24.97/25.08 YES 24.97/25.08 24.97/25.08 Problem 1: 24.97/25.08 24.97/25.08 (VAR v_NonEmpty:S x1:S) 24.97/25.08 (RULES 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ) 24.97/25.08 24.97/25.08 Problem 1: 24.97/25.08 24.97/25.08 Dependency Pairs Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(a(x1:S)))) -> B(a(a(b(x1:S)))) 24.97/25.08 A(b(b(a(x1:S)))) -> B(x1:S) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(a(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 Problem 1: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(a(x1:S)))) -> B(a(a(b(x1:S)))) 24.97/25.08 A(b(b(a(x1:S)))) -> B(x1:S) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(a(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(a(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 24.97/25.08 The problem is decomposed in 2 subproblems. 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(a(x1:S)) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 Natural Numbers 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = 2.X + 2 24.97/25.08 [b](X) = 2.X + 2 24.97/25.08 [B](X) = 2.X 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(a(x1:S))) 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 Natural Numbers 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = 2.X + 2 24.97/25.08 [b](X) = 2.X + 2 24.97/25.08 [B](X) = 2.X 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 B(b(a(a(x1:S)))) -> B(b(b(a(x1:S)))) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 All rationals 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = 2 24.97/25.08 [b](X) = 1/2.X + 1/2 24.97/25.08 [B](X) = X 24.97/25.08 24.97/25.08 Problem 1.1: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 Empty 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 There is no strongly connected component 24.97/25.08 24.97/25.08 The problem is finite. 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 Natural Numbers 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = 2.X + 2 24.97/25.08 [b](X) = 2.X + 2 24.97/25.08 [A](X) = 2.X 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(a(x1:S)))) -> A(b(x1:S)) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 Natural Numbers 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = X + 1 24.97/25.08 [b](X) = X + 1 24.97/25.08 [A](X) = 2.X 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 Reduction Pair Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(b(x1:S))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 -> Usable rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Interpretation type: 24.97/25.08 Linear 24.97/25.08 ->Coefficients: 24.97/25.08 Natural Numbers 24.97/25.08 ->Dimension: 24.97/25.08 1 24.97/25.08 ->Bound: 24.97/25.08 2 24.97/25.08 ->Interpretation: 24.97/25.08 24.97/25.08 [a](X) = X + 1 24.97/25.08 [b](X) = X + 1 24.97/25.08 [A](X) = 2.X 24.97/25.08 24.97/25.08 Problem 1.2: 24.97/25.08 24.97/25.08 SCC Processor: 24.97/25.08 -> Pairs: 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 -> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.08 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.08 ->Strongly Connected Components: 24.97/25.08 ->->Cycle: 24.97/25.08 ->->-> Pairs: 24.97/25.08 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.08 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.08 ->->-> Rules: 24.97/25.08 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.08 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 24.97/25.09 Problem 1.2: 24.97/25.09 24.97/25.09 Reduction Pair Processor: 24.97/25.09 -> Pairs: 24.97/25.09 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.09 A(b(b(b(x1:S)))) -> A(b(x1:S)) 24.97/25.09 -> Rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 -> Usable rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 ->Interpretation type: 24.97/25.09 Linear 24.97/25.09 ->Coefficients: 24.97/25.09 Natural Numbers 24.97/25.09 ->Dimension: 24.97/25.09 1 24.97/25.09 ->Bound: 24.97/25.09 2 24.97/25.09 ->Interpretation: 24.97/25.09 24.97/25.09 [a](X) = 2.X + 2 24.97/25.09 [b](X) = 2.X + 2 24.97/25.09 [A](X) = 2.X 24.97/25.09 24.97/25.09 Problem 1.2: 24.97/25.09 24.97/25.09 SCC Processor: 24.97/25.09 -> Pairs: 24.97/25.09 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.09 -> Rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 ->Strongly Connected Components: 24.97/25.09 ->->Cycle: 24.97/25.09 ->->-> Pairs: 24.97/25.09 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.09 ->->-> Rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 24.97/25.09 Problem 1.2: 24.97/25.09 24.97/25.09 Reduction Pair Processor: 24.97/25.09 -> Pairs: 24.97/25.09 A(b(b(b(x1:S)))) -> A(a(a(b(x1:S)))) 24.97/25.09 -> Rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 -> Usable rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 ->Interpretation type: 24.97/25.09 Linear 24.97/25.09 ->Coefficients: 24.97/25.09 Natural Numbers 24.97/25.09 ->Dimension: 24.97/25.09 2 24.97/25.09 ->Bound: 24.97/25.09 1 24.97/25.09 ->Interpretation: 24.97/25.09 24.97/25.09 [a](X) = [0 1;0 0].X 24.97/25.09 [b](X) = [0 0;1 0].X + [1;0] 24.97/25.09 [A](X) = [1 0;0 1].X 24.97/25.09 24.97/25.09 Problem 1.2: 24.97/25.09 24.97/25.09 SCC Processor: 24.97/25.09 -> Pairs: 24.97/25.09 Empty 24.97/25.09 -> Rules: 24.97/25.09 a(b(b(a(x1:S)))) -> b(a(a(b(x1:S)))) 24.97/25.09 a(b(b(b(x1:S)))) -> a(a(a(b(x1:S)))) 24.97/25.09 b(b(a(a(x1:S)))) -> b(b(b(a(x1:S)))) 24.97/25.09 ->Strongly Connected Components: 24.97/25.09 There is no strongly connected component 24.97/25.09 24.97/25.09 The problem is finite. 24.97/62.73 EOF