60.11/60.20 NO 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 (VAR v_NonEmpty:S x:S) 60.11/60.20 (RULES 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 ) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 Valid CTRS Processor: 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 -> The system is a deterministic 3-CTRS. 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 Dependency Pairs Processor: 60.11/60.20 60.11/60.20 Conditional Termination Problem 1: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> A 60.11/60.20 F(d) -> F(a) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 60.11/60.20 Conditional Termination Problem 2: 60.11/60.20 -> Pairs: 60.11/60.20 A -> B 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 SCC Processor: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> A 60.11/60.20 F(d) -> F(a) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 ->Strongly Connected Components: 60.11/60.20 ->->Cycle: 60.11/60.20 ->->-> Pairs: 60.11/60.20 F(d) -> F(a) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 ->->-> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 Conditional Narrowing Processor: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> F(a) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 ->Narrowed Pairs: 60.11/60.20 ->->Original Pair: 60.11/60.20 F(d) -> F(a) 60.11/60.20 ->-> Narrowed pairs: 60.11/60.20 F(d) -> F(d) | b ->* g(d) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 SCC Processor: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> F(d) | b ->* g(d) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 ->Strongly Connected Components: 60.11/60.20 ->->Cycle: 60.11/60.20 ->->-> Pairs: 60.11/60.20 F(d) -> F(d) | b ->* g(d) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 ->->-> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 Narrowing on Condition Processor: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> F(d) | b ->* g(d) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 ->Narrowed Pairs: 60.11/60.20 ->->Original Pair: 60.11/60.20 F(d) -> F(d) | b ->* g(d) 60.11/60.20 ->-> Narrowed pairs: 60.11/60.20 F(d) -> F(d) | g(d) ->* g(d) 60.11/60.20 60.11/60.20 Problem 1: 60.11/60.20 60.11/60.20 Infinite Processor: 60.11/60.20 -> Pairs: 60.11/60.20 F(d) -> F(d) | g(d) ->* g(d) 60.11/60.20 -> QPairs: 60.11/60.20 Empty 60.11/60.20 -> Rules: 60.11/60.20 a -> x:S | b ->* g(x:S) 60.11/60.20 b -> g(d) 60.11/60.20 f(d) -> f(a) 60.11/60.20 -> Pairs in cycle: 60.11/60.20 F(d) -> F(d) | g(d) ->* g(d) 60.11/60.20 60.11/60.20 The problem is infinite. 60.11/60.21 EOF