The TRS R consists of the following rules: 2.84/1.34 2.84/1.34 f(s(a), s(b), x) -> f(x, x, x) 2.84/1.34 g(f(s(x), s(y), z)) -> g(f(x, y, z)) 2.84/1.34 cons(x, y) -> x 2.84/1.34 cons(x, y) -> y 2.84/1.34 2.84/1.34 2.84/1.34 2.84/1.34 Outermost Strategy. 2.84/1.34 2.84/1.34 ---------- Loop: ---------- 2.84/1.34 2.84/1.34 f(cons(s(a), s(b)), cons(s(a), s(b)), cons(s(a), s(b))) -> f(cons(s(a), s(b)), s(b), cons(s(a), s(b))) with rule cons(x', y') -> y' at position [1] and matcher [x' / s(a), y' / s(b)] 2.84/1.34 2.84/1.34 f(cons(s(a), s(b)), s(b), cons(s(a), s(b))) -> f(s(a), s(b), cons(s(a), s(b))) with rule cons(x', y) -> x' at position [0] and matcher [x' / s(a), y / s(b)] 2.84/1.34 2.84/1.34 f(s(a), s(b), cons(s(a), s(b))) -> f(cons(s(a), s(b)), cons(s(a), s(b)), cons(s(a), s(b))) with rule f(s(a), s(b), x) -> f(x, x, x) at position [] and matcher [x / cons(s(a), s(b))] 2.84/1.34 2.84/1.34 Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 2.84/1.34 2.84/1.34 Context: [] 2.84/1.34 2.84/1.34 We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop. 2.84/1.34 ---------------------------------------- 2.84/1.34 2.84/1.34 (2) 2.84/1.34 NO 2.98/1.38 EOF