60.14/60.23 NO 60.14/60.23 60.14/60.23 Problem 1: 60.14/60.23 60.14/60.23 (VAR v_NonEmpty:S x:S) 60.14/60.23 (RULES 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 ) 60.14/60.23 60.14/60.23 Problem 1: 60.14/60.23 Valid CTRS Processor: 60.14/60.23 -> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 -> The system is a deterministic 3-CTRS. 60.14/60.23 60.14/60.23 Problem 1: 60.14/60.23 60.14/60.23 Dependency Pairs Processor: 60.14/60.23 60.14/60.23 Conditional Termination Problem 1: 60.14/60.23 -> Pairs: 60.14/60.23 C -> A 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 -> QPairs: 60.14/60.23 Empty 60.14/60.23 -> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 60.14/60.23 Conditional Termination Problem 2: 60.14/60.23 -> Pairs: 60.14/60.23 F(x:S) -> F(x:S) 60.14/60.23 -> QPairs: 60.14/60.23 C -> A 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 -> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 60.14/60.23 Problem 1: 60.14/60.23 60.14/60.23 SCC Processor: 60.14/60.23 -> Pairs: 60.14/60.23 C -> A 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 -> QPairs: 60.14/60.23 Empty 60.14/60.23 -> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 ->Strongly Connected Components: 60.14/60.23 ->->Cycle: 60.14/60.23 ->->-> Pairs: 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 -> QPairs: 60.14/60.23 Empty 60.14/60.23 ->->-> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 60.14/60.23 Problem 1: 60.14/60.23 60.14/60.23 Infinite Processor: 60.14/60.23 -> Pairs: 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 -> QPairs: 60.14/60.23 Empty 60.14/60.23 -> Rules: 60.14/60.23 a -> b 60.14/60.23 c -> f(a) 60.14/60.23 c -> g(b) 60.14/60.23 f(a) -> c 60.14/60.23 f(x:S) -> g(x:S) | f(x:S) ->* g(b) 60.14/60.23 -> Pairs in cycle: 60.14/60.23 C -> F(a) 60.14/60.23 F(a) -> C 60.14/60.23 60.14/60.23 The problem is infinite. 60.14/60.23 EOF