26.13/26.35 YES 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 (VAR v_NonEmpty:S x1:S) 26.13/26.35 (RULES 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ) 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 Dependency Pairs Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(x1:S)) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 SCC Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(x1:S)) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Strongly Connected Components: 26.13/26.35 ->->Cycle: 26.13/26.35 ->->-> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(x1:S)) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 ->->-> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 Reduction Pair Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(x1:S)) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 -> Usable rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Interpretation type: 26.13/26.35 Linear 26.13/26.35 ->Coefficients: 26.13/26.35 Natural Numbers 26.13/26.35 ->Dimension: 26.13/26.35 1 26.13/26.35 ->Bound: 26.13/26.35 2 26.13/26.35 ->Interpretation: 26.13/26.35 26.13/26.35 [a](X) = 2.X + 2 26.13/26.35 [b](X) = 2.X + 2 26.13/26.35 [A](X) = 2.X 26.13/26.35 [B](X) = 2.X + 2 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 SCC Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Strongly Connected Components: 26.13/26.35 ->->Cycle: 26.13/26.35 ->->-> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 ->->-> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 Reduction Pair Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(a(b(x1:S))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 -> Usable rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Interpretation type: 26.13/26.35 Linear 26.13/26.35 ->Coefficients: 26.13/26.35 Natural Numbers 26.13/26.35 ->Dimension: 26.13/26.35 1 26.13/26.35 ->Bound: 26.13/26.35 2 26.13/26.35 ->Interpretation: 26.13/26.35 26.13/26.35 [a](X) = 2.X + 2 26.13/26.35 [b](X) = 2.X + 2 26.13/26.35 [A](X) = 2.X 26.13/26.35 [B](X) = 2.X + 2 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 SCC Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Strongly Connected Components: 26.13/26.35 ->->Cycle: 26.13/26.35 ->->-> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 ->->-> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 Reduction Pair Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 A(a(b(a(x1:S)))) -> B(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 -> Usable rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Interpretation type: 26.13/26.35 Linear 26.13/26.35 ->Coefficients: 26.13/26.35 Natural Numbers 26.13/26.35 ->Dimension: 26.13/26.35 1 26.13/26.35 ->Bound: 26.13/26.35 2 26.13/26.35 ->Interpretation: 26.13/26.35 26.13/26.35 [a](X) = 2.X + 2 26.13/26.35 [b](X) = 2.X + 2 26.13/26.35 [A](X) = 2.X + 1 26.13/26.35 [B](X) = 2.X + 2 26.13/26.35 26.13/26.35 Problem 1: 26.13/26.35 26.13/26.35 SCC Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(a(x1:S))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> A(b(b(a(x1:S)))) 26.13/26.35 B(b(a(b(x1:S)))) -> A(x1:S) 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Strongly Connected Components: 26.13/26.35 ->->Cycle: 26.13/26.35 ->->-> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 ->->-> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->->Cycle: 26.13/26.35 ->->-> Pairs: 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.35 ->->-> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 26.13/26.35 26.13/26.35 The problem is decomposed in 2 subproblems. 26.13/26.35 26.13/26.35 Problem 1.1: 26.13/26.35 26.13/26.35 Reduction Pair Processor: 26.13/26.35 -> Pairs: 26.13/26.35 A(a(b(a(x1:S)))) -> A(b(a(b(x1:S)))) 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 -> Usable rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Interpretation type: 26.13/26.35 Linear 26.13/26.35 ->Coefficients: 26.13/26.35 Natural Numbers 26.13/26.35 ->Dimension: 26.13/26.35 2 26.13/26.35 ->Bound: 26.13/26.35 1 26.13/26.35 ->Interpretation: 26.13/26.35 26.13/26.35 [a](X) = [0;1] 26.13/26.35 [b](X) = [0 0;1 0].X + [1;0] 26.13/26.35 [A](X) = [0 1;1 1].X 26.13/26.35 26.13/26.35 Problem 1.1: 26.13/26.35 26.13/26.35 SCC Processor: 26.13/26.35 -> Pairs: 26.13/26.35 Empty 26.13/26.35 -> Rules: 26.13/26.35 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.35 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.35 ->Strongly Connected Components: 26.13/26.35 There is no strongly connected component 26.13/26.35 26.13/26.35 The problem is finite. 26.13/26.35 26.13/26.35 Problem 1.2: 26.13/26.35 26.13/26.35 Reduction Pair Processor: 26.13/26.35 -> Pairs: 26.13/26.35 B(b(a(b(x1:S)))) -> B(a(x1:S)) 26.13/26.35 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.36 -> Rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 -> Usable rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 ->Interpretation type: 26.13/26.36 Linear 26.13/26.36 ->Coefficients: 26.13/26.36 Natural Numbers 26.13/26.36 ->Dimension: 26.13/26.36 1 26.13/26.36 ->Bound: 26.13/26.36 2 26.13/26.36 ->Interpretation: 26.13/26.36 26.13/26.36 [a](X) = 2.X + 2 26.13/26.36 [b](X) = 2.X + 2 26.13/26.36 [B](X) = 2.X 26.13/26.36 26.13/26.36 Problem 1.2: 26.13/26.36 26.13/26.36 SCC Processor: 26.13/26.36 -> Pairs: 26.13/26.36 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.36 -> Rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 ->Strongly Connected Components: 26.13/26.36 ->->Cycle: 26.13/26.36 ->->-> Pairs: 26.13/26.36 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.36 ->->-> Rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 26.13/26.36 Problem 1.2: 26.13/26.36 26.13/26.36 Reduction Pair Processor: 26.13/26.36 -> Pairs: 26.13/26.36 B(b(a(b(x1:S)))) -> B(b(a(x1:S))) 26.13/26.36 -> Rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 -> Usable rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 ->Interpretation type: 26.13/26.36 Linear 26.13/26.36 ->Coefficients: 26.13/26.36 Natural Numbers 26.13/26.36 ->Dimension: 26.13/26.36 1 26.13/26.36 ->Bound: 26.13/26.36 2 26.13/26.36 ->Interpretation: 26.13/26.36 26.13/26.36 [a](X) = 2.X + 2 26.13/26.36 [b](X) = 2.X + 2 26.13/26.36 [B](X) = 2.X 26.13/26.36 26.13/26.36 Problem 1.2: 26.13/26.36 26.13/26.36 SCC Processor: 26.13/26.36 -> Pairs: 26.13/26.36 Empty 26.13/26.36 -> Rules: 26.13/26.36 a(a(b(a(x1:S)))) -> a(b(a(b(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(a(a(a(x1:S)))) 26.13/26.36 b(b(a(b(x1:S)))) -> a(b(b(a(x1:S)))) 26.13/26.36 ->Strongly Connected Components: 26.13/26.36 There is no strongly connected component 26.13/26.36 26.13/26.36 The problem is finite. 26.13/71.93 EOF