0.60/0.87 YES 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 (VAR X) 0.60/0.87 (STRATEGY CONTEXTSENSITIVE 0.60/0.87 (a) 0.60/0.87 (f 1) 0.60/0.87 (g 1) 0.60/0.87 (h 1) 0.60/0.87 (b) 0.60/0.87 ) 0.60/0.87 (RULES 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 ) 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 Dependency Pairs Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(X,X) -> A 0.60/0.87 F(X,X) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding Rules: 0.60/0.87 Empty 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 SCC Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(X,X) -> A 0.60/0.87 F(X,X) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 ->Strongly Connected Components: 0.60/0.87 ->->Cycle: 0.60/0.87 ->->-> Pairs: 0.60/0.87 F(X,X) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 ->->-> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 ->->-> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 Instantiation Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(X,X) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 ->Instantiated Pairs: 0.60/0.87 ->->Original Pair: 0.60/0.87 F(X,X) -> H(a) 0.60/0.87 ->-> Instantiated pairs: 0.60/0.87 F(b,b) -> H(a) 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 SCC Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(b,b) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 ->Strongly Connected Components: 0.60/0.87 ->->Cycle: 0.60/0.87 ->->-> Pairs: 0.60/0.87 F(b,b) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 ->->-> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 ->->-> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 Forward Instantiation Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(b,b) -> H(a) 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 ->Instantiated Pairs: 0.60/0.87 ->->Original Pair: 0.60/0.87 G(a,X) -> F(b,X) 0.60/0.87 ->-> Instantiated pairs: 0.60/0.87 G(a,b) -> F(b,b) 0.60/0.87 ->->Original Pair: 0.60/0.87 H(X) -> G(X,X) 0.60/0.87 ->-> Instantiated pairs: 0.60/0.87 H(a) -> G(a,a) 0.60/0.87 0.60/0.87 Problem 1: 0.60/0.87 0.60/0.87 SCC Processor: 0.60/0.87 -> Pairs: 0.60/0.87 F(b,b) -> H(a) 0.60/0.87 G(a,b) -> F(b,b) 0.60/0.87 H(a) -> G(a,a) 0.60/0.87 -> Rules: 0.60/0.87 a -> b 0.60/0.87 f(X,X) -> h(a) 0.60/0.87 g(a,X) -> f(b,X) 0.60/0.87 h(X) -> g(X,X) 0.60/0.87 -> Unhiding rules: 0.60/0.87 Empty 0.60/0.87 ->Strongly Connected Components: 0.60/0.87 There is no strongly connected component 0.60/0.87 0.60/0.87 The problem is finite. 0.60/0.87 EOF