206.48/208.70 YES 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 (VAR v_NonEmpty:S x1:S) 206.48/208.70 (RULES 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Dependency Pairs Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(a(x1:S))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 SCC Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(a(x1:S))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Strongly Connected Components: 206.48/208.70 ->->Cycle: 206.48/208.70 ->->-> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(a(x1:S))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 ->->-> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Reduction Pair Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(a(x1:S))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 -> Usable rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Interpretation type: 206.48/208.70 Linear 206.48/208.70 ->Coefficients: 206.48/208.70 Natural Numbers 206.48/208.70 ->Dimension: 206.48/208.70 1 206.48/208.70 ->Bound: 206.48/208.70 2 206.48/208.70 ->Interpretation: 206.48/208.70 206.48/208.70 [a](X) = 2.X + 2 206.48/208.70 [b](X) = 2.X + 2 206.48/208.70 [A](X) = X + 2 206.48/208.70 [B](X) = X + 2 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 SCC Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Strongly Connected Components: 206.48/208.70 ->->Cycle: 206.48/208.70 ->->-> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 ->->-> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Reduction Pair Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> A(a(x1:S)) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 -> Usable rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Interpretation type: 206.48/208.70 Linear 206.48/208.70 ->Coefficients: 206.48/208.70 Natural Numbers 206.48/208.70 ->Dimension: 206.48/208.70 1 206.48/208.70 ->Bound: 206.48/208.70 2 206.48/208.70 ->Interpretation: 206.48/208.70 206.48/208.70 [a](X) = X + 2 206.48/208.70 [b](X) = X + 2 206.48/208.70 [A](X) = 2.X + 2 206.48/208.70 [B](X) = 2.X + 2 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 SCC Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Strongly Connected Components: 206.48/208.70 ->->Cycle: 206.48/208.70 ->->-> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 ->->-> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Reduction Pair Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(a(b(x1:S))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 -> Usable rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Interpretation type: 206.48/208.70 Linear 206.48/208.70 ->Coefficients: 206.48/208.70 Natural Numbers 206.48/208.70 ->Dimension: 206.48/208.70 1 206.48/208.70 ->Bound: 206.48/208.70 2 206.48/208.70 ->Interpretation: 206.48/208.70 206.48/208.70 [a](X) = X + 2 206.48/208.70 [b](X) = X + 2 206.48/208.70 [A](X) = X + 2 206.48/208.70 [B](X) = X + 2 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 SCC Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Strongly Connected Components: 206.48/208.70 ->->Cycle: 206.48/208.70 ->->-> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 ->->-> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Reduction Pair Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> A(b(x1:S)) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 -> Usable rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Interpretation type: 206.48/208.70 Linear 206.48/208.70 ->Coefficients: 206.48/208.70 Natural Numbers 206.48/208.70 ->Dimension: 206.48/208.70 1 206.48/208.70 ->Bound: 206.48/208.70 2 206.48/208.70 ->Interpretation: 206.48/208.70 206.48/208.70 [a](X) = 2.X + 2 206.48/208.70 [b](X) = 2.X + 2 206.48/208.70 [A](X) = 2.X + 1 206.48/208.70 [B](X) = 2.X + 1 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 SCC Processor: 206.48/208.70 -> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 -> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 ->Strongly Connected Components: 206.48/208.70 ->->Cycle: 206.48/208.70 ->->-> Pairs: 206.48/208.70 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.70 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.70 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.70 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.70 ->->-> Rules: 206.48/208.70 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.70 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.70 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.70 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.70 206.48/208.70 Problem 1: 206.48/208.70 206.48/208.70 Reduction Pair Processor: 206.48/208.71 -> Pairs: 206.48/208.71 A(a(b(a(x1:S)))) -> B(a(b(a(x1:S)))) 206.48/208.71 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.71 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 -> Usable rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Interpretation type: 206.48/208.71 Linear 206.48/208.71 ->Coefficients: 206.48/208.71 Natural Numbers 206.48/208.71 ->Dimension: 206.48/208.71 2 206.48/208.71 ->Bound: 206.48/208.71 1 206.48/208.71 ->Interpretation: 206.48/208.71 206.48/208.71 [a](X) = [0 1;1 0].X + [1;0] 206.48/208.71 [b](X) = [1 0;1 0].X + [1;0] 206.48/208.71 [A](X) = [0 1;1 0].X + [1;1] 206.48/208.71 [B](X) = [1 0;1 0].X + [0;1] 206.48/208.71 206.48/208.71 Problem 1: 206.48/208.71 206.48/208.71 SCC Processor: 206.48/208.71 -> Pairs: 206.48/208.71 B(a(a(b(x1:S)))) -> A(a(a(b(x1:S)))) 206.48/208.71 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Strongly Connected Components: 206.48/208.71 ->->Cycle: 206.48/208.71 ->->-> Pairs: 206.48/208.71 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 ->->-> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 206.48/208.71 Problem 1: 206.48/208.71 206.48/208.71 Reduction Pair Processor: 206.48/208.71 -> Pairs: 206.48/208.71 B(b(b(a(x1:S)))) -> B(a(a(a(x1:S)))) 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 -> Usable rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Interpretation type: 206.48/208.71 Linear 206.48/208.71 ->Coefficients: 206.48/208.71 Natural Numbers 206.48/208.71 ->Dimension: 206.48/208.71 2 206.48/208.71 ->Bound: 206.48/208.71 1 206.48/208.71 ->Interpretation: 206.48/208.71 206.48/208.71 [a](X) = [0 1;1 0].X 206.48/208.71 [b](X) = [1 0;1 0].X + [1;0] 206.48/208.71 [B](X) = [1 0;1 0].X 206.48/208.71 206.48/208.71 Problem 1: 206.48/208.71 206.48/208.71 SCC Processor: 206.48/208.71 -> Pairs: 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Strongly Connected Components: 206.48/208.71 ->->Cycle: 206.48/208.71 ->->-> Pairs: 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 ->->-> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 206.48/208.71 Problem 1: 206.48/208.71 206.48/208.71 Reduction Pair Processor: 206.48/208.71 -> Pairs: 206.48/208.71 B(b(b(b(x1:S)))) -> B(a(a(b(x1:S)))) 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 -> Usable rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Interpretation type: 206.48/208.71 Linear 206.48/208.71 ->Coefficients: 206.48/208.71 Natural Numbers 206.48/208.71 ->Dimension: 206.48/208.71 2 206.48/208.71 ->Bound: 206.48/208.71 1 206.48/208.71 ->Interpretation: 206.48/208.71 206.48/208.71 [a](X) = [0 1;1 0].X 206.48/208.71 [b](X) = [1 0;1 0].X + [1;0] 206.48/208.71 [B](X) = [1 1;0 1].X 206.48/208.71 206.48/208.71 Problem 1: 206.48/208.71 206.48/208.71 SCC Processor: 206.48/208.71 -> Pairs: 206.48/208.71 Empty 206.48/208.71 -> Rules: 206.48/208.71 a(a(b(a(x1:S)))) -> b(a(b(a(x1:S)))) 206.48/208.71 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S)))) 206.48/208.71 b(b(b(a(x1:S)))) -> b(a(a(a(x1:S)))) 206.48/208.71 b(b(b(b(x1:S)))) -> b(a(a(b(x1:S)))) 206.48/208.71 ->Strongly Connected Components: 206.48/208.71 There is no strongly connected component 206.48/208.71 206.48/208.71 The problem is finite. 206.62/208.76 EOF