1.15/1.27 YES 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 (VAR v_NonEmpty:S x1:S) 1.15/1.27 (RULES 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Dependency Pairs Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> C(c(x1:S)) 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> C(c(x1:S)) 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 C(f(x1:S)) -> C(c(x1:S)) 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> C(c(x1:S)) 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 1 1.15/1.27 ->Bound: 1.15/1.27 2 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = X 1.15/1.27 [f](X) = 2.X + 2 1.15/1.27 [n](X) = 2.X + 2 1.15/1.27 [s](X) = X 1.15/1.27 [C](X) = 2.X 1.15/1.27 [F](X) = 2.X 1.15/1.27 [N](X) = 2.X 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> C(x1:S) 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 1 1.15/1.27 ->Bound: 1.15/1.27 2 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = X 1.15/1.27 [f](X) = 2.X + 2 1.15/1.27 [n](X) = 2.X + 2 1.15/1.27 [s](X) = 2 1.15/1.27 [C](X) = 2.X + 2 1.15/1.27 [F](X) = 2.X + 2 1.15/1.27 [N](X) = 2.X + 2 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 C(f(x1:S)) -> F(c(c(x1:S))) 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 1 1.15/1.27 ->Bound: 1.15/1.27 2 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = X 1.15/1.27 [f](X) = 2.X + 2 1.15/1.27 [n](X) = 2.X + 2 1.15/1.27 [s](X) = 1 1.15/1.27 [C](X) = X + 1 1.15/1.27 [F](X) = 2.X + 2 1.15/1.27 [N](X) = 2.X + 2 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> C(c(x1:S)) 1.15/1.27 F(x1:S) -> C(x1:S) 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(f(x1:S)) -> N(x1:S) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 1 1.15/1.27 ->Bound: 1.15/1.27 2 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = X 1.15/1.27 [f](X) = 2.X + 2 1.15/1.27 [n](X) = 2.X + 2 1.15/1.27 [s](X) = 2 1.15/1.27 [F](X) = 2.X + 2 1.15/1.27 [N](X) = 2.X + 2 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 N(s(x1:S)) -> F(s(s(x1:S))) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 1 1.15/1.27 ->Bound: 1.15/1.27 2 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = 0 1.15/1.27 [f](X) = 2.X 1.15/1.27 [n](X) = 2.X 1.15/1.27 [s](X) = 2 1.15/1.27 [F](X) = 2 1.15/1.27 [N](X) = 2.X + 2 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 ->->Cycle: 1.15/1.27 ->->-> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 ->->-> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 Reduction Pair Processor: 1.15/1.27 -> Pairs: 1.15/1.27 F(x1:S) -> N(c(c(x1:S))) 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 -> Usable rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Interpretation type: 1.15/1.27 Linear 1.15/1.27 ->Coefficients: 1.15/1.27 Natural Numbers 1.15/1.27 ->Dimension: 1.15/1.27 2 1.15/1.27 ->Bound: 1.15/1.27 1 1.15/1.27 ->Interpretation: 1.15/1.27 1.15/1.27 [c](X) = [1 0;0 0].X 1.15/1.27 [f](X) = [1 0;0 1].X + [1;0] 1.15/1.27 [n](X) = [1 1;0 1].X 1.15/1.27 [s](X) = [1 0;0 0].X + [0;1] 1.15/1.27 [F](X) = [1 0;0 1].X + [1;1] 1.15/1.27 [N](X) = [1 1;0 1].X + [0;1] 1.15/1.27 1.15/1.27 Problem 1: 1.15/1.27 1.15/1.27 SCC Processor: 1.15/1.27 -> Pairs: 1.15/1.27 N(f(x1:S)) -> F(n(x1:S)) 1.15/1.27 -> Rules: 1.15/1.27 c(c(x1:S)) -> c(x1:S) 1.15/1.27 c(f(x1:S)) -> f(c(c(x1:S))) 1.15/1.27 f(x1:S) -> n(c(c(x1:S))) 1.15/1.27 n(f(x1:S)) -> f(n(x1:S)) 1.15/1.27 n(s(x1:S)) -> f(s(s(x1:S))) 1.15/1.27 ->Strongly Connected Components: 1.15/1.27 There is no strongly connected component 1.15/1.27 1.15/1.27 The problem is finite. 1.15/1.28 EOF