0.00/0.05 YES 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 (VAR v_NonEmpty:S x:S y:S) 0.00/0.05 (RULES 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 ) 0.00/0.05 (STRATEGY INNERMOST) 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 Dependency Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) 0.00/0.05 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) 0.00/0.05 G(s(f(x:S))) -> G(f(x:S)) 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) 0.00/0.05 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) 0.00/0.05 G(s(f(x:S))) -> G(f(x:S)) 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) 0.00/0.05 ->->-> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) 0.00/0.05 ->->-> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 0.00/0.05 0.00/0.05 The problem is decomposed in 2 subproblems. 0.00/0.05 0.00/0.05 Problem 1.1: 0.00/0.05 0.00/0.05 Reduction Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 G(c(x:S,s(y:S))) -> G(c(s(x:S),y:S)) 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 -> Usable rules: 0.00/0.05 Empty 0.00/0.05 ->Interpretation type: 0.00/0.05 Linear 0.00/0.05 ->Coefficients: 0.00/0.05 Natural Numbers 0.00/0.05 ->Dimension: 0.00/0.05 1 0.00/0.05 ->Bound: 0.00/0.05 2 0.00/0.05 ->Interpretation: 0.00/0.05 0.00/0.05 [f](X) = 0 0.00/0.05 [g](X) = 0 0.00/0.05 [c](X1,X2) = 2.X2 0.00/0.05 [fSNonEmpty] = 0 0.00/0.05 [s](X) = 2.X + 2 0.00/0.05 [F](X) = 0 0.00/0.05 [G](X) = 2.X 0.00/0.05 0.00/0.05 Problem 1.1: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 0.00/0.05 Problem 1.2: 0.00/0.05 0.00/0.05 Reduction Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 F(c(s(x:S),y:S)) -> F(c(x:S,s(y:S))) 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 -> Usable rules: 0.00/0.05 Empty 0.00/0.05 ->Interpretation type: 0.00/0.05 Linear 0.00/0.05 ->Coefficients: 0.00/0.05 Natural Numbers 0.00/0.05 ->Dimension: 0.00/0.05 1 0.00/0.05 ->Bound: 0.00/0.05 2 0.00/0.05 ->Interpretation: 0.00/0.05 0.00/0.05 [f](X) = 0 0.00/0.05 [g](X) = 0 0.00/0.05 [c](X1,X2) = 2.X1 0.00/0.05 [fSNonEmpty] = 0 0.00/0.05 [s](X) = 2.X + 2 0.00/0.05 [F](X) = 2.X 0.00/0.05 [G](X) = 0 0.00/0.05 0.00/0.05 Problem 1.2: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 f(c(s(x:S),y:S)) -> f(c(x:S,s(y:S))) 0.00/0.05 g(c(x:S,s(y:S))) -> g(c(s(x:S),y:S)) 0.00/0.05 g(s(f(x:S))) -> g(f(x:S)) 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 There is no strongly connected component 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 EOF