36.60/36.77 YES 36.60/36.77 36.60/36.77 Problem 1: 36.60/36.77 36.60/36.77 (VAR v_NonEmpty:S x:S y:S) 36.60/36.77 (RULES 36.60/36.77 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.77 g(0) -> 0 36.60/36.77 g(s(x:S)) -> s(g(x:S)) 36.60/36.77 ) 36.60/36.77 (STRATEGY INNERMOST) 36.60/36.77 36.60/36.77 Problem 1: 36.60/36.77 36.60/36.77 Dependency Pairs Processor: 36.60/36.77 -> Pairs: 36.60/36.77 F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) 36.60/36.77 F(g(x:S),s(0),y:S) -> G(s(0)) 36.60/36.77 G(s(x:S)) -> G(x:S) 36.60/36.77 -> Rules: 36.60/36.77 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.77 g(0) -> 0 36.60/36.77 g(s(x:S)) -> s(g(x:S)) 36.60/36.77 36.60/36.77 Problem 1: 36.60/36.77 36.60/36.77 SCC Processor: 36.60/36.77 -> Pairs: 36.60/36.77 F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) 36.60/36.77 F(g(x:S),s(0),y:S) -> G(s(0)) 36.60/36.77 G(s(x:S)) -> G(x:S) 36.60/36.77 -> Rules: 36.60/36.77 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.77 g(0) -> 0 36.60/36.77 g(s(x:S)) -> s(g(x:S)) 36.60/36.77 ->Strongly Connected Components: 36.60/36.77 ->->Cycle: 36.60/36.77 ->->-> Pairs: 36.60/36.77 G(s(x:S)) -> G(x:S) 36.60/36.77 ->->-> Rules: 36.60/36.77 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.77 g(0) -> 0 36.60/36.77 g(s(x:S)) -> s(g(x:S)) 36.60/36.77 ->->Cycle: 36.60/36.77 ->->-> Pairs: 36.60/36.77 F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) 36.60/36.77 ->->-> Rules: 36.60/36.77 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.77 g(0) -> 0 36.60/36.77 g(s(x:S)) -> s(g(x:S)) 36.60/36.77 36.60/36.77 36.60/36.77 The problem is decomposed in 2 subproblems. 36.60/36.77 36.60/36.77 Problem 1.1: 36.60/36.77 36.60/36.77 Subterm Processor: 36.60/36.78 -> Pairs: 36.60/36.78 G(s(x:S)) -> G(x:S) 36.60/36.78 -> Rules: 36.60/36.78 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.78 g(0) -> 0 36.60/36.78 g(s(x:S)) -> s(g(x:S)) 36.60/36.78 ->Projection: 36.60/36.78 pi(G) = 1 36.60/36.78 36.60/36.78 Problem 1.1: 36.60/36.78 36.60/36.78 SCC Processor: 36.60/36.78 -> Pairs: 36.60/36.78 Empty 36.60/36.78 -> Rules: 36.60/36.78 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.78 g(0) -> 0 36.60/36.78 g(s(x:S)) -> s(g(x:S)) 36.60/36.78 ->Strongly Connected Components: 36.60/36.78 There is no strongly connected component 36.60/36.78 36.60/36.78 The problem is finite. 36.60/36.78 36.60/36.78 Problem 1.2: 36.60/36.78 36.60/36.78 Instantiation Processor: 36.60/36.78 -> Pairs: 36.60/36.78 F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) 36.60/36.78 -> Rules: 36.60/36.78 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.78 g(0) -> 0 36.60/36.78 g(s(x:S)) -> s(g(x:S)) 36.60/36.78 ->Instantiated Pairs: 36.60/36.78 ->->Original Pair: 36.60/36.78 F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) 36.60/36.78 ->-> Instantiated pairs: 36.60/36.78 F(g(x:S),s(0),g(x4:S)) -> F(g(s(0)),g(x4:S),g(x:S)) 36.60/36.78 36.60/36.78 Problem 1.2: 36.60/36.78 36.60/36.78 SCC Processor: 36.60/36.78 -> Pairs: 36.60/36.78 F(g(x:S),s(0),g(x4:S)) -> F(g(s(0)),g(x4:S),g(x:S)) 36.60/36.78 -> Rules: 36.60/36.78 f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) 36.60/36.78 g(0) -> 0 36.60/36.78 g(s(x:S)) -> s(g(x:S)) 36.60/36.78 ->Strongly Connected Components: 36.60/36.78 There is no strongly connected component 36.60/36.78 36.60/36.78 The problem is finite. 36.60/36.78 EOF