4.21/2.28 NO 4.21/2.28 We consider the system theBenchmark. 4.21/2.28 4.21/2.28 Alphabet: 4.21/2.28 4.21/2.28 0 : [] --> b 4.21/2.28 1 : [] --> b 4.21/2.28 cons : [e * f] --> f 4.21/2.28 f : [c] --> a 4.21/2.28 false : [] --> d 4.21/2.28 filter : [e -> d * f] --> f 4.21/2.28 filter2 : [d * e -> d * e * f] --> f 4.21/2.28 g : [b * b] --> c 4.21/2.28 map : [e -> e * f] --> f 4.21/2.28 nil : [] --> f 4.21/2.28 s : [b] --> c 4.21/2.28 true : [] --> d 4.21/2.28 4.21/2.28 Rules: 4.21/2.28 4.21/2.28 f(s(x)) => f(g(x, x)) 4.21/2.28 g(0, 1) => s(0) 4.21/2.28 0 => 1 4.21/2.28 map(h, nil) => nil 4.21/2.28 map(h, cons(x, y)) => cons(h x, map(h, y)) 4.21/2.28 filter(h, nil) => nil 4.21/2.28 filter(h, cons(x, y)) => filter2(h x, h, x, y) 4.21/2.28 filter2(true, h, x, y) => cons(x, filter(h, y)) 4.21/2.28 filter2(false, h, x, y) => filter(h, y) 4.21/2.28 4.21/2.28 This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). 4.21/2.28 4.21/2.28 This system is non-terminating, as demonstrated by our external first-order non-termination checker: 4.21/2.28 4.21/2.28 || The following well-typed term is terminating: f(g(0, 0)) 4.21/2.28 || 4.21/2.28 || proof of resources/system.trs 4.21/2.28 || # AProVE Commit ID: 500ec9b2e2a919720cb177ef26031cb0220e008e fuhs 20130603 4.21/2.28 || 4.21/2.28 || 4.21/2.28 || Termination w.r.t. Q of the given QTRS could be disproven: 4.21/2.28 || 4.21/2.28 || (0) QTRS 4.21/2.28 || (1) NonTerminationProof [EQUIVALENT, 0 ms] 4.21/2.28 || (2) NO 4.21/2.28 || 4.21/2.28 || 4.21/2.28 || ---------------------------------------- 4.21/2.28 || 4.21/2.28 || (0) 4.21/2.28 || Obligation: 4.21/2.28 || Q restricted rewrite system: 4.21/2.28 || The TRS R consists of the following rules: 4.21/2.28 || 4.21/2.28 || f(s(%X)) -> f(g(%X, %X)) 4.21/2.28 || g(0, 1) -> s(0) 4.21/2.28 || 0 -> 1 4.21/2.28 || 4.21/2.28 || Q is empty. 4.21/2.28 || 4.21/2.28 || ---------------------------------------- 4.21/2.28 || 4.21/2.28 || (1) NonTerminationProof (EQUIVALENT) 4.21/2.28 || The following loops were found: 4.21/2.28 || 4.21/2.28 || ---------- Loop: ---------- 4.21/2.28 || 4.21/2.28 || f(g(0, 0)) -> f(g(0, 1)) with rule 0 -> 1 at position [0,1] and matcher [ ] 4.21/2.28 || 4.21/2.28 || f(g(0, 1)) -> f(s(0)) with rule g(0, 1) -> s(0) at position [0] and matcher [ ] 4.21/2.28 || 4.21/2.28 || f(s(0)) -> f(g(0, 0)) with rule f(s(%X)) -> f(g(%X, %X)) at position [] and matcher [%X / 0] 4.21/2.28 || 4.21/2.28 || Now an instance of the first term with Matcher [ ] occurs in the last term at position []. 4.21/2.28 || 4.21/2.28 || Context: [] 4.21/2.28 || 4.21/2.28 || 4.21/2.28 || ---------------------------------------- 4.21/2.28 || 4.21/2.28 || (2) 4.21/2.28 || NO 4.21/2.28 || 4.21/2.28 EOF